Interior Point Decoding for Linear Vector Channels

TL;DR

This paper introduces an interior point decoding algorithm for LDPC codes over linear vector channels, leveraging convex optimization and interior point methods to improve decoding performance and complexity.

Contribution

It presents a novel convex optimization-based decoding algorithm for linear vector channels, including practical channels like ISI and partial response channels.

Findings

Achieves better BER performance than conventional decoders.

Reduces decoding complexity in many partial response channel cases.

Utilizes interior point methods with barrier functions for decoding.

Abstract

In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem. The proposed decoding algorithm is based on a numerical optimization technique so called interior point method with barrier function. Approximate variations of the gradient descent and the Newton methods are used to solve the convex optimization problem. In a decoding process of the proposed algorithm, a search point always lies in the fundamental polytope defined based on a low-density parity-check matrix. Compared with a convectional joint message passing decoder, the proposed decoding algorithm achieves better BER performance with less complexity in the case of partial response channels in many cases.