NB-LDPC Codes with High Rates Achieving Low BER over the AWGN Channel with QAM Signaling

The paper investigates high-rate Low-Density-Parity-Check (LDPC) codes, able to achieve a low bit error rate (BER). Such an operational regime of LDPC codes finds its application in optical transmissions. For this reason the considered transmission model is the one close to optical communications: it is a M-ary Quadrature-Amplitude Modulation (QAM) signaling over the M-ary input additive Gaussian channel.We study three main points: a) which LDPC codes of fixed codelength can achieve low BER for a code rate R ≥ 0.8; b) whether non-binary LDPC (NB-LDPC) codes, defined over GF(Q), are efficient in this setting; c) how to keep a reasonable decoding complexity for a given modulation order. Our performance analysis is complete and it is based on the calculation of the average bit error rate of a given ensemble, by using both asymptotic and finite-length tools of sparse-graph codes.Our results show that NB-LDPC codes with moderate values of Q, together with a Symbol Interleaved Coded Modulation (SICM) approach, offer the best performance at low BER.