Syndrome Decoding of Binary Rate-1/2 Convolutional Codes

The classical Viterbi decoder recursively finds the trellis path (code word) closest to the received data. Given the received data, the syndrome decoder first forms a syndrome instead. Having found the syndrome, that only depends on the channel noise, a recursive algorithm like Viterbi's determines the noise sequence of minimum Hamming weight that can he a possible cause of this syndrome. Given the estimate of the noise sequence, one derives an estimate of the original data sequence. The bit error probability of the syndrome decoder is no different from that of the classical Viterbi decoder. However, for short constraint length codes the syndrome decoder can be implemented using a read-only memory (ROM), thus obtaining a considerable saving in hardware. The syndrome decoder has at most
\frac{3}{4}
as many path registers as does the Viterbi decoder. There exist convolutional codes for which the number of path registers can be even further reduced.