The Detection of Errors After Error-Correction Decoding

In data transmission and storage systems, combined error correction and detection procedures are often used to provide high reliability. This paper considers the use of separate concatenated codesCandDfor error correction and detection, respectively. It examines the error detection performance of codeDto determine how the probability of undetected error depends on the choice ofCandD. A comparison is made of the probability of undetected error achievable by codeDwith and without error correction, respectively. Asymptotic bounds for low bit error rates are developed which provide criteria to be considered when choosing codesCandD.