Expurgated bounds, bhattacharyya distance, and rate distortion functions

We examine new low rate error upper bounds for M equally likely code words used over discrete input channels. When optimized over the code ensemble probability distribution, these bounds coincide with the optimized expurgated bounds and the error exponents satisfy rate distortion equations for natural Bhattacharyya distances. Proofs for these error bounds do not require expurgation of code words, and for certain “modular” channels including all binary input memoryless channels, the bounds extend to convolutional codes