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.