Efficiently Computable Converses for Finite-Blocklength Communication

TL;DR

This paper introduces a computationally efficient method to derive finite-blocklength converses for discrete memoryless channels, enabling accurate bounds for various channel types using dynamic programming and Fourier methods.

Contribution

It develops a general finite-blocklength converse framework expressed as a stochastic control problem, applicable to arbitrary DMCs and solvable efficiently.

Findings

Comparable accuracy to existing bounds for BSC and BEC

Applicable to channels like BAC and quantized amplitude-constrained AWGN

Efficient computation via dynamic programming and Fourier methods

Abstract

This paper presents a method for computing a finite-blocklength converse for the rate of fixed-length codes with feedback used on discrete memoryless channels (DMCs). The new converse is expressed in terms of a stochastic control problem whose solution can be efficiently computed using dynamic programming and Fourier methods. For channels such as the binary symmetric channel (BSC) and binary erasure channel (BEC), the accuracy of the proposed converse is similar to that of existing special-purpose converse bounds, but the new converse technique can be applied to arbitrary DMCs. We provide example applications of the new converse technique to the binary asymmetric channel (BAC) and the quantized amplitude-constrained AWGN channel.