Error-trellis syndrome decoding techniques for convolutional codes

In the paper, a new error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is specialised then to the entire class of systematic convolutional codes. Finally, this algorithm is applied to the high-rate Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a 3/4 rate code, is treated in the paper. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decoding is than, say, Viterbi decoding would be if applied to the same problem. For standard Viterbi decoding, 64 states would be required, whereas in the example only seven states are needed. Also, within the seven states required for decoding, many less transitions are needed between the states.