A Tighter Bhattacharyya Bound for Decoding Error Probability

The Bhattacharyya bound has been widely used to upper bound the pair-wise probability of error when transmitting over a noisy channel. However, the bound as it appears in most textbooks on channel coding can be improved by a factor of 1/2 when applied to the frame error probability. For the particular case of symmetric channels, the pairwise error probability can also be improved by a factor of 1/2. This letter provides a simple proof of these tighter bounds that has the same simplicity as the proof of the standard Bhattacharyya bound currently found in textbooks