This paper introduces a random multiple access method for satellite communications, named Network Coding-based Slotted Aloha (NCSA). The goal is to improve diversity of data bursts on a slotted-ALOHA-like channel thanks to error correcting codes and Physical-layer Network Coding (PNC). This scheme can be considered as a generalization of the Contention Resolution Diversity Slotted Aloha (CRDSA) where the different replicas of this system are replaced by the different parts of a single word of an error correcting code. The performance of this scheme is first studied through a density evolution approach. Then, simulations confirm the CRDSA results by showing that, for a time frame of @math slots, the achievable total throughput is greater than @math , where @math is the maximal throughput achieved by a centralized scheme. This paper is a first analysis of the proposed scheme which open several perspectives. The most promising approach is to integrate collided bursts into the decoding process in order to improve the obtained performance.
LDPC codes are one of the hottest topics in coding theory today. Originally invented in the early 1960’s, they have experienced an amazing comeback in the last few years. Unlike many other classes of codes, LDPC codes are already equipped with very fast (probabilistic) encoding and decoding algorithms. The question is that of the design of the codes such that these algorithms can recover the original codeword in the face of large amounts of noise. New analytic and combinatorial tools make it possible to solve the design problem. This makes LDPC codes not only attractive from a theoretical point of view, but also perfect for practical applications. In this note I will give a brief overview of the origins of LDPC codes and the methods used for their analysis and design.