Source and channel coding using Fountain codes

The invention of Fountain codes is a major advance in the field of error correcting codes. The goal of this work is to study and develop algorithms for source and channel coding using a family of Fountain codes known as Raptor codes. From an asymptotic point of view, the best currently known sum-product decoding algorithm for non binary alphabets has a high complexity that limits its use in practice. For binary channels, sum-product decoding algorithms have been extensively studied and are known to perform well. In the first part of this work, we develop a decoding algorithm for binary codes on non-binary channels based on a combination of sum-product and maximum-likelihood decoding. We apply this algorithm to Raptor codes on both symmetric and non-symmetric channels. Our algorithm shows the best performance in terms of complexity and error rate per symbol for blocks of finite length for symmetric channels. Then, we examine the performance of Raptor codes under sum-product decoding when the transmission is taking place on piecewise stationary memoryless channels and on channels with memory corrupted by noise. We develop algorithms for joint estimation and detection while simultaneously employing expectation maximization to estimate the noise, and sum-product algorithm to correct errors. We also develop a hard decision algorithm for Raptor codes on piecewise stationary memoryless channels. Finally, we generalize our joint LT estimation-decoding algorithms for Markov-modulated channels. In the third part of this work, we develop compression algorithms using Raptor codes. More specifically we introduce a lossless text compression algorithm, obtaining in this way competitive results compared to the existing classical approaches. Moreover, we propose distributed source coding algorithms based on the paradigm proposed by Slepian and Wolf

Effets De La Regulation Et Du Developpement Institutionnel Sur Le Secteur Bancaire De La Cemac

The objective of this study is to assess the impact of the regulation (of requirements in equity capital) and of the institutional development on some performances of the ‘’CEMAC’’ banking sector. The secondary data used come from the publications of the World Bank (World Bank Development Indicators) and from the services of ‘’BEAC’’ and ‘’COBAC’’. The method of estimation is that of the Generalized Moment Method (GMM) in dynamic panel via the model of Arellano and Bond (1991). The study spans a period of 8 years (2005-2012) and takes into account the six countries of the CEMAC subregion. The results of the study are presented as follows: (1) the level of the prescribed equity capital does not affect neither the “banking development” nor the “capacity of mobilization of the domestic saving” and just as the “economies financing capacity”. (2) The level of legal and institutional development influences negatively and significantly the “banking development” and the “volume of domestic saving”. (3) Also, the level of legal and institutional development influences positively and significantly the “capacity of the banking sector to finance the economies”. These results lead therefore to some implications of economic policy such as: the public authorities should reinforce the financing capacity of the “CEMAC” economies in setting up a real financial market. They should also develop and in a significant way political and institutional infrastructures in order to stimulate the confidence of savers and investors

Fountain codes for piecewise stationary channels

In this paper, two fixed per-information symbol complexity lossless source coding algorithms are modified for estimation and incremental LT decoding over piecewise stationary memoryless channels (PSMC's) with a bounded number of abrupt changes in channel statistics. In particular, as a class of PSMC's, binary symmetric channels are considered with a crossover probability that changes a bounded number of times with no repetitions in the statistics. Simulation results are given which illustrate the benefits of using our algorithms, both in terms of probability of error and in terms of redundancy

Fountain Codes for the Slepian-Wolf Problem

In this paper, we describe one solution to the two-user Slepian-Wolf problem in a certain part of the achievable region using fountain codes. Symmetric case of memoryless compression of two correlated sources is considered and modeled by a BSC channel. The compression is done by two separate compressors without any exchange of information between them. The decompressor uses a Belief propagation algorithm in conjunction with the Blind Iterative Doping strategy. Simulation results indicate performance close to the Slepian-Wolf limit