Correct Undetected Errors with Context List Decoding in ARQ Error-Control Systems

Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, sub-optimal source coding and joint source-channel coding, constrains among successive codewords may be utilized to improve decoding performance. In this paper, list decoding is used to correct the undetected errors. The benefit proportion of the correction is obviously improved especially on Hamming codes and Reed-Muller codes, which achieves about $40\%$ in some cases. But this improvement is significant only after the selection of final codewords from the lists based on the constrains among the successive transmitted codewords. The selection algorithm is investigated here to complete the list decoding program in the application of Markov context model. The performance of the algorithm is analysed and a lower bound of the correctly selected probability is derived to determine the proper context length.

[1]  Jehoshua Bruck,et al.  Enhanced Error Correction via Language Processing , 2015 .

[2]  Tsachy Weissman,et al.  Universal discrete denoising: known channel , 2003, IEEE Transactions on Information Theory.

[3]  Peter Elias,et al.  List decoding for noisy channels , 1957 .

[4]  Fady Alajaji,et al.  Joint source-channel turbo coding for binary Markov sources , 2006, IEEE Transactions on Wireless Communications.

[5]  Daniel J. Costello,et al.  Error Control Coding, Second Edition , 2004 .

[6]  Torleiv Kløve,et al.  Codes for Error Detection , 2007, Series on Coding Theory and Cryptology.

[7]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[8]  Venkatesan Guruswami,et al.  List decoding of error correcting codes , 2001 .

[9]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[10]  Hatem Boujemaa.  Mobile Networks Performance of truncated hybrid ARQ schemes with noisy feedback for DS-CDMA systems , 2010, Eur. Trans. Telecommun..

[11]  Anxiao Jiang,et al.  Error correction through language processing , 2015, 2015 IEEE Information Theory Workshop (ITW).

[12]  G. David Forney,et al.  Concatenated codes , 2009, Scholarpedia.

[13]  Vladimir M. Blinovsky,et al.  List decoding , 1992, Discret. Math..