An Improved Decoding Algorithm for the Davey-MacKay Construction

Abstract

Abstract-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.

Forensic data hiding optimized for JPEG 2000

“…While this assumption clearly gives some mismatch at the receiver, a reliable estimator has still not been developed for this channel. Unlike the simulations published in [9], we do not put a limit on the burst length I of insertions, resulting in a small improvement on decoding performance. When applied to the output of the watermark decoder, we have observed that the best response is obtained if the received sequence is truncated to 3 000 bits before decoding.…”

“…2) Outer Codes: As outer codes, we use a parallel concatenation of non-binary constituent codes, as presented in [9]. The constituent code is defined over an unterminated trellis, and an S-random interleaver [11] of block size K = 75 and spread S = 7.…”

“…Conventional error-correcting codes, assuming a substitution-only channel, are unusable under these conditions and very few practical codes exist for IDS channels. In this work, we use an improvement on the Davey-MacKay (DM) construction, originally presented in [8]; the improvements used here are those presented in [9], [10].…”

“…This code has been chosen because it is known to give good performance in channels with a high rate of insertions and deletions. We decode using the symbol-level decoder presented in [9].…”

Codebook and marker sequence design for synchronization-correcting codes

“…An optimal symbol-level decoding algorithm was presented in [8] for the DM inner code; at the same decoding complexity, the new decoder takes sums over each possible sparse symbol when determining synchronization. This has two principal advantages: a) it allows the decoder to make use of a priori information for the sparsely-represented symbols, and b) it allows the use of non-sparse representations of the message.…”