Sequential decoding

Sequential decoding is a limited memory technique for decoding tree codes. There is a range of sequential decoding approaches based on choice of metric and algorithm.

Sequential decoding is mainly use is as an approximate decoding algorithm for long constraint-length convolutional codes. This approach may not be as accurate as the Viterbi algorithm but save substantial amounts of computer memory.

Sequential decoding explores the tree code in such a way to try and minimise the computational cost and memory requirements to store the tree.

Fano metric

Given a partially explored tree (represented by a set of nodes which are limit of exploration), we would like to know the best node from which to explore further. The Fano metric (named after Robert Fano) allows one to calculate from which is the best node to explore further.

Algorithms

The simplest algorithm to describe is the "stack algorithm" in which the best $N$ paths found so far are stored. Sequential decoding may introduce an additional error above Viterbi decoding when the correct path has $N$ or more more highly scoring paths above it; at this point the best path will drop off the stack and be no longer considered.

The famous Fano algorithm (named after Robert Fano) has a very low memory requirement and hence is suited to hardware implementations. This algorithm explores backwards and forward from a single point on the tree.

References

• John Wozencraft and B. Reiffen, Sequential decoding, ISBN 0262230062
• Rolf Johannsesson and Kamil Sh. Zigangirov, Funamentals of convolutional coding (chapter 6), ISBN 0470276835