Improving the Finite-Length Performance of Spatially Coupled LDPC Codes by Connecting Multiple Code Chains

摘要

In this paper, we analyze the finite-length performance of codes on graphsconstructed by connecting spatially coupled low-density parity-check (SC-LDPC)code chains. Successive (peeling) decoding is considered for the binary erasurechannel (BEC). The evolution of the undecoded portion of the bipartite graphremaining after each iteration is analyzed as a dynamical system. Whenconnecting short SC-LDPC chains, we show that, in addition to superioriterative decoding thresholds, connected chain ensembles have betterfinite-length performance than single chain ensembles of the same rate andlength. In addition, we present a novel encoding/transmission scheme to improvethe performance of a system using long SC-LDPC chains, where, instead oftransmitting codewords corresponding to a single SC-LDPC chain independently,we connect consecutive chains in a multi-layer format to form a connected chainensemble. We refer to such a transmission scheme to as continuous chain (CC)transmission of SC-LDPC codes. We show that CC transmission can be implementedwith no significant increase in encoding/decoding complexity or decoding delaywith respect a system using a single SC-LDPC code chain for encoding.