Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels

TL;DR

This paper develops new upper bounds for the capacity of noisy runlength constrained channels using the dual capacity method, providing tighter estimates than previous bounds for various channel types.

Contribution

It introduces a dual capacity approach with Markov test distributions satisfying KKT conditions, yielding simplified and improved upper bounds for multiple channel models.

Findings

Bounds are very close to achievable rates.

Bounds improve upon previous feedback-based bounds.

Simplified bounds for BEC, BSC, and AWGN channels.

Abstract

Binary-input memoryless channels with a runlength constrained input are considered. Upper bounds to the capacity of such noisy runlength constrained channels are derived using the dual capacity method with Markov test distributions satisfying the Karush-Kuhn-Tucker (KKT) conditions for the capacity-achieving output distribution. Simplified algebraic characterizations of the bounds are presented for the binary erasure channel (BEC) and the binary symmetric channel (BSC). These upper bounds are very close to achievable rates, and improve upon previously known feedback-based bounds for a large range of channel parameters. For the binary-input Additive White Gaussian Noise (AWGN) channel, the upper bound is simplified to a small-scale numerical optimization problem. These results provide some of the simplest upper bounds for an open capacity problem that has theoretical and practical relevance.