Sequential decoding

Sequential decoding is a limited memory technique for decoding tree codes. Sequential decoding is mainly used is as an approximate decoding algorithm for long constraint-length convolutional codes. This approach may not be as accurate as the Viterbi algorithm but can save a substantial amount of computer memory.

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

There is a range of sequential decoding approaches based on choice of metric and algorithm. Metrics include:

Algorithms include:

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. This metric is optimal given no other constraints (e.g. memory).

For a binary symmetric channel (with error probability ${\displaystyle p}$) the Fano metric can be derived via Bayes theorem. We are interested in following the most likely path ${\displaystyle P_{i}}$ given an explored state of the tree ${\displaystyle X}$ and a received sequence ${\displaystyle {\mathbf {r} }}$. Using the language of probability and Bayes theorem we want to choose the maximum over ${\displaystyle i}$ of:

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