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 E₀ function, such as the cutoff rate, the Bhattacharyya parameter, and the channel dispersion.