Multilevel generalised low-density parity-check codes

Introduction: Multilevel coding (MLC) was proposed by Imai and Hirawaki [1] as a bandwidth-efficient coded modulation scheme designed for protecting each bit of a non-binary symbol with the aid of binary codes, while maintaining different target bit error rates (BERs). Parallel independent decoding (PID) [2] is employed as an efficient decoding strategy with reduced decoding delay, where there is no information exchange across the different protection classes. MLC schemes may be constructed using different component codes. Recently, classic low-density parity-check (LDPC) codes [3] have been commonly used as component codes [4] owing to their flexible code rates and good BER performance. Belief propagation (BP) [3] may be used for iterative soft decoding at each different BER protection level. Against this background, we propose a novel MLC design using generalised LDPC (GLDPC) codes rather than classic LDPC codes [5] as component codes, which has the benefit of an improved BER performance and an implementationally attractive shorter parallel decoding structure. As a benefit of their block-based nature and random generator matrix construction, no channel interleaver is required for LDPC or GLDPC component codes. For our GLDPC codes, instead of using Gallager’s single-error detecting parity-check code [3], we employ binary BCH error-correcting codes [6] as the constituent codes. Simple iterative soft-input soft-output (SISO) decoders [6] are used for each constituent BCH code of the MLC scheme. We invoke both inner iterations within the LDPC=GLDPC component codes and outer iterations exchanging information between the LDPC=GLDPC block codes and the demapper, as shown in Figs. 1 and 2. Gray mapping (GM) of the bits to modulated symbols is used for non-iterative decoding, while set partitioning (SP) based mapping is used for iterative decoding, because it provides improved iteration gains.