Performance of BCH codes with (1 + x)s error detection

The performance is investigated of a combined error correction and detection decoder for BCH codes for which the generator polynomial g(x) has been augmented by a (1 + x)^s term in order to make the informations bits an integral number of bytes. An ARQ retransmission scheme on an additive white Gaussian noise channel is assumed and a comparison with an FEC-only BCH code is given in terms of probability of error against E_b/N₀. It is shown for a BCH (127, 106, 7) code that at high E_b/N₀ the performance improvement is of three orders of magnitude at the cost of a small rate degradation. Goppa codes, whose length is an integral number of bytes, have also been investigated, producing similar results.