Convolutional codes

Abstract

The minimum distance of a code is an important measure of robustness of the code since it provides a means to assess its capability to protect data from errors. Several types of distance can be defined for convolutional codes. Column distances have important characterizations in terms of the generator matrices of the code, but also in terms of its parity check matrices if the code is noncatastrophic. The chapter presents the most important known constructions for maximum distance separable convolutional codes. There are natural connections to automata theory and systems theory, and this was first recognized by J. L. Massey and M. K. Sain in 1967. These connections have always been fruitful in the development of the theory on convolutional codes; the reader might also consult the survey. The chapter also presents decoding techniques for convolutional codes. It describes the decoding of convolutional codes over the erasure channel, where simple linear algebra techniques are applied.