Constellation Design for Improved Iterative LDPC Decoding

Recent advances in iteratively decoded channel codes such as low-density parity-check (LDPC) codes make it possible to operate close to channel capacity limits. The capacity of a coded modulation is therefore a very useful indicator when analyzing the performance of a near infinite-length code under maximum likelihood (ML) decoding. In this work, we analyze the behavior of LDPC codes of moderate lengths using belief propagation (BP) based decoding algorithms. We found that in many cases analyzing the capacity of the coded modulation is not enough to predict which constellation will yield the best error rate performance in a Gaussian noise channel. For the case of M-ary constellations with M=8 and 16 we show how a lower error rate can be achieved by making simple changes to constant envelope phase-shift keying (PSK) constellations. Modifying these constellations translates to an increase in the mean log-likelihood ratio of some of the received bits, resulting in an improvement in performance.