A Unified Framework for Linear-Programming Based Communication Receivers

TL;DR

This paper introduces a unified linear-programming framework for communication receivers, establishing their relationship with sum-product algorithms, analyzing pseudoconfigurations, and demonstrating competitive performance in joint equalization and decoding tasks.

Contribution

It develops a general LP-based receiver framework for systems with SPA-based receivers, proves key properties, and applies it to joint equalization and decoding with promising results.

Findings

LP receiver has maximum likelihood certificate property

LP design can be applied to joint equalization and decoding

LP receiver outperforms turbo equalization in simulations

Abstract

It is shown that a large class of communication systems which admit a sum-product algorithm (SPA) based receiver also admit a corresponding linear-programming (LP) based receiver. The two receivers have a relationship defined by the local structure of the underlying graphical model, and are inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This concept is a generalization of the concept of 'pseudocodewords' for linear codes. It is proved that the LP receiver has the 'maximum likelihood certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. A concept of 'system pseudodistance' is defined which generalizes the existing concept of pseudodistance for binary and nonbinary linear codes. It is demonstrated how the LP design technique may be applied to the problem of joint equalization and decoding of coded transmissions over a frequency selective channel, and a simulation-based analysis of the error events of the resulting LP receiver is also provided. For this particular application, the proposed LP receiver is shown to be competitive with other receivers, and to be capable of outperforming turbo equalization in bit and frame error rate performance.