Pseudo-codeword Landscape

作者: Michael Chertkov , Mikhail Stepanov

DOI: 10.1109/ISIT.2007.4557442

关键词:

摘要: We discuss the performance of low-density-parity-check (LDPC) codes decoded by means linear programming (LP) at moderate and large signal-to-noise-ratios (SNR). Utilizing a combination previously introduced pseudo-codeword-search method new "dendro" trick, which allows us to reduce complexity LP decoding, we analyze dependence frame-error-rate (FER) on SNR. Under maximum-a-posteriori (MAP) decoding dendro-code, having only checks with connectivity degree three, performs identically its original code high-connectivity checks. For number popular LDPC performing over additive-white-Gaussian-noise (AWGN) channel found that either an error-floor sets relatively low SNR, or otherwise transient asymptote, characterized faster decay FER SNR increase, precedes asymptote. explain these regimes in terms pseudo-codeword spectra codes.

参考文章(21)
Niclas Wiberg, Codes and Decoding on General Graphs Ph. D. dissertation, Linkoping Univ., Sweden. ,(1996)
R Michael Tanner, Deepak Sridhara, Tom Fuja, None, A Class of Group-Structured LDPC Codes ,(2001)
Tom Richardson, Error Floors of LDPC Codes ,(2003)
Ralf Koetter, Pascal O. Vontobel, Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes arXiv: Information Theory. ,(2005)
G. David Forney, Ralf Koetter, Frank R. Kschischang, Alex Reznik, On the Effective Weights of Pseudocodewords for Codes Defined on Graphs with Cycles Institute for Mathematics and Its Applications. ,vol. 123, pp. 101- 112 ,(2001) , 10.1007/978-1-4613-0165-3_5
Michael Chertkov, Vladimir Y. Chernyak, Loop Calculus Helps to Improve Belief Propagation and Linear Programming Decodings of Low-Density-Parity-Check Codes allerton conference on communication, control, and computing. ,(2006)
Ralf Koetter, Pascal O. Vontobel, Towards Low-Complexity Linear-Programming Decoding Turbo Codes&Related Topics; 6th International ITG-Conference on Source and Channel Coding (TURBOCODING), 2006 4th International Symposium on. pp. 1- 9 ,(2006)
M. G. Stepanov, V. Chernyak, M. Chertkov, B. Vasic, Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach Physical Review Letters. ,vol. 95, pp. 228701- ,(2005) , 10.1103/PHYSREVLETT.95.228701
CE Shennon, Warren Weaver, A mathematical theory of communication Bell System Technical Journal. ,vol. 27, pp. 379- 423 ,(1948) , 10.1002/J.1538-7305.1948.TB01338.X
David J.C. MacKay, Michael S. Postol, Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes Electronic Notes in Theoretical Computer Science. ,vol. 74, pp. 97- 104 ,(2003) , 10.1016/S1571-0661(04)80768-0