On the undetected error probability for shortened hamming codes on channels with memory

Abstract

In this contribution, the probability of undetected errors on channels with memory is determined. Different error detection strategies (e.g. shortened hamming codes), which have been adopted as international standards, were analyzed. A setup is presented, which is based on a classification of error patterns in blocks by error-length and errorweight. This approach is used to determine the probability of an error pattern being a valid codeword and consequently not detectable. For these investigations a digital channel model, whose characteristics were found by analyzing real shortwave channel connections, was used. As a result of the investigation it is shown, that generator polynomials of the same code rate on channels with memory are the more efficiently the more equidistantly the exponents in the generator polynomial are distributed.