On the Throughput of Channels that Wear Out

TL;DR

This paper analyzes the maximum transmission volume over channels that degrade and fail after a certain damage threshold, providing bounds and optimization methods for finite blocklength codes.

Contribution

It introduces bounds on throughput for channels that wear out and develops a dynamic programming approach for optimizing finite blocklength codes.

Findings

Finite blocklength codes outperform single block codes for streaming sources.

Achievability and converse bounds on throughput are established.

Recursive formulation enables efficient optimization of transmission volume.

Abstract

This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. Constant composition codes are adopted to obtain an achievability bound and the left-concave right-convex inequality is then refined to obtain a converse bound on the log-volume throughput for channels that wear out. Since infinite blocklength codes will always wear out the channel for any finite threshold of failure and therefore cannot convey information at positive rates, we analyze the performance of finite blocklength codes to determine the maximum expected transmission volume at a given level of average error probability. We show that this maximization problem has a recursive form and can be solved by dynamic programming. Numerical results demonstrate that a sequence of block codes is preferred to a single block code for streaming sources.