Triggering Wave-Like Convergence of Tail-biting Spatially Coupled LDPC Codes

Abstract

Spatially coupled low-density parity-check (SC-LDPC) codes can achieve the channel capacity under low-complexity belief propagation (BP) decoding, however, there is a non-negligible rate-loss because of termination effects for practical finite coupling lengths. In this paper, we study how we can approach the performance of terminated SC-LDPC codes by random shortening of tail-biting SC-LDPC codes. We find the minimum required rate-loss in order to achieve the same performance than terminated codes. We additionally study the use of tail-biting SC-LDPC codes for transmission over parallel channels (e.g., bit-interleaved-coded-modulation (BICM)) and investigate how the distribution of the coded bits between two parallel channels can change the performance of the code. We show that a tail-biting SC-LDPC code can be used with BP decoding almost anywhere within the achievable region of MAP decoding. The optimization comes with a mandatory buffer at the encoder side. We evaluate different distributions of coded bits in order to reduce this buffer length.

Submitted to 2016 Annual Conference on Information Science and Systems (CISS)