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 codes
C
and
D
for error correction and detection, respectively. It examines the error detection performance of code
D
to determine how the probability of undetected error depends on the choice of
C
and
D
. A comparison is made of the probability of undetected error achievable by code
D
with and without error correction, respectively. Asymptotic bounds for low bit error rates are developed which provide criteria to be considered when choosing codes
C
and
D
.