New Syndrome Decoding Techniques for Convolutional Codes over GF(q).

摘要

This is a final report on a one-year study of techniques for improving the encoding and decoding of error-correcting codes. For the previous three quarters emphasis was given to methods for making the encoding and decoding of Reed-Solomon codes more efficient. These methods included the possibility of using Winograd's fast transforms for transform encoding and decoding of Reed-Solomon codes, and studies for simplifying the arithmetic of the Galois fields used in error-correcting codes. The latter topic led to an investigation of the architecture needed to realize Berlekamp's new bit-serial multiplier. During the last quarter a new syndrome decoding algorithm for convolutional codes (CC) was conceived by the author. In this report this idea is extended to a greater generality.