Soft-Information Post-Processing for Chase-Pyndiah Decoding Based on Generalized Mutual Information

Chase-Pyndiah decoding is widely used for decoding product codes. However, this method is suboptimal and requires scaling the soft information exchanged during the iterative processing. In this paper, we propose a framework for obtaining the scaling coefficients based on maximizing the generalized mutual information. Our approach yields gains up to 0.11 dB for product codes with two-error correcting extended BCH component codes over the binary-input additive white Gaussian noise channel compared to the original Chase-Pyndiah decoder with heuristically obtained coefficients. We also introduce an extrinsic version of the Chase-Pyndiah decoder and associate product codes with a turbo-like code ensemble to derive a Monte Carlo-based density evolution analysis. The resulting iterative decoding thresholds accurately predict the onset of the waterfall region.

I. Introduction

Product codes [1] when combined with Chase-Pyndiah decoding [2] feature an attractive performance-complexity tradeoff and are therefore widely used for applications with very high throughput requirements (e.g., [3]). Chase-Pyndiah decoding is an efficient iterative soft-decision decoding algorithm that employs suboptimal Chase [4] decoding of the component codes followed by an information combining step to generate the soft messages exchanged. To improve the finite-length performance, Pyndiah further proposed to scale the soft outputs by heuristically-determined parameters [2]. To the best of the authors’ knowledge, no information-theoretically motivated method for optimizing these scaling coefficients has been reported to date.