Triggering Wave-Like Convergence of Tail-biting Spatially Coupled LDPC Codes: Single and Dual-Channel Setup

Spatially coupled low-density parity-check (SC-LDPC) codes can achieve the channel capacity under low-complexity belief propagation (BP) decoding. For practical finite coupling lengths however, there is a non-negligible rate-loss because of termination effects. In this paper, we focus on tail-biting SC-LDPC codes which do not require termination and study how we can approach the performance of terminated SC-LDPC codes by random shortening the code. We find the minimum required rate-loss in order to achieve the same performance than terminated codes. In the second part of this paper, we study the use of tail-biting SC-LDPC codes for transmission over parallel channels, e.g., bit-interleaved-coded-modulation (BICM), multi-level coding, or multi-carrier transmission. We investigate how the distribution of the coded bits between two parallel binary erasure channels and the 4-ASK AWGN channel can change the performance of the code. We show that if the code bits are carefully interleaved between channels, a tail-biting SC-LDPC code can be operated with BP decoding almost anywhere within the achievable region of MAP decoding. The required buffer at the encoder side can be minimized during the optimization process.