Abstract
Summary form only given, as follows. It is well known that for block codes of a given rate, the larger the minimum distance, the better the code will perform at high signal-to-noise ratios. For some applications, such as deep space communications, the behavior of codes at low signal-to-noise ratios is of concern. In a former paper by Swanson, McEliece, and Chao, an expression was derived for the block error probability of binary block codes on the unquantized additive white Gaussian noise (AWGN) channel near the point where the signal-to-noise ratio is zero. Here a similar expression for the bit-error probability with maximum-likelihood decoding is found. Examples of codes, such as orthogonal codes, bi-orthogonal codes, the (24, 12) extended Golary code, and the (15, 6) expurgated BCH code, are discussed. The asymptotic coding gain on the unquantized AWGN channel at low signal-to-noise ratios is also studied.