Vector symbol decoding with lists of alternative vector symbol choices and outer convolutional codes

Vector Symbol Decoding (VSD) with list of alternative vector symbol choices is presented as a relatively simple and high performance decoding technique for convolutional outer codes. The convolutional VSD technique has the advantage over the block VSD technique in that most corrections are almost immediate based on observation of only one or a few syndromes. The list decoding also improves the performance and often simplifies the decoding. One main assumption of VSD is that the error symbols are linearly independent, which usually is true for large symbol size. The performance of VSD is compared to the Reed-Solomon code decoding for various types of inner codes and channel conditions. Interleaved Reed-Solomon codes are also considered. The decoding failure probability of VSD is evaluated by both analytically approach to find the upper bound and computer simulation approach to find the exact probability. The upper bound is shown to be extremely close to the simulation result. The decoding failure probability of VSD is considerably lower than the Reed-Solomon code in most cases.