Optimization of Finite-Length SC-LDPC for Uplink NOMA

Abstract

Due to lack of universality, the achievable channel parameter regions (ACPRs) of conventional channel codes are far from the outer boundary of non-orthogonal multiple access (NOMA) channel capacity region. Spatially coupled low-density parity-check (SC-LDPC) codes show excellent asymptotic performance and their ACPRs are able to approach the outer boundary of NOMA channels. However, the performance of finite-length SC-LDPC codes is not as excellent as its asymptotic counterpart. In this paper, a two-phase algorithm is proposed to construct capacity-approaching SC-LDPC codes with finite codeword length. By jointly optimizing the protograph, the spatial coupling length and the uncoupled code length, the performance loss of SC-LDPC code caused by finite codeword length is minimized. Simulation results show that the ACPR of the optimized SC-LDPC code is only 1.2 dB from the theoretical limit of NOMA channels when the codeword length is 9600.