An Improved Bound on the List Error Probability and List Distance Properties

List decoding of binary block codes for the additive white Gaussian noise (AWGN) channel is considered. The output of a list decoder is a list of the most likely codewords, that is, the signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples.