Performance of Spatially-Coupled LDPC Codes and Threshold Saturation over BICM Channels

TL;DR

This paper investigates the performance of spatially-coupled LDPC codes with BICM schemes over AWGN and Rayleigh channels, demonstrating threshold saturation and capacity-approaching behavior through numerical analysis.

Contribution

It extends area theorem bounds to BICM schemes and demonstrates that SC-LDPC codes achieve threshold saturation and approach BICM capacity on various channels.

Findings

Threshold saturation observed for SC-LDPC codes.

SC-LDPC codes approach BICM capacity.

Bounds approach noise threshold for large degrees.

Abstract

We study the performance of binary spatially-coupled low-density parity-check codes (SC-LDPC) when used with bit-interleaved coded-modulation (BICM) schemes. This paper considers the cases when transmission takes place over additive white Gaussian noise (AWGN)channels and Rayleigh fast-fading channels. The technique of upper bounding the maximum-a-posteriori (MAP) decoding performance of LDPC codes using an area theorem is extended for BICM schemes. The upper bound is computed for both the optimal MAP demapper and the suboptimal max-log-MAP (MLM) demapper. It is observed that this bound approaches the noise threshold of BICM channels for regular LDPC codes with large degrees. The rest of the paper extends these techniques to SC-LDPC codes and the phenomenon of threshold saturation is demonstrated numerically. Based on numerical evidence, we conjecture that the belief-propagation (BP) decoding threshold of SC-LDPC codes approaches the MAP decoding threshold of the underlying LDPC ensemble on BICM channels. Numerical results also show that SC-LDPC codes approach the BICM capacity over different channels and modulation schemes.