LDPC Codes
Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze, Mohammed Ahmed, Mubarak Jibril · Signals and communication technology · 2017
This chapter explores the design and performance of low-density parity-check (LDPC) codes which when combined with soft decision iterative decoding provide currently the best achievable performance in digital communication systems. The application of cyclotomic cosets, idempotents and Mattson–Solomon polynomials is shown to produce many new binary cyclic LDPC codes whose parity-check equations are orthogonal in each position. A key feature of this construction technique is the incremental approach to designing the minimum Hamming distance and the sparseness of the resulting parity-check matrix of the code. Binary cyclic LDPC codes are also constructed by considering idempotents in the Mattson–Solomon domain. It is shown that, for short algebraic LDPC codes, the myth of codes which have cycles of length 4 in their Tanner graph does not converge well with iterative decoding is not necessarily true. It is demonstrated that the cyclotomic coset-based construction can be easily extended to produce good non-binary algebraic LDPC codes. Good irregular LDPC codes may be constructed using the progressive edge-growth algorithm. Many new code results are presented showing the effects of choosing different degree distributions. Guidelines are given for designing the best codes. Methods of producing structured LDPC codes, such as those which have quasi-cyclic structure, are described. These are of interest to industry due to the simplification of the encoder and decoder. An example of such a construction to produce a (64800,48600) LDPC code, using a protograph, is presented along with performance results using iterative decoding. Better results are obtained with this code than the (64800,48600) LDPC code used in the DVB-S2 standard. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.