An Improved Decoding Algorithm for the Davey-MacKay Construction

The Deletion-Insertion Correcting Code construction proposed by Davey and MacKay consists of an inner code that recovers synchronization and an outer code that provides substitution error protection. The inner code uses low-weight codewords which are added (modulo two) to a pilot sequence. The receiver is able to synchronise on the pilot sequence in spite of the changes introduced by the added codeword. The original bit-level formulation of the inner decoder assumes that all bits in the sparse codebook are identically and independently distributed. Not only is this assumption inaccurate, but it also prevents the use of soft a- priori input to the decoder. We propose an alternative symbol-level inner decoding algorithm that takes the actual codebook into account. Simulation results show that the proposed algorithm has an improved performance with only a small penalty in complexity, and it allows other improvements using inner codes with larger minimum distance.