Extremes of Error Exponents

TL;DR

This paper characterizes the feasible range of error exponents for binary-input symmetric channels of fixed capacity, identifying the extremal channels and extending the results to related quantities like cutoff rate and channel dispersion.

Contribution

It establishes the extremal values of error exponents for symmetric channels and provides a proof technique applicable to related information-theoretic quantities.

Findings

Binary symmetric channel attains the maximum error exponent.

Binary erasure channel attains the minimum error exponent.

Results extend to cutoff rate, Bhattacharyya parameter, and dispersion.

Abstract

This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel. The proof technique also provides analogous extremes for other quantities related to Gallager's $E_0$ function, such as the cutoff rate, the Bhattacharyya parameter, and the channel dispersion.