Optimization of Information Rate Upper and Lower Bounds for Channels with Memory

TL;DR

This paper develops iterative EM algorithms to optimize bounds on the information rates of channels with memory, including finite and infinite state channels, significantly tightening these bounds compared to previous methods.

Contribution

The paper introduces novel EM-based algorithms for optimizing auxiliary FSMC parameters to tighten information rate bounds for channels with memory, outperforming existing local optimization methods.

Findings

Algorithms effectively tighten upper and lower bounds on information rates.

Proposed methods outperform Soblex in robustness and efficiency.

Optimizing the lower bound relates to increasing mismatched information rates.

Abstract

We consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete-time channels with memory. The channels we consider can have a finite number of states, such as partial response channels, or they can have an infinite state-space, such as time-varying fading channels. We optimize recently-proposed information rate bounds for such channels, which make use of auxiliary finite-state machine channels (FSMCs). Our main contribution in this paper is to provide iterative expectation-maximization (EM) type algorithms to optimize the parameters of the auxiliary FSMC to tighten these bounds. We provide an explicit, iterative algorithm that improves the upper bound at each iteration. We also provide an effective method for iteratively optimizing the lower bound. To demonstrate the effectiveness of our algorithms, we provide several examples of partial response and fading channels, where the proposed optimization techniques significantly tighten the initial upper and lower bounds. Finally, we compare our results with an improved variation of the \emph{simplex} local optimization algorithm, called \emph{Soblex}. This comparison shows that our proposed algorithms are superior to the Soblex method, both in terms of robustness in finding the tightest bounds and in computational efficiency. Interestingly, from a channel coding/decoding perspective, optimizing the lower bound is related to increasing the achievable mismatched information rate, i.e., the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel, and not to the original channel.