An Algebraic Syndrome Decoding Technique for Certain Convolutional Codes

Abstract

Abstract : In this final report, some of the same machinery developed in an earlier report for syndrome decoding is shown to provide a basis for what is called algebraic syndrome decoding of convolutional codes. Actually, algebraic syndrome decoders were developed quite early in a heuristic manner for certain simple convolutional codes. In particular, syndrome decoders in the form of feed-back decoders were developed for the one error-correcting Wyner-Ash convolutional code. However, the generalization to algebraically constructed syndrome decoders other than feed-back and majority-logic decoders seems to have been largely ignored. In order to demonstrate the general nature of algebraic syndrome decoding, some definitions and terminology are now in order.