A Simple Derivation of Burnashev´s Reliability Function

Feedback coupled with variable-length codes can substantially increase the reliability of a discrete memoryless channel (DMC). Burnashev, in a remarkable paper published in 1976, derived an asymptotically achievable lower bound to the average blocklength needed for a system that communicates at a specified rate and achieves a given error probability. We offer an alternative proof of the lower bound. Our proof is simpler than the original, and clarifies the roles of the quantites that appear in the bound by relating one to uncertainty reduction and the other to binary hypothesis testing. In addition, our derivation of the lower bound closely parallels a derivation of an upper bound by Yamamoto and Itoh.