Low-density parity-check codes for the relay channel

Abstract

Since 1948, when Claude Shannon introduced the notion of channel capacity, the ultimate goal of coding theory has been to find practical capacity-approaching codes. This thesis is concerned with the analysis, design, construction, and, mainly, the decoding of an extremely powerful and flexible family of error-control codes, called low-density parity-check (LDPC) codes. LDPC codes can be designed to perform close to the capacity of many different types of channels with a practical decoding complexity. The main design tool, Density Evolution, which predicts the asymptotic performance of a belief-propagation decoder is analysed. An effective construction method, called configuration model, for picking LDPC codes at random from LDPC ensembles is presented in depth. In addition, a construction tool for LDPC codes of moderate lengths, namely the Progressive Edge Growth algorithm, which tries to maximize the girth of a code is presented. Furthermore, we present the analysis,design, construction and decoding of bilayer LDPC codes for the half-duplex relay channel. To analyse the performance of bilayer LDPC codes, bilayer Density Evolution is presented as an extension of the standard Density Evolution. Finally, we analyse in depth the construction procedure of bilayer LDPC codes as an extension of single user's configuration model.