Towards the maximum-likelihood decoding of long convolutional codes

Abstract

Minimum distance decoding of convolutional codes has generally been considered impractical for other then relatively short constraint length codes, because of the exponential growth in complexity with increasing constraint length. The minimum distance decoding algorithm proposed in the paper, however, uses a sequential decoding approach to avoid an exponential growth in complexity with increasing constraint length, and also utilises the distance and structural properties of convolutional codes to considerably reduce the amount of tree searching needed to find the minimum distance path. In this way the algorithm achieves a complexity that does not grow exponentially with increasing constraint length, and is efficient for both long and short constraint length codes. The algorithm consists of two main processes. Firstly, a direct mapping scheme which automatically finds the minimum distance path in a single mapping operation, is used to eliminate the need fcr all short back-up tree searches. Secondly, when a longer back-up search is required, an efficient tree searching scheme is used to minimise the required search effort. By extending the approach used in the paper to the effective utilisation of soft-decision decoding, the algorithm offers the possibility of maximum-likelihood decoding long convolutional codes.