Evaluation of the Undetected Error Probability of Single Parity-Check Product Codes

In this paper, an expression for the undetected error probability (P\epsilon) of single parity-check product (SPCP) codes used for error detection over a binary symmetric channel is derived. It is shown that square SPCP codes need not obey a certain commonly used bound. Approximate expressions for the maximum (P\epsilon) and the corresponding maximizing e are given.