Research

Rolf Johannesson, Professor emeritus

Our research in coding theory focuses on fundamental problems and covers, e.g., structural properties of convolutional encoders, various decoding algorithms, concatenated convolutional codes, searching for good convolutional codes, tailbiting codes, codes on graphs.

Codes on graphs and graphs on codes

This project is devoted to error-correcting codes over graphs. Such codes have recently drawn strong attention from researchers since they are very interesting from a theoretical point of view and very promising from an applicational point of view. We will essentially broaden this field to block codes with convolutional constituent codes. Very preliminary results show that we can obtain powerful codes of rather low complexity with such constructions. Analytical and numerical methods for estimating distance properties and encoding/decoding complexities will be developed. Of particular interest are algorithms for encoding and decoding. They will be analyzed both analytically and by simulations. Our preliminary investigations show that starting from various tailbiting codes we can obtain optimal graphs with, for example, large girth. Such a graph construction method could have an impact far outside the coding field. The much celebrated Turbo-codes performs close to the Shannon limit, but they suffer from an error floor problem since they have relatively poor distance properties. This is an example of an important problem that could be eliminated with the introduction of codes over graphs. Hence, these codes are strong candidates for future standards in various communication systems.