Jessica Pourraz

Claudie Haxaire

Daniel Arhinful

CHAPTER 1: STRENGTHENING NATIONAL PHARMACEUTICAL REGULATION THROUGH LOCAL PRODUCTION

INTRODUCTION

This chapter provides a history of pharmaceutical regulation from independence to the present in Ghana, Côte d'Ivoire, and Benin-three countries that are geographically close but have unique itineraries and contrasting pharmaceutical profiles, whether from an institutional perspective or in terms of their industrial or commercial structures. In order to underscore the comparison, we have added Côte d'Ivoire to the two countries specifically studied in this book. Its economic resources are close to Ghana, but at the time of independence, Côte d'Ivoire opted to enact different development policies than its anglophone neighbor (Eberhardt and Teal, 2010).

As highlighted briefly in the introduction, the legal framework and pharmaceutical distribution, supply, and production systems vary from country to country, depending on their colonial legacies and post-independence policies for industrial, economic, and health development. The three countries' pharmaceutical regulations also differ considerably. They fall under the national drug policy covering the spectrum of the various ways the State is involved in pharmaceuticals, such as defining the rules and overseeing their implementation.

It is therefore incumbent on the States to establish a drug regulatory system through the intermediary of a national authority. The structure, operations, and legal status of this body varies depending on the countries' administrative organization and economic resources (OMS, 2006). Thus, while Benin has had a technical directorate since the 1960s, Ghana, where the pharmacy industry's infrastructure is much denser, established a semi-autonomous agency with more resources in 2012. Falling between Benin and Ghana in terms of industrial pharmaceutical development, Côte d'Ivoire initiated its process to create an agency in 2015 that culminated in 2019. An analysis of these three case studies reveals how the evolution of pharmaceutical regulatory systems is linked to which pharmaceutical policies were chosen for procurement and support of local drug production. We will examine the various models of pharmaceutical regulation in place in West Africa and how they were constructed over time.

This will shed light on how local drug production played a role in constructing regulatory systems.

Using a socio-historic approach, we have structured our narrative chronologically around the major global events confronting the States in equal measure. These include the debt crisis that caused the oil price shocks of the 1970s, the enforcement of structural adjustment policies in the 1980s, and the devaluation of the CFA franc in 1994 in francophone countries. From the 2000s onwards, these regulatory systems evolved in response to how diverging industrial dynamics interacted with their regulatory methods. Focusing on the role of States, non-State private actors-including private pharmacists, pharmaceutical firms, and wholesalers-as well as transnational actors 1 provides a deeper analysis of how regulatory systems were created. This perspective also reflects the broader reform movements at play in the region, characterized by the process to harmonize pharmaceutical regulations at the community level and the trend to create agencies, as did Ghana and, very recently, Côte d'Ivoire. More broadly, this chapter encourages an examination of how States construct pharmaceutical sovereignty as they take ownership of their drug policies. This issue allows for an analysis of public action, including pharmaceutical and industrial policies, and the role of national and transnational actors and how they interconnect at various levels. 2 By doing so, we will investigate how local production, combined with States' considerable capacity to regulate drugs, is a powerful tool in constructing pharmaceutical sovereignty.

CONTRASTING DEVELOPMENT POLICIES (1960-1973)

At the time of their independence, Côte d'Ivoire and Benin were following the French Public Health Code dictating that pharmacists maintain a monopoly and, in return, perform their job duties in person and on site. 3 Meanwhile, until 1960, Ghana applied British laws under the authority of the Pharmacy and Poison Board, 4 which did not require a monopoly nor any conditions for pharmacy staff, but allowed the jobs of manufacturer, wholesaler, retailer, and drug representative to be combined. Moreover, Ghanaian pharmacists were also not required to hold the majority of pharmaceutical companies' capital as was the case for manufacturers in Côte d'Ivoire from 1986 to 2015. In the francophone countries, the monopoly and its associated obligation to perform tasks in person reduced the sources of capital that could be mobilized to create industrial or commercial pharmaceutical enterprises, since they needed consolidated capital from pharmacists. In anglophone countries, combining jobs promoted 1 These include multilateral United Nations agencies, like WHO and the United Nations Industrial Development Organization (UNIDO), and the United States (USAID), French (Expertise France), German (GIZ), and British (DFID) bilateral aid agencies.

2 Sovereignty is a legal concept governed by public law: "Sovereignty is the quality for a State not to be bound except by its own will, within the limits of the superior principle of law and according to the collective objectives that it is called upon to achieve" (Louis Le Fur, 1896, p. 443) faster accumulation of concentrated capital and allowed smaller companies to start up. After independence, the three countries chose contrasting development policies, whereby Ghana prioritized industrialization but Côte d'Ivoire and Benin promoted the exploitation of agricultural resources. This resulted in the establishment of pharmaceutical manufacturing in Ghana, while the two francophone countries strengthened the drug supply circuits inherited from the colonial period.

In Ghana: prioritizing industrialization and the underpinnings of pharmaceutical regulation

At the time of its independence in 1957, Ghana-which had substantial mineral and agricultural resources-was poorly industrialized. Kwame Nkrumah, who would become President of the First Republic of Ghana in 1960, turned to the economist William Arthur Lewis who recommended a free-enterprise production model and encouraged the use of foreign investors while dissuading the State from becoming a shareholder in or owner of industries (Lewis, 1953). Kwame Nkrumah committed the country to a vast industrialization program to foster economic development by substituting locally produced goods for imports.

When local production began in 1957, Ghana was importing most of its medicines from Europe and the United States. 5 This demanding and specialized industrial sector required public infrastructure (water, electricity, road networks), skilled human resources, and access to capital (Simonetti, Clark, and Wamae, 2015), conditions that Ghana did not fulfill. The government created policies to overcome these technological shortcomings and to mobilize the necessary investments. Since efficient technologies were located in the former colonial empires (Swainson, 1987) Company-NAMCO, a joint venture between a Dutch company and a Ghanaian wholesaler (Boateng, 2009). The public company Ghana Industrial Holding Corporation (GIHOC) Pharmaceuticals Ltd, formed through a partnership with Hungary, began operations in 1967.

A few private local initiatives arose on the sidelines (Gaizer, 2015), such as the still active Ayrton, created in 1965 by a Ghanaian pharmacist trained in England. The law in force in Ghana did not prohibit production units from holding shares in companies performing other functions in the sector,6 making it easier to set up a company there. These companies were even more economically viable because they could combine manufacturing activities with wholesaling, as was the case for NAMCO, or with acting as an agent-importer, in the case of Major & Co (Baxerres, 2018).

Under Kwame Nkrumah, local pharmaceutical production was better able to meet public health priorities by providing medicines as well as the need for industrial and economic development. Local production went hand-in-hand with the development of a regulatory framework focused on enacting new legislation primarily on medicines approval and regulating the practice of the pharmacy as a profession. In 1961, the first Ghanaian legislation regulating the pharmacy profession, pharmaceuticals, and narcotics was passed: the Pharmacy and Drugs Act. This act also provided for the creation of a new authority, the Pharmacy Board, responsible for regulating the pharmacy profession and issuing authorizations to practice and licenses to distribute medicines in the private sector, inspecting manufacturers and granting their authorizations, registering products, and controlling the import and distribution of narcotics.7

Côte d'Ivoire and Benin: prioritizing strengthened supply chains inherited from the colonial period

The two francophone countries focused on maintaining and strengthening the supply systems inherited from the colonial era through central procurement offices located in France that, from their point of view, guaranteed the safety and quality of imported medicines. No plans were made to build any drug production facilities. In Côte d'Ivoire, the public sector continued to be supplied by the Central Pharmacy (Pharmacie Centrale), which replaced the colonial Pharmapro in 1958, while the two private "wholesale-distributors"8 established before independence supplied the few distributors that worked in the country at the time:9 Laborex, a subsidiary of the From a legislative standpoint, the French Public Health Code required some modifications in terms of regulating the profession and the conditions for importing and registering medicines.

The National Order of Pharmacists of Côte d'Ivoire was established in 1960, 11 and its Beninese counterpart was set up in 1973. 12 In addition to protection from the Order, pharmacists in Côte d'Ivoire are also protected by trade unions, and in this liberal economy are even able to establish "mutuelles" (insurance cooperatives), buy shares in pharmaceutical companies, and then set themselves up as financial holding companies, 13 whose importance will be explained below. In Benin, these groups would establish themselves much later (see (Mazuet, 1987). 11 By Act no. 60-272 of September 2, 1960, followed by a code of ethics, established through Act no. 62-249 of July 31, 1962. For the industry, owner-pharmacists who are manufacturing are in one section (B) as opposed to pharmacists who are distributing (C), which clearly separates the two functions, unlike in Ghana. Pharmacists who are salaried employees in industry management fall under section D, distinct from that of owners. 12 Ordinance no. 73-38 of April 21, 1973. 13 These are companies whose shareholders could have an influence on the company's decisions. 14 ordinances16 that decreed that only State-approved structures are authorized to import drugs and are required to report to the DGP. 17 The two countries recognized the need to control imported pharmaceuticals through a sales authorization in Côte d'Ivoire and a visa in Benin, issued by the respective pharmaceutical regulatory authority (DSP in Côte d'Ivoire and DGP in Benin) after checking the manufacturing conditions. In Côte d'Ivoire, the law of 1965 established a registration fee paid to the Treasury for pharmaceuticals, whose rate and payment conditions are fixed by decree, as is also the case in Benin. This law also provided for the creation of a registration commission (or technical commission in Benin) whose composition and function were also defined by decree. However, registration fees paid to the Treasury are not transferred to the Beninese DGP and are only partially transferred to the Ivorian DSP, thus limiting their resources. At that time, drug registration was fairly lax, essentially consisting of paying registration fees to the Public Treasury and providing a technical dossier.

A TURNING POINT IN THE 1980s: THE GLOBAL DEBT CRISIS AND STRUCTURAL ADJUSTMENT PROGRAMS

The oil crisis of the 1970s slowed industrial activity and foreign investments in the pharmaceutical sector in Ghana until the late 1980s (Mackintosh et al., 2015). The crisis also raised countries' costs of imported medicines. In Côte d'Ivoire and Benin, this affected public pharmaceutical supply structures and pushed the countries to consider producing medicines locally, a move that challenged the global trend to deindustrialize. At the international level, the essential medicines policy, initiated by WHO in 1977, encouraged the use of generics and establishing production units in the Global South.

The flight of multinationals from Ghana and the advent of Indian initiatives

Throughout the 1970s and early 1980s, the Ghanaian economy experienced a severe crisis that forced many health professionals to leave the country (Senah, 1997). Jerry John Rawlings, who assumed power through a military coup d'état in 1981, was compelled to adopt structural adjustment programs imposed by the Bretton Woods financial institutions until 1992 (Whitfield and Jones, 2007). The launch of an economic recovery program in 1983, combined with trade liberalization, brought an end to the protectionist measures implemented under Kwame Nkrumah. Opening the market to competition, however, highlighted the lack of competitiveness of pharmaceutical companies based in Ghana. Starting in the late 1980s, the global crisis, coupled with economic reforms, led pharmaceutical multinationals to decrease, if not cease, activities with their subsidiaries (Boateng, 2009).

During this period, only two Indian-owned companies were established: Letap Pharmaceuticals Limited in 1983 and M&G Pharmaceuticals Ltd in 1989. Development of the pharmaceutical industry in India, starting in the 1970s (Chaudhuri, 2005), triggered changes in the structure and circulation of global drug markets, especially from Asia to Africa. Indian companies began to play a major role in technology transfer to the African continent.

Reorganizing public procurement and the start of an industrial policy in francophone countries

In Côte d'Ivoire, local actors developed initiatives in response to the international events. In his pursuit for long-term economic sovereignty, the first president, Felix Houphouët-Boigny, sought to develop local pharmaceutical production. 18 This required training for pharmacists.

Although planned for several years, the School of Pharmacy was not opened until 1977. 19 The school offered international-level training reserved for Ivorian citizens, adapted to the needs of local populations. 20 However, Ivorian pharmacists envisaged pharmaceutical sovereignty from a financial perspective. A type of association based on capital drawn from professionals emerged in Côte d'Ivoire that would play a major role there. These were holding companies that gave pharmacists considerable influence on the companies in which they were shareholders. Private pharmacists primarily owned shares in the two wholesale-distributors (Laborex and GOMPCI). In 1975, some of these pharmacist shareholders united in the Eurapharma holding company, so they could pressure the French central procurement office, Continental Pharmaceutique, based in Rouen, the office that Laborex depended on. 21 In under a license (Barral, 2008). The first Ivorian law on the pharmaceutical industry was enacted in 1986, requiring Ivorian pharmacists to hold senior-level manufacturing and control positions, as well as stipulating that they be the majority shareholders of the company's capital. Ivorian private pharmacists could then join forces to mobilize the necessary capital and, like the wholesale-distributors, invest in the first production company, Cipharm, opened in May 1988, operating under the Rhône-Poulenc license. 22 From the time of its creation until the International Monetary Fund (IMF) put an end to it, this firm enjoyed a reserved market. 23 A second private production company, Galefomy, specializing in dermatological preparations, was established in 1989 in Bouaké, the country's second largest city. It was financed by a private pharmacist24 who had accumulated capital through his shares in the wholesaledistributors' capital fund, just as Western pharmacies of the nineteenth century once did (Ruffat, 1996). He was able to get around the rules requiring a pharmacist to run the company and forbidding pharmaceutical functions from being combined through a one-time agreement with the president of the Order of Pharmacists, who wanted to promote the establishment of production facilities.

This process resulted in strengthening the institutions that oversee regulation in Côte d'Ivoire. Commission was created. 26 The first national list of essential medicines was created in 1989.

Benin was also facing a dire economic situation, and in 1980, the ONP and Pharmapro went bankrupt, causing severe drug shortages. In response, the Beninese State, which had minimal financial resources of its own, entered a phase to privatize the pharmaceutical supply and distribution systems. The private sector, thus far repressed by the Marxist government, found a place in the pharmaceutical landscape (Baxerres, 2013)

PRIVATIZATION OF THE PHARMACEUTICAL SECTOR IN THE 1990s

Serious drug shortages continued in the 1990s in the three countries, generated in part by the phenomenon of deindustrialization described above in Ghana and by the devaluation of the CFA franc in 1994 in Benin and Côte d'Ivoire. No longer able to pay the bills for imported drugs, these two francophone countries used less expensive generic medicines. This was all the more necessary because the cost recovery policy promoted by the Bamako Initiative required that populations cover a portion of medicine prices. In Ghana, this meant the implementation of the "cash and carry" policy starting in 1992 (Arhinful, 2003). From then on, privatization of the pharmaceutical sector then underway seemed to solve the availability problems surrounding pharmaceuticals.

Recovering industrial investment through local private capital and strengthening drug regulation in Ghana

Since the mid-1990s, industrial investment has picked up in Africa, in large part due to local investors (Mackintosh et al., 2015). In Ghana, the flight of multinationals allowed private Ghanaian entrepreneurs, some who were pharmacists, to buy back production facilities created after independence and to start manufacturing drugs, thus contributing to the "indigenization" of the pharmaceutical sector. 27 The capital mobilized by this new generation of Ghanaian industrialists came from their business activities in medicine importation, promotion, and distribution (see Chapter 3). The Ghanaian State continued to play a determining role in supporting local industry by promoting the creation of markets reserved for local manufacturers using a list of 14 medicines prohibited for import and reserved for local production28 and a 15% discount on prices for public tenders. Fiscal advantages were also granted to local producers, such as tax exemptions on imported raw materials, machines, and equipment needed to manufacture finished products29 and simplified registration. Thus, the interventionist policy implemented by the Ghanaian State offers the market conditions that local industries need in order to develop and is a form of "educational protectionism" (Guennif and Mfuka, 2003, p.85). It does not, however, solve the problem facing local companies that want access to capital and technology.

Besides the need to regulate, support, and guide increased local production, Ghana's national regulatory authority was confronted with increasingly more generic medicines coming from Asia during the 1990s that needed quality and origin inspections before registration. It became necessary to separate the regulation of products from the regulation of professional practice and to create an independent authority solely for regulating products, whether imported or Pharmaceutical companies exporting their medicines to Ghana had to pay a fee when registering their medicines to cover the costs associated with conducting inspections at their production sites. 30 Ghanaian inspectors carried out about 30 inspections abroad per year, mainly in Asia where most of the generic medicines came from (FDA, 2011-2015). They also received training within multinationals, such as Cipla in India, the US FDA, and the Medicines and Healthcare products Regulatory Agency in the United Kingdom.

The indigenization of the industry and distribution in francophone countries

In Côte d'Ivoire, the early 1990s witnessed the deployment of Ivorian pharmacists' competencies and capital throughout the pharmaceutical sector.

THE 2000s: DIFFERING LOCAL INDUSTRIAL DYNAMICS

Continuing Ghana's industrial policy

Throughout the 2000s in Ghana, continuation of the industrial policy led to the creation of drug manufacturing pharmaceutical companies by Ghanaian pharmacists-such as Kinapharma, Danadams, and Ernest Chemists-bringing the total number of companies to 36.

Most started out as import wholesalers for international companies. Once seen as intermediaries, these wholesaler-retailers became manufacturers by accumulating capital (Braudel, 1985; Baxerres, 2018). They received Indian and/or Chinese technical assistance:

for example, Danadams was created through a Sino-Ghanaian partnership. In the same period, new Indian Ghanaian companies 39 -such as Eskay Therapeutics Ltd in 1998, Pharmanova

Limited in 2005, and Unichem Industries in 2010-opened in Ghana, taking advantage of an environment that made it easier for them to produce generic versions of drugs still under patents. 40

How the Ivorian political crisis affected the industrialization process

In Côte d'Ivoire, the military-political crisis that began in 2000 saw Laurent Gbagbo's accession to the presidency and ignited ten years of turbulence and deregulation resulting in clashes, after which Alassane Ouattara came to power. 37 The decree grants the Technical Commission for Medicines, in charge of issuing the Marketing Authorization (MA), the power to consult experts in order to deepen document assessment and analysis. 38 By Decree No. 91-654 of October 9, 1991.

39 These three companies are owned or were set up by Indians who had Ghanaian nationality. 40 Ghana is one of the countries that is not bound to the World Trade Organization (WTO) agreements on Trade-Related Aspects of Intellectual Property Rights (TRIPS).

The wholesaler-distributors Ubipharm and Eurapharma managed to hold on during the crisis, as did the local pharmaceutical companies Cipharm 41 and Pharmivoire Nouvelle. Despite the 1986 law in force, in 2007 the Gbagbo government authorized the establishment of the Olea company using Italian capital and belonging to non-pharmacist Milanese businessmen. The new initiatives fall under a form of capitalism that bypasses the rules on monopolies and the origin of capital. Other companies tried to start up with no lasting success, including a subsidiary of the Canadian firm Rougier. However, in those troubled times, wholesalerdistributors no longer risked investing in local production as they did when Cipharm was created.

Starting in 2011, the government of Alassane Ouattara set out to promote the development of local pharmaceutical companies to ensure better access to medicines, seeing more investment opportunities in a booming market (Coulibaly, 2018). Conditions for setting up manufacturers were facilitated by the creation of free zones. 42 A new law, promulgated in 2015, 43 finally allowed non-pharmacists to inject capital into the pharmaceutical industry (Amari and Pabst, 2016). Two Moroccan pharmaceutical companies and Asian generic manufacturers, including the Indian firm Pharmanova, were approved and began building factories at the end of 2018.

The Tunisian company SAIPH broke ground for its production facility in June 2017, 44 joining the 10 already-established Ivorian companies in 2015 (DPML, 2015).

Failed industrial projects in Benin

In Benin, none of the technological, financial, or economic conditions encouraged local pharmaceutical production. While drug imports were tax-exempt, imported raw materials were not. Energy, such as electricity, was also very expensive. Local manufacturers were disadvantaged compared to foreign firms that exported medicines in Benin (West and Banda, 2015), which explains why requests to create firms never materialized, other than one from Pharmaquick in 1982. Of the 11 requests submitted to the DPMED between 2001 and 2009, 45 primarily from Beninese, Cameroonian, North African, and Chinese developers, only 5 companies received authorization to establish in Benin, primarily for the production of 41 Because of the crisis, when international firms withdrew capital from Cipharm, their stocks were purchased by the current Director (Ibrahim Diawara), who had still kept some of their licenses. 42 The Decree of December 6, 2012 created a Public Establishment of an Administrative nature, facilitating the "one-stop shop" approach that could give the pharmaceutical industry advantages: the CEPICI, Center for the Promotion of Investments in Côte d'Ivoire. solutes, generics, and medical consumables, but none of these projects ever came to fruition. 46 With no industrial policy supporting local medicine production over imports and because of the way its supply chains operated, Benin became an enclave reserved for medicine imports.

The industrial dynamics described above appear to be linked to the regulatory models adopted by the countries and the resources available to them, as we shall see below.

DIFFERENT REGULATORY MODES: TECHNICAL DIRECTORATE VERSUS AGENCY

Limits placed on regulation by the Ivorian and Beninese technical directorates

In The experts' impartiality might be challenged, knowing that the pharmaceutical companies cover all mission expenses and offer luxury services to the visitors. 53 More specifically in Benin, the DPMED's lack of resources means employees cannot ensure medicines undergo quality control, conduct inspections abroad, or evaluate Marketing Authorization (MA) applications. For these functions, Benin relies on the expertise of international regulatory authorities and importers based in France and Europe, delegating the bulk of the evaluation and quality control work to them for imported drugs. In the eyes of DPMED regulators, these intermediaries offer sufficiently reliable and robust quality assurance systems. This last point, especially evident in the case of Benin, clearly shows how processes that mutually reinforce local production and pharmaceutical regulation are entangled. Côte d'Ivoire, which has strengthened the capacities of its National Laboratory, performs these controls and evaluations itself. However, since products come from central procurement offices located in 50 The majority of deputy directors are professors at the School of Pharmacy. 53 Interview in August 2017 with a staff member from the regional pharmaceutical sector.

France, such as Planet pharma, a subsidiary of Ubipharm, the country takes advantage of the guarantees offered by established supply chains.

In closing, the DPMED's organization complicates the effective performance of its duties since it has five units that focus on all regulatory functions. 54 The Pharmaceutical Legislation, Regulation, and Governance Unit, for example, covers five of the regulatory functions on its own (WHO, 2003; WHO, 2006), 55 each of which must be assigned to a single unit. The lack of financial resources adds to these shortcomings. Both countries have a backlog of MA applications and follow-up monitoring. 56 The fees charged for MAs by the two directorates are low, and their lack of resources prevents them from developing sufficiently solid expertise that would justify raising their fees.

In

An agency model: the Food and Drug Authority in Ghana

In October 2012, the Ghanaian parliament approved the Public Health Act, which created the Food and Drugs Authority (FDA), a legal entity separate from the State, responsible for providing and enforcing norms and standards for the sale of medicines (Republic of Ghana, 2012). One year after its creation, the organization that transitioned to the FDA was restructured and five specialized divisions were created, including the drug registration and inspectorate division 57 (WHO, 2014), which oversees the departments that support local industry and law enforcement. This reform also prompted the hiring of ten additional pharmacist-inspectors, primarily from the industrial sector, who were assigned to the new Drug Enforcement Department. The quality control laboratory is under the direct responsibility of the FDA chief executive officer and is located within the FDA's institutional headquarters in Accra, which has housed the entire staff since 2013 in a brand-new three- story building. 58 The FDA has nearly 500 employees, including about 50 pharmacists (FDA, 2014). That same year, the FDA department supporting local industry developed a road map to guide local companies in the process to meet the standards of good manufacturing practices (GMP) by 2020, ensuring the drug's quality at each step of its production. 59 The road map also provides for the creation of a regional center in Ghana for bioequivalence studies so that Ghanaian companies can conduct these studies locally at a lower cost. These studies are required for WHO prequalification certification, in addition to GMP standards, to guarantee a generic's similarity with the reference medicine (Lantenois and Coriat, 2014). The FDA has a dual goal: to guarantee the quality of medicines distributed on the private market and to support Ghanaian companies in their quest to obtain WHO prequalification, a precondition for access to markets subsidized by transnational actors, such as the Global Fund.

Although it remains under the Ministry of Health, the FDA's new status grants it greater autonomy than that of a conventional public service administration. 60 The Public Health Act authorizes the FDA to hire the staff needed to perform its functions, but like all public health institutions it must obtain a financial authorization for each new hire (FDA, 2012), causing delays. The government would ultimately like the FDA to pay its staff with its own funds, which will give it greater autonomy and independence (Benamouzig and Besançon, 2005).

Hence, the FDA in Ghana has gradually come into being through an endogenous process since the 1990s with occasional financial and technical support from external partners (USAID, WHO, USP), with the primary goal of ensuring the quality of drugs distributed on the domestic market.

Creation of the Ivorian Pharmaceutical Regulatory Agency (AIRP)

In Côte d'Ivoire, plans to create an agency, driven by Ivorian specialists in the pharmaceutical sector, materialized much faster on the recommendations of the ECOWAS and international experts, 61 and with technical and financial support from the French Development Agency ) 63 Penalties may range from suspension to permanent withdrawal of the authorization to practice, cancellation of the MA, or destruction of products. They may also be financial (up to one billion CFA francs) or criminal (ranging from two months to ten years in prison).

CONCLUSION

Where medicines are made and how they are procured-direct imports, via a central procurement office and/or local production-affect the instruments deployed by States to guarantee the quality of the products distributed to their populations. Control systems, applied through factory inspections and drug registration, are key factors, requiring learning and investment. In Ghana, the presence of local drug production developed since independence and the importation of generics directly from Asia helped build robust national regulation.

The phenomenon of cooperation (Hauray, 2006) between the regulatory authority and the local companies also plays an important role by creating a space for mutual learning between manufacturers and regulators. Comparing this to the situations of Benin and Côte d'Ivoire highlights the importance of strengthening institutional regulatory capacities to attract direct foreign investment and to structure the industrial landscape. More than the legal form of the national regulatory authority, the training and number of pharmacists dedicated to regulatory issues promote the emergence of regulatory systems and industry growth.

In order to eliminate the heterogeneity of regulation between West African States, a regulatory harmonization process was launched at the regional level to homogenize laws and transform technical directorates into autonomous agencies. 64 Desired by the region's countries themselves, this process is seen as a public health tool whose goal is to promote access to quality medicines. It is accompanied by the creation of a common market aimed at increasing trade in the region. Far from being complete or free of any challenges, this homogenization does help develop and support local drug production, making it instrumental in establishing pharmaceutical sovereignty for countries in the West-African region.

64 http://www.nepad.org/programme/african-medicines-regulatory-harmonisation-amrh, accessed July1, 2019.

  , Kwame Nkrumah called on investors from the United States and Europe to develop a local industrial foundation. He initiated an industrial policy in support of setting up pharmaceutical factories through administrative, financial, and fiscal facilities and market protections for locally produced medicines that penalized imports. As a result, the British firm Major & Co. began producing medicines in Ghana in 1957, followed by Ghana Laboratories Ltd Pioneer Companies Relief Incorporation in 1958; the English companies J.L Morrison & Sons and Kingsway Chemists; Sterling Products Ltd (United States); Dumex Limited (Denmark); Pharco Laboratory (India); and the Netherlands African Manufacturing

  Chapter 2). The 1960 decree defining the powers of the Ivorian Ministry of Public Health 14 created the Directorate of Pharmaceutical Services (DSP; Direction des Services Pharmaceutiques); Benin's General Directorate of Pharmacies (DGP) was established that same year. Both issue installation licenses and inspect pharmaceutical establishments. In addition to private pharmacies, these directorates oversee the Chemistry and Fraud Laboratory and the Central Pharmacy in Côte d'Ivoire; and Pharmapro and the ONP in Benin. In 1965, 15 Côte d'Ivoire reaffirmed the criteria governing drug registration, which did not occur in Benin until between 1973 and 1976 through the enactment of an initial series of 10 Created by Jean Mazuet, the first French pharmacist posted in Côte d'Ivoire in 1936, and later developed in other francophone African countries

Following the 1983

 1983 Etats Généraux de la Santé, a citizens' forum to gather health information, the Ministry of Health was reorganized to favor the relative autonomy of its subsidiary structures. The Central Pharmacy became the Côte d'Ivoire Pharmacy of Public Health (PSPCI), established as a Public Institution of an Industrial and Commercial Nature (EPIC in French). 25 In 1984, the Laboratory of Chemistry and Fraud became a central autonomous directorate of the Ministry of Health. Later, a National Pharmacovigilance

  produced locally. The Pharmacy Board disappeared and was replaced by the newly created Pharmacy Council and the Food and Drugs Board (FDB). In 1994, Pharmacy Act 489 created the Pharmacy Council to control the pharmacy practice and the registration of pharmacists and licensed chemical sellers. The Food and Drugs Board (FDB), created in 1997 following the enactment in 1992 of the Food and Drugs Law, managed the control of drug manufacturing, import, export, distribution, use, and advertisement. Overseen by the Ministry of Health, the FDB enjoys relative autonomy and independence in its decision-making.Comprising two divisions at its beginnings-with one dedicated to medicines, cosmetics, medical devices, and household chemical substances and the other dedicated to foods-the governing board was composed of 14 individuals, including 5 pharmacists. Operationally the FDB seeks the support of external actors to implement some activities: USAID for quality surveillance, and the United States Pharmacopeia (USP) and WHO for laboratory equipment and training. The industrial policy was combined with strengthening the regulatory authorities' capacities and competencies since the FDB was gradually acquiring a pool of pharmacist-inspectors who, on average, conducted about 20 inspections of manufacturing plants each year in Ghana. Over time, the expertise acquired during these inspections gradually gave FDB officials the necessary expertise to conduct inspections abroad.

  the course of the 2000s, technical directorates in Côte d'Ivoire and Benin underwent several institutional reforms to raise their level of expertise. In Côte d'Ivoire, the Gbagbo government reformed operations in the Pharmacy of Public Health (PSP) in 2002 47 and reorganized the DPML in 2006 to make it responsible for applying the government's health policy for pharmaceutical matters. The role of the National Laboratory of Public Health (LNPS) was strengthened through Order no. 198/MSHP of 2009, which made quality control mandatory for all imported medicines. Despite these reforms, these institutions were not satisfactory. In 2008, the National Program for the Development of Pharmaceutical Activity (PNDAP) 48 was created. Directly attached to the Directorate General of Health Services (DGS), it was charged with implementing the National Pharmaceutical Plan. However, it seemed its mission partially overlapped with the DPLM until its role was better defined. In Benin, functions pertaining to diagnostic explorations were reassigned to the DPM in 2010, which has now become the Directorate of Pharmacy, Medicine, and Diagnostic Investigations (DPMED). 49 The National Quality Control Laboratory (LNCQ) was created in 2005 with French support from the Chirac and Pierre Fabre Foundations, which provided equipment to improve the quality control of imported medicines. Although the DPML and the DPMED were made up of sub-directorates that carved up the pharmaceutical sector along different lines, and despite Côte d'Ivoire having better staffed 46 These were the International Pharmaceutical Solutes Company (Société Internationale de Solutés Pharmaceutiques), a Beninese NGO project; the Benin-Pharma BTL SA company for generics production; Biovegemed SA from a technology transfer from the French Pharmaceutical Group Michel Iderne to develop local medicine products based on plant extracts; a Chinese company producing medicines and mineral water, Texmed-Bénin SARL; and another Beninese enterprise to manufacture and package medical consumables. human resources than Benin, these technical directorates shared similar dysfunctions. Firstly, in terms of human resources, the DPML in Côte d'Ivoire has about 30 pharmacists, but most of them do not work full-time and/or have not been trained in regulatory matters. 50 It employs young contract pharmacists who are waiting to open their own pharmacies. The Beninese DPMED suffers from an even greater lack of staff: in December 2016, they numbered six pharmacists (DPMED, 2016): two were civil servants and four were young contractors who were graduates with no specialized training, just as in Côte d'Ivoire. The precariousness of contract employees adds to staff instability and prevents having a body of specialized experts in pharmaceutical regulation. Moreover, the skills developed by the Beninese 51 and Ivorian technical directorates in inspection remained quite limited given the industry's small scale. There are still no legally recognized and sworn pharmacist-inspectors in Benin or Côte d'Ivoire, thus rendering their recommendations and decisions ineffective and without legal value. This legal vacuum means that none of the national regulatory authorities of UEMOA member States 52 conduct inspections abroad. For its part, Côte d'Ivoire does not conduct inspections but rather makes site visits, organized by the companies themselves when requested by the Ivorian directorate.

  summary, the technical directorates of Benin and Côte d'Ivoire have little functional autonomy compared to the Ministry of Health and suffer from inefficient internal organization and inadequate financial resources and technical staff, hampering their analytical capacities and offering minimal scientific expertise to the State. We will now use the case of Ghana and more recently Côte d'Ivoire, to see whether an agency can serve as a model to address the dysfunctions noted in the technical directorates.

(

  AFD). In 2015, the Ivorian government set out to reorganize the existing regulatory institutions to create an agency through the Debt Reduction-Development Contract (C2D)62 and the Project to Support the Revitalization of Côte d'Ivoire's Health Sector (PARSSI) funded and managed by the French Development Agency(Allemand, 2017). First, the Pharmacy of Public Health changed its status to become an N-PSPCI, a nonprofit organization, thus granting it the autonomous management that it had lacked. The National Laboratory of Public Health's capacities bolstered through staff training and the provision of equipment and reference samples. The DPML's legal powers were also strengthened, and the various sub-directorates' responsibilities were redefined. This process prepared for reconfiguring the existing institutions by redefining their functions, organizing them into the three specializations covered by the Ivorian agency(Ouattara, 2018). At the same time, various legal provisions point to the Ivorian system's similarities to the Ghanaian model. For example, the Order of Pharmacists of Côte d'Ivoire was reorganized in 2015 and now categorizes producers, wholesale-distributors, and promotion agencies together.Launched in 2015, the process to create the Ivorian Pharmaceutical Regulatory Agency culminated in 2017 with a vote on Act no. 2017-541 of August 3 and its implementation decree in February 2019. Responsible for the management of the pharmaceutical sector, it conducts surveillance and enforces penalties for violators, 63 which entails establishing a body of inspectors made up of sworn pharmacists(Ouattara 2018). According to these promoters, this agency should be able to guarantee industrial investments by cleaning up the market, especially by eliminating informal circuits(Ouattara, 2018). While it is difficult to assess the effects of such recent changes, an analysis of the creation process for the AIRP in Côte d'Ivoire highlights the role played by local medicine production in constructing regulatory systems. The local protagonists supporting the AIRP defended the plan to create the agency as a way to install a regulatory system that is robust enough to meet the development goals of the national pharmaceutical industry. 61 Sources: minutes from the seminar to share results of the experts' work (Professor Amor Toumi, Professor of Pharmacy, Tunisia; and legal experts Mr. Bernard Hody of Belgium and Ms. Victoire Ayeoura of Côte d'Ivoire) and discussions with the various involved regulatory bodies, April 27, 2015 in Abidjan. 62 The 1st C2D-Debt Reduction-Development Contract-managed by AFD for Côte d'Ivoire, was signed on December 1, 2012 in Abidjan for an amount of 630 million euros, or 413.25 billion CFA francs. The second C2D (2014-2020) was signed on December 3, 2014 in Paris for an amount of 738 billion CFA francs. The C2D enables countries to reconvert French debt through grants to fund development. (C2D.gouv.CI, accessed November 25, 2018.

  West Africa Trading Company (SCOA; Société Commerciale d'Afrique de l'Ouest), an importer since 1949, and the Pharmaceutical Group of Côte d'Ivoire (GOMPCI; Groupement Pharmaceutique de Côte d'Ivoire). 10 During the first ten years following independence, Ivorian pharmacists, primarily trained in France, opened private pharmacies or held positions in pharmaceutical companies or Ministry of Health directorates.

	At this time, Dahomey, which would become the People's Republic of Benin in 1975, was
	experiencing political instability that hampered investment. From independence in 1960 to
	Mathieu Kérékou's assumption of power in 1972, the industrial sector remained
	underdeveloped and the pharmaceutical industry was inexistent. As will be discussed in the
	next chapter, the public sector was still supplied by Pharmapro, backed since 1964 by the
	Benin National Office of Pharmacies (ONP; Office National des Pharmacies du Bénin) that
	oversees drug distribution to a few private pharmacies and health facilities.

  Decree no. 61-34 of January 14, 1961, on the re-organization of the Ministry of Public Health, later changed to Decree no.69-48 of January 20, 1969.

15

Act no.

65-250 of August 4, 1965.

  1980, the consequences of the global crisis, structural adjustment programs, and the withdrawal of French development aid programs led Felix Houphouët-Boigny to enlist actors from the pharmaceutical sector to consider setting up a drug production facility in Côte d'Ivoire. With no support from wholesale-distributors or French industrials, it took six years to carry out the project. Côte d'Ivoire benefited from the problems of Rhône-Poulenc, which planned to outsource its production abroad in units acting as manufacturers and working

18

Interview with the first faculty dean, André Rambaud, (November 2018) and his presentation in June 2018 during the 40year commemoration of the Research and Training Unit (UFR, Unité de Formation et de Recherche) for pharmaceutical sciences at the Houphouët-Boigny University in Cocody (Abidjan).

19

By President Felix Houphouët-Boigny, Professor Michel Attiso, and pharmacist Jean Baptiste Mokey.

20

By 2015, it had trained over 2000 graduates

(DPML, National Pharmaceutical Policy, 2015, p 18)

.

21

These actors are also present in Benin, which will be discussed in the next chapter.

  . In 1982, President Mathieu Kérékou used the family-owned capital of a Beninese biologist living in France who created the private firm Pharmaquick to produce medicines locally and reduce the cost of imports. The industrialist's arrival crystalized numerous tensions among Beninese private pharmacists, who accused him of violating the monopoly rules since he was not a pharmacist. In 1987, IMF programs imposed economic measures on Benin aimed at decreasing public expenses and thus endorsed State withdrawal from the health sector(Baxerres, 2013). Benin was subject to two structural adjustment programs, first from 1989 to 1991 and then from 1991 to 1994. The Central Purchasing Office of Essential Medicines and Medical Consumables, or CAME, was created in 1989 to replace the ONP and Pharmapro, prompted by the World Bank and other development partners (see Chapter 2).

  The cooperative of private pharmacists, Copharm, promoted financial assistance within the profession, 31 based on the model of cooperatives described bySueur (2017) in France. Two new pharmaceutical companies were created, with an even more uncertain future than Cipharm. They were Dermopharm 32 in 1992 and Pharmivoire in 1991. Pharmivoire, created by two university pharmacists who got loans from Proparco, a subsidiary of the French Development Agency, Confronted with drug shortages caused by the devaluation of the CFA franc, the local firms Cipharm and Pharmivoire Nouvelle were able to provide some essential medicines and infusion solutions. They were joined by the Pharmaceutical Laboratory of Côte d'Ivoire (LPCI, Laboratoire Pharmaceutique de Côte d'Ivoire), created in 1997 by Ivorian university pharmacists to prepare herbal medicines, but whose activity was limited to repackaging, and by Lic Pharma, created in 2002 with Chinese capital.35 Lic Pharma has a unique financial arrangement relative to the 1986 law on pharmaceutical companies, which requires that pharmacists hold the majority of a company's capital. This resulted in a bilateral agreement between the government of the new president Henri Konan Bédié and the Chinese State in 1995, resulting in a series of projects funded by the Chinese Exim-Bank in 1996(Caubin, 2010). Loans to the Ivorian government were lent on to private operators to fund productive projects through joint ventures, including Lic Pharma. In Benin, the devaluation of the CFA franc and the procurement crisis helped strengthen the role of the CAME, which purchases In Benin, the Directorate of Pharmacies and Laboratories' prerogatives were broadened to become the Directorate of Pharmacies and Diagnostic Investigations (DPED, Direction des Pharmacies et des Explorations Diagnostiques). Between 1994 and 1995 in Benin, the WHO essential medicines program supported strengthening registration procedures for medicines for human use.36 These procedures were revised in 1997 with Decree no. 97-632 of December 31 to increase pre-regulation screening and make the registration process more transparent and rigorous.37 This went hand in hand with creating or strengthening quality control systems.In Benin, the creation of an analytical laboratory was created in 1999. In Côte d'Ivoire, the national laboratory, created in 1991,38 was upgraded to a Public Establishment of an Administrative nature (an EPA in French) and became the National Laboratory of Public Health (LNPS). Despite these institutional reforms, the skills developed by Beninese and Ivorian technical directorates particularly for inspection remained very limited in comparison to those of the FDB in Ghana, where a dense industrial infrastructure platform encouraged the FDB to build up production site inspection capacities early on. This last factor is key to highlighting how local production processes are entangled with pharmaceutical regulation.

	"a 100% African success story" (Coulegnon, 2013). Owners of private pharmacies also sat on
	wholesale-distributors' boards of directors. Therefore, Ivorian pharmacists continued to seek
	economic sovereignty with share buyouts in order to claim majority ownership in two new
	wholesale-distributors: Copharmed in 1996 and DPCI in 1999. 34
	30 In 2009, this fee was USD 700 for a local firm and USD 20,000 for a foreign firm (source: FDA).
	31 In 1993, the Order of Pharmacists of Côte d'Ivoire entrusted a colleague trained in management with the task of "creating
	a cooperative, COPHARM, to mobilize savings, provide financial assistance between pharmacists, and carry out joint
	projects" (interview with Elisabeth Kakou conducted by S Cessou for Afrique Méditerranée Business, April-May 2017, p
	32-35).

which supports the private sector by granting loans. It would become Pharmivoire Nouvelle in 1999, following a recapitalization by Copharm

(Aouely et al., 2017)

.

At the same time, the process to indigenize wholesale-distributors' capital continued when 161 Ivorian private pharmacists, 33 who were shareholders of the Ivorian branch of Laborex, or Laborex-CI, repurchased the majority of the capital of this company (55%) in 1990. They did this by exchanging their Laborex shares for shares in Pharmafinance, the holding company provided for by Ivorian law that they had just created and that they used to take control of this former Ivorian subsidiary from the SCOA group, namely Laborex-CI. Thus in 1991, Pharmafinance created Pharmaholding, which became Ubipharm, and, in 2000, acquired a purchasing platform, Planet pharma, approved by the French Agency for the Safety of Health Products. Today, Ubipharm is the leading drug distributor in francophone African countries,

32

Dermopharm presents itself as a family business created by an Ivorian private pharmacist, who died in 2016.

33

Interview with the Director General of Ubipharm, Gérard Mangoua, for Forbes Afrique

(Coulegnon, 2013)

.

34

Through the creation of a holding company with Ivorian capital in 1996, Copharmed, to control their shares in Eurapharma (repurchased by the CFAO Group in 1996). However, unlike Laborex-CI, Copharmed remains a partner of the Eurapharma group.

and distributes generic medicines, as well as the private company Pharmaquick, which produces them locally. The second structural adjustment program from 1991 to 1994 strengthened the country's commitment to a phase of economic liberalism

(Gbetoenonmon, 2013

). The procurement system was gradually expanding with the establishment of two new private wholesale-distributors (see Chapter 2). Just as in Ghana, sourcing generics from Asia and creating new local industries in Côte d'Ivoire required strengthening Beninese and Ivorian regulations on importation and registration. As a result, the technical directorates of the Ministries of Health were restructured. In Côte d'Ivoire in 1994, President Bédié reorganized the Directorate of Pharmaceutical Services, which became the Directorate of Pharmacy, Medicine, and Laboratories (DPML, Direction de la Pharmacie et du Médicament et des Laboratoires) in 1997.

  51 Its employees have only conducted one inspection of the Pharmaquick production site, on March 15-17, 2010. To our knowledge, it is the only inspection carried out, for which documents were archived in the Pharmaquick files at the DPMED in Cotonou (Source: observation within the DPMED Pharmaceutical Establishments Unit between 2014 and 2016).52 Created in 1994, the West Africa Economic and Monetary Union is composed of eight francophone member States, with the goal of creating a harmonized and integrated economic zone. Source: http://www.uemoa.int/fr/presentation-de-luemoa, accessed March 3, 2019.

  Nevertheless, its fiscal plans are still subject to approval by the Ministry of Finance and Economic Planning, since it receives an annual operating budget, allocated by the State and approved by the Parliament, defined according to planned activities. Until 2012, approximately 75% of the operating budget came from the government (WHO, 2014). Drug registration fees are another source of considerable funding. The FDA keeps half of the amounts received and pays the other half to the State.

January 1960, Public Records and Archives Administration Department (PRAAD), Ministry of Industry, GH/PRADD/RG.7/1/39, Accra, Ghana.

Information confirmed by former officials from the Pharmacy Council and the FDB of Ghana during the Globalmed symposium in Ouidah in 2018.

Interview with a former FDB executive in Accra on April 1, 2015.

This profession will be discussed in Chapter 3.

There were 42 private pharmacists in 1970.

For example, Ordinance no. 75-7 of January 27, 1975, on governing medicines in Dahomey.

Ordinance no. 73-68 of September 27, 1973, defining the conditions for the importation of pharmaceuticals and wound care products in Dahomey.

The capital was distributed as follows: Rhône-Poulenc 26%, Roussel-Hoechst 13%, Sanofi 13%, Ivorian pharmacists 28%, GOMPCI 10%, and Laborex 10%. CIPHARM manufactured the specialties of three pharmaceutical companies: Nivaquine®, aspirin, and Flavoquine®.

Interview with Assane Coulibaly, head pharmacist and deputy director of Cipharm until December 2014: medicines produced by Cipharm are not imported.

Interview with Dr. Mamadou Yacine Fofana in February 2018.

By Decree no. 84-764 of June 6, 1984.

By Order no. 249 MSP DSPH of November 18, 1988.

"Indigenization" describes the origin of capital and indicates that it comes from local private individuals. It differs from nationalization, which means that capital belongs to the State.

This includes paracetamol, ampicillin, chloramphenicol, tetracycline, aspirin, and diazepam.

Compared to 10% import taxes on finished products.

According to our sources, the capital is now entirely Chinese, coming from a construction company, and is not a branch of a Chinese pharmaceutical company. The Chinese staff is also not from the pharmaceutical industry; instead, they are chemical and agribusiness technicians supervised by Ivorian pharmacists.

WHO Archives, E19-445-3BEN, WHO Action Programme on Essential Drugs-Benin, 1989, Jacket No. 3.

It gave the PSP the opportunity to manufacture and package some medicines commonly used in hospitals: Act no.202-334 of June 13, 2002.

It was created by Order no. 308/MSHP/CAB of December 11, 2008.

According to Order no. 4482/MS/DC/SGM/CTJ/DPMED/SA of August 12, 2010 on the attributions, organization, and functioning of the Directorate of Pharmacy, Medicine, and Diagnostic Investigations (DPMED).

The FDA has its headquarters in Accra, nine regional offices, set up between 2003 and 2011 across the country, along with control offices at the country's official entry and exit points for goods (the Port of Tema and Kotoka International Airport).

UNIDO, the United Nations Industrial Development Organization, has supported this initiative on a regional scale since 2015.

In 2013, the cost of registering an imported drug was USD 3600 and USD 270 for locally produced drugs.


E Aubert
email: eddy.aubert@safrangroup.com

E N Diaw

V Ury

S Le Roy

G Teyssedre

Preliminary Measurements and Simulations for Space Charges in Aeronautical Cables

This paper deals with the growing need of electrical energy in aeronautical domain, which appears since several years. We focus on HVDC: over the "classical" 28 V dc, this voltage level is used and will be used more and more for supplying electrical devices. Conduction current measurements were performed on cables for different temperature and electric field values. The objective is to observe a temperature and electric field dependence of the electrical of cables' insulations. The results of current measurements were used as input for multi-physics models. Measurements demonstrate the conductivity varies very slightly with the temperature and field.

I.

INTRODUCTION

The aeronautical domain has faced profound paradigm shifts over the last 20 years, during which the number of electrical and electronic equipment has not ceased to increase, replacing hydraulic and pneumatic loads. Nowadays, there are more than 500 km of cables in an A380 supplying the electrical loads and insuring the safety of the flight. In order to supply all the equipment and their increasing demand in electrical power, new voltage supplies emerge in the onboard systems: the HVAC (230 V AC variable frequency…instead of 115 V AC fixed frequency), PWM (Pulse Width Modulation -10 or 20 kHz switching frequency) and HVDC (540 V DC in addition to the "classical" 28 V DC).

The main challenges in aeronautics are the mass and fuel consumption reduction, thus, the mass and the volume of cables have to be extremely reduced. Therefore, the cables' electrical insulation thickness is very small, around 250 ȝm. For mechanical, arc tracking, environment and safety reasons, the materials used for aeronautical insulator systems are PI, PTFE, etc.

When combining the voltage levels applied and the thicknesses of the insulation systems, the electrical field constraint becomes extremely important. Under HVDC constraint, space charges might accumulate between the insulator layers and increase locally the electrical fields, accelerating the aging of the cables. In order to predict the space charges associated risks, we need to be able to model the space charges circulations inside and between the insulating layers.

This paper is composed of two chapters. The first one presents a set of experiments and the associated results for the characterization of the insulator materials. The second chapter focuses on the modelling and simulation of cables, using the experimental data described in the previous paragraph. The aim of the simulation part is to obtain the electrical field repartition within the insulator materials. These models will enable the establishment of space charges repartition in the electrical insulation system of aeronautical cables.

II. EXPERIMENTATION RESULTS

In order to determine the space charges repartition in the electrical insulators of cables, several steps must be performed, the first one being the identification of the variation on the electrical conductivity of the material versus the electrical field applied. This chapter will describe the test setup and all the preliminary measurements permitting to determine this characteristic of the insulators.

The current study is performed on standard aeronautical cables. We have used an 8 AWG (American Wire Gauge) cable; Table I presents the cable characteristics. One can notice the small thickness of the insulator layers, explaining the high level of electrical field constraint applied on aeronautical cables.

A. Experimental set up

An experimental test bench was put in place in order to determine the conductivity vs electrical field characteristics of insulator materials. The aeronautical cable used does not have an external electrode allowing the direct measurement of the electrical conductivity of the insulators.

Figure 1 presents the test setup configuration as follows: a DC high voltage generator is directly connected to the core of the cable. As the cable used does not have an external electrode allowing the direct measurement of the conductivity of the insulator, a copper ribbon is placed on the surface of the PTFE layer. The goal is to sandwich the insulators for measurements in the volume. A 4 cm electrode, placed 1 cm away from a guard electrode, is connected to an electrometer. A DC voltage is applied on the cable core. The electrometer is interfaced with a computer through a General Purpose Interface Bus (GPIB) for data acquisition. The cable is placed in an oven allowing to vary the temperature from 30° C up to 90° C with a precision of the order of 1° C. The measurements were carried out for voltages varying between 0.5 and 10 kV in isothermal condition under different thermal gradients. The duration of polarization / depolarization is 1 hour / 1 hour. Current values are recorded every 2 seconds during the entire polarization / depolarization phase.

B. Experimental results

This subchapter presents the different steps made for determining the variation of the electrical conductivity of insulators as a function of the electrical field and of the temperature, under DC constraint. The insulators were tested at different voltage levels and their response current vs time were observed. [START_REF] Segui | Diélectriques -Courants de conductions[END_REF] Figure 2 shows one of the results obtained for a 13 kV/mm field level applied. One can observe in Figure 2 the time evolution of the discharge current. Firstly, a rapid decrease of the conduction current which stabilizes around 14 -40 seconds as a function of the applied E field and then appears a nearly constant slope corresponding to a decrease of the current. Whether in polarization or depolarization, we note that the current values are proportional to the applied E fields. It can therefore be supposed that the discharge current comes from the polarization phenomena involved.

At 1 hour, the transient current is still decreasing for all temperatures. It is necessary to intend to increase the time of polarization to observe the stabilization of the current which is going to correspond of conduction current.

Various experimental results from the literature show that in the case of polymer insulators, the conductivity is a function of both the electric field and the temperature. Therefore, we have performed supplementary tests on our cable insulators. Figure 3 shows the evolution of the current density (conduction) versus field strength in the case of PTFE / PI material for four different temperatures. It shows that the slope of the conduction current density characteristics as a function of the field (J-E) is close to a slope of coefficient 1 at a weak field. Any injected charge is immediately extracted in this ohmic regime. As a result, no charges accumulate within an insulating material in isothermal condition [START_REF] Fabiani | Polymeric HVDC Cable Design and Space Charge Accumulation[END_REF].

It is possible that under higher fields, the slope becomes greater than 1, thus implying that materials start having anonlinear conductivity. The objective of this representation was the identification of threshold field values which indicate a change in the current density versus electrical field behavior. As it can be noticed, no threshold can be easily identified in Figure 3. The hypothesis on this non-occurrence of threshold fields is that the applied fields are too weak to have nonlinear behavior that could be attributed to a space charge limited mechanism phenomenon (SCLC) [START_REF] Fabiani | Polymeric HVDC Cable Design and Space Charge Accumulation[END_REF].

The final measurements performed were the electrical conductivity versus electrical field under different temperatures (30, 50, 70, 90°C) and the corresponding results obtained are presented hereby in Figure 4. From the field-current data for different temperatures, the dependence of the conductivity as a function of the temperature is shown for some field values (2, 13 and 20 kV/mm) in Figure 5.

At this stage, given the small electrical conductivity values measured, no immediate conclusions can be drawn concerning the dependence of this parameter on the field or the temperature variations. We have noticed that the variation of the conductivity follows an Arrhenius like curve, given by equation (1); it would be possible to characterize the dependence of the conductivity with temperature from an Arrhenius type relationship.

(1) However, the results show us that the conductivity varies only very slightly with the temperature so the activation energy would be negligible. The same remark would apply to the variation of the conductivity due to the electrical field variation.

As seen previously, the temperature-sensitive conductivity essentially drives the distribution of the electric field in the HVDC-stressed cable. In future experiments, we will increase the maximum temperature and electric field levels to obtain non-linear behaviors. It will permit to integrate (1) in future models.

III. FEM SIMULATION

This chapter presents the models and simulations that were performed in order to assess the electric field in the cable. 2D multi-physics (electro-static and thermal) models were developed using a finite element method (FEM) in COMSOL Multiphysics®. The cable model consists of two regions: conductor layer and insulation layers (Polyimide and PTFE) as shown in Figure 6. Table II gives the thicknesses of each layer. As shown in Figure 6, 19 wire strands in copper compose the conductor layer and the insulation layers are composed of Polyimide and PTFE sublayers. A gauge 16 AWG cable was chosen in order to reduce the model complexity. An "extremely fine" mesh is defined for the different insulator layers (Polyimide, PTFE) and adapted to the thickness of each layer; a "normal" precision mesh is used for the air inside the cable. The mesh of the electrostatic analysis is shown in Figure 7 [3]. Boundaries conditions were defined for the electrostatic analysis. The voltage applied at the wire strands of the cable is 540V. In the real environment of the cable, the electrical reference of the cable can be located within some millimeters from the PTFE layer. To model at best, the electric environment of the cable, we made the hypothesis that there is a layer of air between the PTFE layer and the electrical reference located at 1.88 mm from the center of the cable.

The electrostatic analysis of this model is based on some assumptions:

• Electrical properties of materials are constant (Table III) except thermal conductivity of copper which depends on the temperature. Electrical conductivity of insulators is supposed to be dependent on the temperature and/or electric field. • DC voltage is applied to the cable. In DC cable, the field distribution is resistive and the resistivity of the insulators can depend on nonlinear temperature and electrical field. In this case, electrical conductivity must be characterized for each material in order to supply the numerical model.

In this model, only the dependence on the temperature is considered and electrical conductivity is defined as [START_REF] Roy | Modelling Space Charge in a Cable Geometry[END_REF]:

(2)
Where E is the electric field, T the temperature, kB the Boltzmann's constant and Ea is the energy of activation. Equation ( 3) is the input data used in the numerical model in order to assess the electric field.

The radial distribution of electric field is shown Figure 8. The profile of the electric field below shows a distribution of the electric field, which is different according to the material, used (difference of permittivity). An intensification of the electric field is observed (Figure 9) near contact points/interfaces between the insulator and the conductive layers.

IV. CONCLUSIONS

The dielectric tests made it possible to characterize the dielectric behaviors as a function of the electric field and the temperature. Indeed, these two parameters can be at the origin of the accumulation of charges within the insulator consequently responsible for a local intensification of the field in the dielectric, which can generate a premature aging of the cable. The dielectric characterizations of the samples made it possible to determine the dielectric behavior of the cables used under HVDC constraints. The results made it possible to demonstrate a linearity of the conduction current in the insulator as a function of the electric field. Contrary to our expectations, the temperature in the [30°C -90°C] range is not an aggravating factor on the generation of the conduction current. Indeed, the results showed that the conductivity and therefore the resistivity did not vary a lot with the temperature and very slightly with the electric field within the defined limits.

The macroscopic model developed in this study allowed the construction of a precise cable model with respect to its real geometry, materials used, but also their electrical characteristics obtained previously by measurement. The 2D coupled electrostatic-thermal simulation and the stationary study allows determining the distribution of the electric field in the insulator layers. In the future, it will however be necessary to take into account the transport and the electrical charges accumulation in the volume of insulator materials or at the interfaces between different insulators through a microscopic temporal model of transport of charges (to have space charge results simulations). These models will be completed by experimental results space charge of insulator samples.

Figure 1 .

 1 Figure 1. Experimental set up

Figure 2 .

 2 Figure 2. Transient current for different thermal gradients under a polarization of 13kV/mm

Figure 3 .

 3 Figure 3. Density of current versus electric field for different temperatures

Figure 4 .

 4 Figure 4. Conductivity versus to the electric field for different temperatures

Figure 5 .

 5 Figure 5. Conductivity versus to temperature for different Electric field

Figure 6 .

 6 Figure 6. Aeronautic cable observed in the optical microscope

Figure 7 .

 7 Figure 7. Electric field domain and mesh

Figure 8 .

 8 Figure 8. Profile of the electric field in the cable

Figure 9 .

 9 Figure 9. Electric field mapping

TABLE II .

 II LAYER THICKNESS OF THE CABLE

	Layer	Thickness
	Conductor	1.456 mm
	Polyimide	40.73 μm
	PTFE	184.52 μm

TABLE III .

 III PROPERTIES OF MATERIALS

	Material	Permittivity	Thermal conductivity (W/m.K)
	PI	3.4	0.15
	PTFE	2	0.24
	Air	1	24


Joachim Rosseel
email: joachim.rosseel@cea.fr

Valérian Mannoni
email: valerian.mannoni@cea.fr

Valentin Savin
email: valentin.savin@cea.fr

Inbar Fijalkow
email: inbar.fijalkow@ensea.fr

Error Structure Aware Parallel BP-RNN Decoders for Short LDPC Codes

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I. INTRODUCTION

Short-packet machine-to-machine communications, central to the emerging Internet of Things (IoT) technology, have revitalized interest in research and practice of efficient error correcting codes, for messages ranging from a few tens up to a few hundred bits. While important progress has been made over the last years in understanding the limits of coding at short block lengths [START_REF] Polyanskiy | Channel coding rate in the finite blocklength regime[END_REF], the design of efficient short codes and decoding algorithms still raises many challenges [START_REF] Cos ¸kun | Efficient error-correcting codes in the short blocklength regime[END_REF].

Low Density Parity Check (LDPC) codes [START_REF] Gallager | Low density parity check codes[END_REF] are a class of error correcting codes defined by sparse bipartite graphs [START_REF] Tanner | A recursive approach to low complexity codes[END_REF]. They are well-known for their excellent error correction performance at long block lengths, achieving near Shannon channel capacity performance under Belief Propagation (BP) decoding, in the asymptotic limit of the code length [START_REF] Richardson | Design of capacityapproaching irregular low-density parity-check codes[END_REF]. For codes defined by cycle-free bipartite graphs, BP decoding outputs the maximum a posteriori estimates of the coded bits [START_REF] Wiberg | Codes and decoding on general graphs[END_REF]. Although bipartite graphs associated with practical codes contain cycles, BP decoding may still take effective advantage of sparse, long enough graphs, devoid of short cycles. However, for short codes, short cycles may not be avoidable, thus significantly degrading the BP performance. This is even more pronounced for High Density Parity Check (HDPC) codes, defined by higher density bipartite graphs [START_REF] Dimnik | Improved random redundant iterative HDPC decoding[END_REF].

To reduce the impact of short cycles, a weighted BP decoding has been introduced in [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF], where the weights are optimized using a Neural Network (NN). The topology of the NN mimics the BP decoding process, with unwrapped decoding iterations. The approach may use either a feedforward (FF) This work was partially supported by the ECSEL Joint Undertaking (JU) programme, under grant number N°826276 (CPS4EU project).

or a Recurrent NN (RNN). The corresponding decoders are termed as BP-FF and BP-RNN. It has been shown in [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF] that the BP-RNN is able to outperform the usual BP decoder for short Bose-Chaudhuri-Hocquenghem (BCH) codes, belonging to the class of HDPC codes. Subsequently, several variants of NN-based BP decoding have been proposed in the literature. [START_REF] Xiao | Designing finite alphabet iterative decoders of ldpc codes via recurrent quantized neural networks[END_REF] proposed the design of new decoding rules for finitealphabet iterative decoders, based on a quantized NN model. [START_REF] Buchberger | Pruning neural belief propagation decoders[END_REF] developed a pruning method of irrelevant check nodes in a neural BP model, aimed at jointly optimizing the code construction and the decoding. In [START_REF] Doan | Neural belief propagation decoding of crc-polar concatenated codes[END_REF], a neural BP decoding approach was proposed for cyclic redundancy check (CRC)assisted polar codes.

In this paper, we focus on BP-RNN decoding of short block length LDPC codes. To improve the decoding performance, our approach aims at specializing BP-RNN decoders to difficult error events. To do so, we first propose a classification of the error events, according to the structure of the induced subgraph. The classification is driven by the impact of the induced sub-graph on the BP decoding performance. Then, a parallel construction, comprising several BP-RNN decoders running in parallel, is described, where each BP-RNN is specialized to a specific error class. Finally, we discuss the training of the parallel BP-RNN decoders, and provide a method to reduce their number, without jeopardizing the decoding performance, by introducing a similarity rate metric.

The paper is organized as follow. Section II introduces the notations and recalls the BP-RNN decoding algorithm. Section III defines the classification of the error events, the parallel construction of BP-RNN decoders, the training of the BP-RNN decoders, and the similarity metric used to reduce their number. Finally, Section IV presents the numerical results, and Section V concludes the paper.

II. NEURAL BP DECODING

We consider an LDPC code defined by a Tanner (bipartite) graph with N variable-nodes and M check-nodes, denoted respectively by n ∈ {1, . . . , N } and m ∈ {1, . . . , M }. We further denote by N (m) the set of variable-nodes connected to a check-node m, and by M(n) the set of check-nodes connected to a variable-node n.

BP decoding consists of an iterative exchange of messages along the edges of the Tanner graph, where each message provides an estimation of the incident variable-node. BP-RNN and BP-FF decoding algorithms are weighted variants of the BP decoding, where exchanged messages are multiplied by weights learned through an either RNN or FF-NN approach. The underlying NN contains three types of neural layers, each one corresponding to a step of the BP algorithm. The checkpass layer and the data-pass layer carry out the computation of messages outgoing from check-nodes and variable-nodes, respectively. Each one of them contains a number of neurons equal to the number of edges of the Tanner graph. In addition, the a posteriori Log Likelihood Ratio (LLR) layer consists of N neurons, computing the a posteriori LLR values of the N variable-nodes. The three layers of the NN are connected such that a check pass layer, followed by a data pass layer and an a posteriori LLR layer model one iteration of the BP decoding. In particular, it is worth stressing out the differences between the edges of the Tanner graph (corresponding to neurons in the check-pass and data-pass layers), and the edges of the NN.

The formulas below detail the calculation of messages within each layer. We denote by β m→n and α n→m the messages computed by the check-pass and data-pass layers (where (m, n) is an edge of the Tanner graph), and by Ln the messages computed by the a posteriori LLR layer. The observed (channel) LLR values are denoted by L ch,n , and are used to initialize α n→m messages prior to the first iteration.

β m→n = 2 tanh -1   n ∈N (m)\n tanh α n →m 2   (1)
α n→m = L ch,n + m ∈M(n)\m w m →n→m β m →n (2)
Ln = L ch,n + m∈M(n) wm→n β m→n (3)
It can be observed that weights are applied only on the NN edges incoming to the data-pass (2) and a posteriori LLR (3) layers. Each weight corresponds to one specific edge of the NN. In (2) the weights are denoted by w m →n→m , where the subscript indicates both the corresponding neuron n → m in the data-pass layer, and the incoming NN edge from neuron m → n in the check-pass layer. In (3) the weights are denoted by wm→n , where the subscript indicates the corresponding neuron n in the a posteriori LLR layer, and the incoming NN edge from neuron m → n in the check-pass layer. For the BP-RNN, the weights only depend on the corresponding edges of the NN, while for the BP-FF they also depend on the iteration number (note that, to simplify notation, we have not indicated the iteration number on the above formulas). It is worth noticing that despite the reduced number of trained weights, the BP-RNN achieves similar performance to the BP-FF [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF]. An alternative approach suggested in [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF] to further reduce the number of weights is based on the following datapass layer,

α n→m = L ch,n + w n→m m ∈M(n)\m β m →n , (4)
where the applied weight only depends on the data-pass neuron. This simplification reduces the training complexity and makes it possible to reuse conventional BP decoding architectures for efficient hardware implementation. The BP-RNN using (4) will be referred to as BP-RNN Hardware Friendly Implementation (BP-RNN-HFI).

To train the BP-RNN, we use the following Bit Error Rate (BER) loss function, assuming without loss of generality that the zero codeword is transmitted:

Loss( L) = -1 N N -1 n=0 log(σ( Ln )) (5)
where σ(x) = (1 + exp(-x)) -1 is the sigmoid function, converting the LLRs into probability values. The loss function is minimized during the NN training, thus improving the BER of the trained decoder.

III. SPECIALIZING BP-RNN DECODERS ACCORDING TO AN ERROR EVENTS CLASSIFICATION A. Absorbing-type classification of error events

Let V be a set of variable-nodes, and C be the set of check-nodes connected to at least one variable-node in V . We denote by O(V ) ⊂ C the set of check-nodes connected an odd number of times to V (that is, they have odd degree in the sub-graph induced by V ). Thus, E(V ) := C\O(V ) is the set of check-nodes connected an even number of times to V . The set V is said to be an absorbing set [START_REF] Dolecek | Predicting error floors of structured ldpc codes: Deterministic bounds and estimates[END_REF], if each variable-node in V has fewer neighbors in O(V ) than in E(V ). Fig. 1(a) shows an example of absorbing set, where each variable-node of V is connected to one check-node in O(V ) and two check-nodes in E(V ). While absorbing sets are combinatorial substructures of the Tanner graph, defined independently of the particular decoding algorithm, they are known to be particularly harmful to BP or other forms of message-passing decoding. Indeed, assuming that the set of errors V is an absorbing set, then each variable-node in V has less neighbor check-nodes indicating an error (unsatisfied), than indicating no error (satisfied). Consequently, V represents a difficult error event, yielding a decoding failure with high probability.

We are interested in classifying error events with a given number of errors ν. Let V a set of variable-nodes, with card(V ) = ν. We define the absorbing type of V as the pair (ω, ε), where ω := card(O(V )) and ε := card(E(V )). We shall sometimes denote the absorbing type as ν-(ω, ε), to also account for the cardinality of V . Note that the absorbing type indicates the total number of (unsatisfied, satisfied) checknodes, in case the variable-nodes in V are in error. However, variable-node sets of same absorbing type may induce different (precisely, non-isomorphic) sub-graphs. Such an example is illustrated in Fig. 1, for two variable-node sets of absorbing type 3-(3, 3), the first of which is an absorbing set (a), but not the second (b). For the set V in (b), it can be seen that variable-node n is connected to two unsatisfied checknodes and one satisfied (most favorable case among the three variable-nodes), n to only satisfied check-nodes (worst case),

B. Proposed parallel BP-RNN decoders

To improve the decoding performance of LDPC codes at short coding length, we propose to specialize (i.e., train) a BP-RNN decoder for each error class ν-(ω, ε, s), according to the classification from the previous subsection. The number of different error classes, and thus of BP-RNN decoders, depend on the particular Tanner graph defining the LDPC code, and the value of ν. For a given short LDPC codes, we determine all the possible error classes, by considering all the variablenode subsets V of cardinality ν. In this work, we consider ν = 2, 3, thus the proposed approach is particularly relevant to high coding rate LDPC codes, correcting a small number of errors.

Once a BN-RNN decoder has been trained for each error class (the training procedure will be detailed in next subsection), we consider a parallel decoding architecture, where all the trained decoders are run in parallel (note that different architectural choices are possible and not discussed in this paper). We include the conventional BP decoder in the parallel structure. If none of the parallel decoders outputs a codeword (which is verified by computing the syndrome), decoding fails. Otherwise, among the decoded codewords, we select the one that has been outputted the most often (in case different decoders output different codewords). Decoding is successful if the selected codeword is equal to the transmitted one.

C. Training of the parallel BP-RNN decoders

We propose in this section a construction of the training set, used to train the BP-RNN decoder for a particular error class. We assume that coded bits are mapped to ±1 modulated symbols, which undergo real additive white Gaussian noise (AWGN). Since both the noise model and the BP-RNN decoder are symmetric [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF], we may assume the all-zero codeword is transmitted, corresponding to an all +1 modulated signal. Hence, under the AWGN model, received symbols are given by y n = 1+z n , n = 1, . . . , N , where z n denotes a real-valued normal distributed random variable, with mean 0, and variance σ 2 .

To generate a random error event in a given error class ν-(ω, ε, s), we first consider an underlying variable-node error set V , randomly chosen from those corresponding to the given error class, and then generate received symbols y n , by

y n = 1 + z n , ∀n = 1, . . . , N (6)
where

z n ∼ N (0, σ 2 , -∞, -1), if n ∈ V N (0, σ 2 , -1, ∞), otherwise (7)
where N (0, σ 2 , a, b) denotes the truncated normal distribution with mean 0 and variance σ 2 , taking values in the interval (a, b). The training set is obtained by repeating the above procedure multiple times, for each variable-node set V in the given error class. In this way, the training set is representative of the error class, and thus the trained BP-RNN decoder becomes specialized to error events in the class.

D. Complementary selection of trained BP-RNNs

In practical applications, it is desirable to reduce the number of decoders running in parallel. To this end, in this subsection we propose a complementarity metric between the trained decoders. Intuitively, two decoders are complementary if the probability to fail on the same error event is low. This maximizes the gain when the two decoders are run in parallel.

We define the similarity rate between two decoders D p and D q , p = q, as the probability that both decoders fail, when either one of them fails. Precisely, we define S(D p , D q ) := Pr (D p and D q fail | either D p or D q fails) (8)

In practice, this metric can be numerically estimated by Monte-Carlo simulation, using

S(D p , D q ) ≈ N p,q N p + N q -N p,q , (9)
where N p (resp. N q ) is the number of times the decoder D p (resp. D q ) failed, and N p,q is the number times they both failed. Consequently, S(D p , D q ) measures the effectiveness of specialized training in producing decoders able to correct different error events. Put differently, it characterizes the level of complementary between the two decoders. An overall similarity coefficient is then calculated for each decoder D p , by averaging the similarity rate between D p and the other decoders.

S(D

p ) = 1 D -1 q =p S(D p , D q ) (10)
where D denotes the total number of parallel BP-RNN decoders. Subsequently, given a similarity threshold value S th , we keep only the decoders with overall similarity coefficient S(D p ) less than S th . Hence, only the most complementary decoders are maintained in the final parallel structure. We note that the choice of the S th value may yield different trade-offs between complexity and decoding performance.

IV. NUMERICAL RESULTS

A. Simulation Settings

Two LDPC codes with regular variable-node degree have been considered in our simulations. Code parameters are provided in Table I, where N denotes the code length, K the number of information bits, R c := K/N the coding rate, d v the variable nodes degree, d c the check nodes degree, and n 4-cycles the number of length-4 cycles. The Tanner graphs of the two codes have been constructed by using the Progressive Edge Growth (PEG) algorithm [START_REF] Hu | Regular and irregular progressive edge-growth Tanner graphs[END_REF], a greedy algorithm making the best-effort to reduce the number of short cycles in the constructed graph. Yet, for small code length, short cycles, including cycles of length-4, cannot be completely avoided.

The number of decoding iterations was set to ten, for all the decoders. Since we consider codes with high coding rate, the error events classification was conducted for error sets V of size ν = 2, 31 . Applying the error classification procedure described in Section III-A, we found three 2-(ω, ε, s) classes, for both Code-1 and Code-2, and ten (resp. eleven) 3-(ω, ε, s) error classes for Code-1 (resp. Code-2). Thus, a total of thirteen (resp. fourteen) BP-RNNs were used in parallel, alongside the BP decoder. Each BP-RNN was trained independently with the training set construction technique described in Section III-C.

The same procedure was repeated for the BP-RNN-FHI decoder, for both Code-1 and Code-2, in order to assess the weight reduction in (4). In addition, we also trained a single BP-RNN decoder according to the procedure described in [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF], to provide a benchmark for our parallel BP-RNNs approach.

To train the BP-RNN decoders, we used the Keras library, with the hyper parameters shown in Table II. All BP-RNNs were trained for each signal-to-noise ratio (SNR) value ranging from 1 dB to 8 dB, with a step of 1 dB, thus providing eight optimized weight sets for each decoder. While this increases Finally, we used the similarity metric introduced in Section III-D, in order to reduce the number of parallel decoders. The similarity coefficient has been numerically estimated by using ( 9) and ( 10), based on the first simulation results. We fixed a similarity threshold value S th = 0.6 (resp. S th = 0.56) for Code-1 (resp. Code-2), at a FER of 10 -4 , which led to the selection of only eight (resp. nine) trained BP-RNN decoder alongside the conventional BP. Then, new independent simulations were run for both resulting parallel structures, to assess their FER performance.

B. FER performance

We compare the different decoding strategies discussed in the previous section, in terms of FER. Reported SNR gains are evaluated at a FER of 10 -4 .

Simulation results for Code-1 are shown in Fig. 2. The BP-RNN trained as in [START_REF] Nachmani | Deep learning methods for improved decoding of linear codes[END_REF] yields an SNR gain of 0.18 dB, with respect to conventional BP. Using the proposed structure, with specialized BP-RNNs, the SNR gain is increased to 0.42 dB. The parallel BP-RNN-FHIs exhibit only negligible performance degradation compared to the parallel BP-RNNs, due to the weight reduction constraint in (4). Finally, it can be observed that the parallel BP-RNNs construction with complementary selection shows virtually the same FER performance as the original complete construction of parallel BP-RNNs. Therefore, choosing S th = 0.6 leads to a selection of eight decoders which effectively complement each others.

Simulation results for Code-2 are shown in Fig. 3. Despite the increase in the length of the code, it should be noted that Code-2 exhibits an increased number of length-4 cycles, due to its higher coding rate. However the parallel BP-RNN decoder yields a similar SNR gain, of 0.42 dB, with respect to the conventional BP. The parallel BP-RNN-FHIs tend to be a little less efficient. Furthermore, Fig. 3 also corroborates the relevance of the complementary selection, the corresponding parallel BP-RNNs construction yielding again almost the same performance as the original complete construction of parallel BP-RNNs.

Finally, Fig. 4 provides a comparison in terms of the number of decoding failures, for various values of ν (size of the error event), for an SNR of 8 dB. It demonstrates that for both Code-1 and Code-2, the parallel BP-RNNs are clearly able to correct numerous error events which are not decoded by the BP, especially for the two and three error events (ν = 2, 3). Therefore, we conclude that the specialization of the training for the 2-(ω, ε, s) and the 3-(ω, ε, s) error classes effectively induces an understanding of the BP-RNNs of how to decode several type of size two and three error events. Furthermore, some error events of size four and five are also successfully decoded thanks to the previous specialization.

V. CONCLUSION AND PERSPECTIVES

In this paper, we addressed the problem of enhancing the BP-RNN performance at short coding length. To this end, we studied and classified error events according to the impact of the induced sub-graphs on the BP decoding performance. Then, we proposed a new decoding strategy consisting of parallel specialized BP-RNN decoders where each BP-RNN was trained for a specific error class. In addition, we introduced a complementary selection method of the trained BP-RNN decoders, proven to be efficient in keeping the most relevant trained decoders in the final parallel structure.

This work is a first step towards a framework of specialized neural BP decoders, and we believe that further work may reveal alternative specialization strategies. The final aim would be to approach maximum likelihood decoding performance at short to moderate code-length, for which we will probably need to rely on a bunch of practical decoders, rather than a unique one.

Fig. 1 .

 1 Fig. 1. Example of two sets V , with card(O(V )) = card(E(V )) = 3. If variable-nodes in V are in error, check-nodes marked by an U are unsatisfied, while those marked by an S are satisfied.

Fig. 2 .

 2 Fig. 2. FER results for Code-1.

Fig. 3 .

 3 Fig. 3. FER results for Code-2.

Fig. 4 .

 4 Fig. 4. Number of failed decoding according to the size of an error event.

  Error Structure Aware Parallel BP-RNN Decoders for Short LDPC Codes Joachim Rosseel * † , Valérian Mannoni * , Valentin Savin * , Inbar Fijalkow †

For comparison, a BCH code with either (N, K) = (63, 45) or (N, K) = (127, 106) has minimum distance d = 7, thus may correct 3 errors