Joint Iterative Decoding of LDPC Codes and Channels with Memory
Henry D. Pfister, Paul H. Siegel · 2007
Introduction Sequences of irregular low-density parity-check (LDPC) codes that achieve the capacity of the binary erasure channel (BEC) under iterative decoding were first constructed by Luby, et al. in [11]. This was followed by the work of Chung, et al., which provided evidence suggesting that sequences of iteratively decoded LDPC codes can also achieve the channel capacity of the binary-input additive white Gaussian noise (AWGN) channel [3]. Since then, density evolution (DE) [13] has been used to optimize irregular LDPC codes for a variety of memoryless channels (e.g., [6]), and the results suggest, for each channel, that sequences of iteratively decoded LDPC codes can indeed achieve the channel capacity. In fact, the discovery of a channel whose capacity cannot be approached by LDPC codes would be more surprising than a proof that iteratively decoded LDPC codes can achieve the capacity of any binary-input symmetric channel (BISC). The idea of decoding a code transmitted over a c