1Extremes of Error Exponents

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