Graph-Based Decoding in the Presence of ISI

TL;DR

This paper introduces a graph-based approximation method for maximum-likelihood detection in ISI channels, enabling efficient decoding that can be integrated with LDPC codes, with proven exactness for certain channels.

Contribution

The authors develop a linear programming and message passing approach that approximates ML detection in ISI channels, compatible with LDPC decoding, and analyze its error performance.

Findings

Exact ML solution for some channels without exponential complexity

Method has a non-zero failure probability for certain channels at high SNR

Analysis of error events under linear programming approximation

Abstract

We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We show that, for a certain class of channels and in the absence of coding, the proposed technique provides the exact ML solution without an exponential complexity in the size of channel memory, while for some other channels, this method has a non-diminishing probability of failure as SNR increases. Some analysis is provided for the error events of the proposed technique under linear programming.