Soft Decision Fano Decoding of Block Codes Over Discrete Memoryless Channel Using Tree Diagram

A novel low complexity soft decision technique which allows the decoding of block codes with tree structure is proposed. These codes are shown to have a convenient tree structure that allows Fano decoding techniques to be used to decode them. The Fano algorithm searches through the tree structure of the block code for a path which has the optimal value of the Fano metric function. When a new candidate codeword is found, an optimality check is performed on it by using the threshold. If checked successfully, the candidate codeword is the most likely codeword and the search stops. The basic idea of this approach is to achieve a good error performance progressively in a minimum number of steps. For each decoding step, the error performance is tightly bounded and the decoding is terminated at the stage where either optimum or near optimum error performance is achieved. As a result, more flexibility in the trade off between performance and decoding complexity is provided. Some examples of the tree construction and the soft decision Fano decoding procedure are discussed.