On the decoder error probability of linear codes

Abstract

By using coding and combinatorial techniques, an approximate formula for the weight distribution of decodable words of most linear block codes is evaluated. This formula is then used to give an approximate expression for the decoder error probability P(sub E)(u) of linear block codes, given that an error pattern of weight u has occurred. It is shown that P(sub E)(u) approaches the constant Q as u gets large, where Q is the probability that a completely random error pattern will cause decoder error.