Research On Concatenated Codes For Synchronization Errors

Synchronization errors exist widely in many kinds of communication systems. This kind of error with memory will cause severe error propagation. Traditional error correction coding scheme can't correct the errors. Concatenated code scheme in which an inner code is used to infer the position of insertion/deletion errors and outer code corrects errors caused by substitutions and misidentified synchronization errors can effectively correct multiple insertions, deletions and substitutions, but has high decoding complexity. The reverse concatenated watermark codes which change the structure of encoder in concatenated watermark codes can reduce the decoding complexity. The scheme avoids the computation of the sparse code word likelihood ratio in inner decoder, but leads to the loss of performance. Therefore, this paper designs a iterative decoding algorithm for reverse concatenated watermark codes. The scheme can improve the performance of reverse concatenated watermark codes with little increaing in decoding complexity.To be specific, a hard decision iterative decoding algorithm between the internal decoder and the external decoder is proposed for improving the performance of reverse concatenated watermark codes in which the estimated codeword from the outer decoder is fed back to the inner decoder by using the special structure of the inner decoder and the outer decoder. The inner decoder uses the information to resynchronize. Simulation results show that the scheme can make the inner decoder identify the position of synchronization error more accuratly, which improves the performance of reverse concatenated watermark codes.Furthermore, the complexity of the iterative reverse concatenated watermark codes is analyzed and compared with original watermark codes, reverse concatenated watermark codes in this paper. The number of addition, multiplication, index and logarithmic in the various steps required by the three decoders are showed The analysis shows the iterative reverse concatenated watermark codes can realize good compromise between performance and complexity within a certain number of iterations. The optimal overall number of iterations can be determined by the simulation.To sum up, this paper presents an iterative reverse concatenated scheme which improves the performance of the system at the cost of little complexity. Then the complexity of decoders in the three schemes is analyzed, which can explain the relationship of the iterative number with complexity and performance.