EE229B - Final Project Capacity-Approaching Low-Density Parity-Check Codes

The class of low-density parity-check (LDPC) codes was introduced by Gallager in his thesis in 1961 [2]. Until the invention of turbo codes, they were largely neglected, but received a lot of interest lately, due to the possibility of designing LDPC codes within 0.0045 dB of the Shannon limit. We review in this project techniques used to analyze the performance of LDPC codes under a message-passing decoding algorithm, namely belief propagation (BP) [4][5]. This analysis gives us the tools to design good LDPC codes. We will first take the simpler example of transmission over the class of binary erasure channels (BEC). We will then see how it is possible to extend the results for the BEC to the much more general class of symmetric channels.