Soft Syndrome Decoding of Binary Convolutional Codes

We present an efficient recursive algorithm for accomplishing maximum likelihood (ML) soft syndrome decoding of binary convolutional codes. The algorithm consists of signal–by–signal hard decoding followed by a search for the most likely error sequence. The number of error sequences to be considered is substantially larger than in hard decoding, since the metric applied to the errorbits is the magnitude of the log likelihood ratio rather than the Hamming weight. An error–trellis (alternatively, a decoding table) is employed for describing the recursion equations of the decoding procedure. The number of its states is determined by the states indicator, which is a modified version of the constraint length of the check matrix. Methods devised for eliminating error patterns and degenerating error–trellis sections enable accelerated ML decoding. In comparison with the Viterbi algorithm, the syndrome decoding algorithm achieves substantial reduction in the average computational complexity, particularly for moderately noisy channels.