Extremes of Error Exponents

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.