Linear-Programming Receivers

TL;DR

The paper demonstrates that communication systems with sum-product receivers also have equivalent linear-programming receivers, providing a new analytical framework and applying it to joint equalization and decoding.

Contribution

It establishes the relationship between SP and LP receivers, introduces the concept of pseudoconfigurations, and proves the LP receiver's optimality and equivalence to graph-cover pseudoconfigurations.

Findings

LP receiver has the 'optimum certificate' property.

LP and SP receivers share the same pseudoconfiguration phenomena.

The LP design technique can be applied to joint equalization and decoding.

Abstract

It is shown that any communication system which admits a sum-product (SP) receiver also admits a corresponding linear-programming (LP) 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 'optimum certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. While the LP receiver is generally more complex than the corresponding SP receiver, the LP receiver and its associated pseudoconfiguration structure provide an analytic tool for the analysis of SP receivers. As an example application, we show how the LP design technique may be applied to the problem of joint equalization and decoding.