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One statistical model that has been proposed for the generation of errors in telephone circuits consists of errors with successive inter-arrival times drawn independently from a Pareto distribution, resulting in errors that tend to occur in bursts. These error statistics are applied to a class of burst correcting codes due to Hagelbarger, with particular attention to codes capable of correcting very long error bursts. For such codes, asymptotic expressions are derived for the expected number of output errors per data digit error and also the expected number of false corrections per data digit error. These expressions are what one might intuitively expect, indicating that the results obtained here can perhaps be extended to other codes by simple intuitive reasoning.
Date of Publication: Oct 1965