Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels

LIU Jia; MA Xiao; BAI Baoming

Article Contents

Article Navigation > Chinese Journal of Electronics > 2014 > 23(3): 458-463

LIU Jia, MA Xiao, BAI Baoming. Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels[J]. Chinese Journal of Electronics, 2014, 23(3): 458-463.

Citation:

LIU Jia, MA Xiao, BAI Baoming. Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels[J]. Chinese Journal of Electronics, 2014, 23(3): 458-463.

LIU Jia, MA Xiao, BAI Baoming. Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels[J]. Chinese Journal of Electronics, 2014, 23(3): 458-463.

Citation:

LIU Jia, MA Xiao, BAI Baoming. Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels[J]. Chinese Journal of Electronics, 2014, 23(3): 458-463.

PDF( 293 KB)

Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels

1.
College of Information Science and Technology, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China;
2.
Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou 510006, China;
3.
State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China

Funds: This work is supported by the National Basic Research Program of China(973 Program) (No.2012CB316100), the National Natural Science Foundation of China (No.61172082), the Science and Technology Planning Project of Guangdong Province (No.2011B020313022) and the Soft Science Project of Guangdong Province (No.2010B070300096).

More Information

Corresponding author: MA Xiao
Received Date: 2013-01-01
Rev Recd Date: 2013-06-01
Publish Date: 2014-07-05

Abstract

Abstract

In this paper, simple upper bounds are derived on the frame and bit error probabilities of binary linear codes over Additive white Gaussian noise (AWGN) channels. The conventional union bound is first truncated and then amended, which can be justified by invoking Gallager's first bounding technique (GFBT). Different from most other works, the "good region" is specified by a suboptimal list decoding algorithm. The error probability caused by the good region can be upper-bounded by the union bounds using pair-wise error probability and tripletwise error probability, which can be further tightened by exploiting the independence between the error events and certain components of the receiving signal vector. The proposed bounds are simple since they involve only the Q-function. The proposed bounds improve our recently proposed bounds. Numerical results are also presented to compare the proposed bounds with the Divsalar bound, which is a simple tight upper bound with closed-form, and the Tangential-sphere bound (TSB), which is considered as one of the tightest upper bounds.

FullText(HTML)

References(20)

References

S. Shamai, I. Sason, "Variations on the Gallager bounds, connections, and applications", IEEE Transactions on Information Theory, Vol.48, No.3, pp.3029-3051, 2002.

I. Sason, S. Shamai, "Performance analysis of linear codes under maximum-likelihood decoding: A tutorial", Foundations and Trends in Communications and Information Theory, Vol.3, No.1-2, pp.1-225, 2006.

E. R. Berlekamp, "The technology of error correction codes", Proceedings of the IEEE, Vol.68, No.5, pp.564-593, 1980.

T. Kasami, T. Fujiwara, T. Takata, S. Lin, "Evaluation of the block error probability of block modulation codes by the maximum-likelihood decoding for an AWGN channel", Proc. of 1993 IEEE International Symposium on Information Theory, San Antonio, Texas, pp.68, 1993.

H. Herzberg, G. Poltyrev, "Techniques of bounding the probability of decoding error for block coded modulation structures", IEEE Transactions on Information Theory, Vol.40, No.3, pp.903-911, 1994.

G. Poltyrev, "Bounds on the decoding error probability of binary linear codes via their spectra", IEEE Transactions on Information Theory, Vol.40, No.4, pp.1284-1292, 1994.

D. Divsalar, "A simple tight bound on error probability of block codes with application to turbo codes", TMO Progress Report, JPL, pp.42-139, 1999.

I. Sason, S. Shamai, "Improved upper bounds on the ML decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum", IEEE Transactions on Information Theory, Vol.46, No.1, pp.24-47, 2000.

J. Zangl, R. Herzog, "Improved tangential sphere bound on the bit error probability of concatenated codes", IEEE Journal on Selected Areas in Communications, Vol.19, No.5, pp.825-830, 2001.

D. Divsalar, E. Biglieri, "Upper bounds to error probabilities of coded systems beyond the cutoff rate", IEEE Transactions on Communications, Vol.51, No.12, pp.2011-2018, 2003.

S. Yousefi, A. K. Khandani, "Generalized tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN interference", IEEE Transactions on Information Theory, Vol.50, No.11, pp.2810-2815, 2004.

S. Yousefi, A. K. Khandani, "A new upper bound on the ML decoding error probability of linear binary block codes in AWGN interference', IEEE Transactions on Information Theory, Vol.50, No.12, pp.3026-3036, 2004.

S. Yousefi, "Gallager first bounding technique for the performance evaluation of maximum likelihood decoded linear binary block codes", Communications, IEE Proceedings, Vol.153, No.3, pp.317-332, 2006.

A. Mehrabian, S. Yousefi, "Improved tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN and block fading channels", Communications, IEE Proceedings, Vol.153, No.6, pp.885-893, 2006.

X. Ma, C. Li, B. Bai, "Maximum likelihood decoding analysis of LT codes over AWGN channels", Proc. of the 6th International Symposium on Turbo Codes and Iterative Information Processing, Brest, France, pp.285-288, 2010.

X. Ma, J. Liu, B. Bai, "New techniques for upper-bounding the MLD performance of binary linear codes", Proc. of 2011 IEEE International Symposium on Information Theory, Saint-Petersburg, Russian Federation, pp.2910-2914, 2011.

X. Ma, J. Liu, B. Bai, "New techniques for upper-bounding the ML decoding performance of binary linear codes", IEEE Transactions on Communications, Vol.61, No.3, pp.842-851, 2013.

M. Twitto, I. Sason, "On the error exponents of improved tangential sphere bounds", IEEE Transactions on Information Theory, Vol.53, No.3, pp.1196-1210, 2007.

M. Twitto, "Tightened upper bounds on the ML decoding error probability of binary linear block codes and applications", Master thesis, Technion-Israel Institute of Technology, Haifa, Israel, 2006.

A. M. Barg, I. I. Dumer, "On computing the weight spectrum of cyclic codes", IEEE Transactions on Information Theory, Vol.38, No.4, pp.1382-1386, 1992.

Relative Articles

Supplements(0)

Cited By

Proportional views