Spatially-Coupled Binary MacKay-Neal Codes for Channels with Non-Binary Inputs and Affine Subspace Outputs

TL;DR

This paper investigates the performance of spatially-coupled binary MacKay-Neal codes over channels with non-binary inputs and affine subspace outputs, revealing how decoding thresholds are affected and can be improved.

Contribution

It introduces a joint iterative decoding scheme for such channels and analyzes the impact of channel parameters on decoding thresholds using density evolution.

Findings

Decoding thresholds degrade with increasing input alphabet size m.

Wiggles in EXIT-like curves cause threshold degradation.

Increasing randomized window size mitigates threshold degradation.

Abstract

We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in \mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in \mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from which $\underline{z}=\underline{y}-\underline{x}$ is uniformly chosen. Or equivalently, the receiver receives an affine subspace $\underline{y}-V$ where $\underline{x}$ lies. We consider a joint iterative decoder involving the channel detector and the LDPC decoder. The decoding system considered in this paper can be viewed as a simplified model of the joint iterative decoder over non-binary modulated signal inputs e.g., $2^m$-QAM. We evaluate the performance of binary spatially-coupled MacKay-Neal codes by density evolution. The iterative decoding threshold is seriously degraded by increasing $m$. EXIT-like function curve calculations reveal that this degradation is caused by wiggles and can be mitigated by increasing the randomized window size. The resultant iterative decoding threshold values are very close to the Shannon limit.