Memoryless Channels and LDPC Codes

Abstract

As stated in Chapter 1, the introduction of low-density parity-check (LDPC) codes has allowed to achieve near-capacity transmission over some simple channels, such as, for example, the binary input additive white Gaussian noise (BIAWGN) channel, the binary erasure channel (BEC), or the binary symmetric channel (BSC) [9,12,13,33]. Although the performance of LDPC codes transmitted over binary-input memoryless channels is known and well studied in the literature, a formal proof of their potential to achieve channel capacity is still lacking. Moreover, the application of LDPC codes to generic memoryless channels, and, in particular, for medium to high spectral efficiency signaling over the AWGN channel, represents a promising evolution of established coding techniques, such as, for example, trellis coded modulations (TCM), and have been the subject of attention in the scientific community. In this chapter, we address the performance of LDPC codes transmitted through a memoryless channel, as described in the following paragraphs.