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.

This work was supported in part by the International Joint Project 2008/R2 of the Royal Society, in part by the Australian Research Council under ARC Discovery Grant DP0986089, and in part by the European Research Council under ERC grant agreement 259663. A. Martinez was supported in part by the Ministry of Economy and Competitiveness (Spain) under Grant RYC-2011-08150 and in part by the European Union’s 7th Framework Programme (PEOPLE-2011-CIG) under Grant 303633.