Improved union bound on linear codes for the input-binary AWGN channel, with applications to turbo codes

Abstract

While improved bounds have been central to proofs of the coding theorem and the tightness of the random coding bound for rates near capacity, most results for specific codes, both block and convolutional, have been based on the simple union bound. We present an improved bound for the input-binary AWGN channel in terms of the weights of the code-words of a linear block code.