Performance of binary block codes at low signal-to-noise ratios

Creators: Chao, Chi-Chao; McEliece, Robert J.; Swanson, Laif; Rodemich, Eugene R.

Abstract

The performance of general binary block codes on an unquantized additive white Gaussian noise (AWGN) channel at low signal-to-noise ratios is considered. Expressions are derived for both the block error and the bit error probabilities near the point where the bit signal-to-noise ratio is zero. These expressions depend on the global geometric structure of the code, although the minimum distance still seems to play a crucial role. Examples of codes such as orthogonal codes, biorthogonal codes, the (24,12) extended Golay code, and the (15,6) expurgated BCH code are discussed. The asymptotic coding gain at low signal-to-noise ratios is also studied.

Additional Information

© Copyright 1992 IEEE. Reprinted with permission Manuscript received November 12, 1990; revised February 25, 1992. The contributions of L. Swanson and E. Rodemich, and part of the contribution of R. McEliece, were done at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The contribution of C. Chao while he was a doctoral student at Caltech, and part of the contribution of R. McEliece, were supported by the Air Force Office of Scientific Research under Grant No. AFOSR-91-0037. This work was presented in part at the 1988 IEEE International Symposium on Information Theory, Kobe, Japan, June 1988 and in part at the 1990 IEEE International Symposium on Information Theory, San Diego, California, Jan. 14-19, 1990.

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