Abstract
In ref. [3] we introduced a simplified ensemble of serially concatenated “turbo-like” codes which we called repeat-accumulate, or RA codes. These codes are very easy to decode using an iterative decoding algorithm derived from belief propagation on the appropriate Tanner graph, yet their performance is scarcely inferior to that of full-fledged turbo codes. In this paper, we prove that on the AWGN channel, RA codes have the potential for achieving channel capacity. That is, as the rate of the RA code approaches zero, the average required bit Eb/N0 for arbitrarily small error probability with maximum-likelihood decoding approaches log 2, which is the Shannon limit. In view of the extreme simplicity of RA codes, this result is both surprising and suggestive.
This work was supported by NSF grant no. CCR-9804793, and grants from Sony and Qualcomm.
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References
C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo codes,” Proc. 1993 IEEE International Conference on Communications, Geneva, Switzerland (May 1993), pp. 1064–1070.
D. Divsalar, “A simple tight bound on error probability of block codes with application to turbo codes,” in preparation.
D. Divsalar, H. Jin, and R. McEliece. “Coding Theorems for ‘Turbo-Like’ Codes.” Proc. 1998 Allerton Conf., pp. 201–210.
D. Divsalar, S. Dolinar, H. Jin, and R. McEliece, “AWGN Coding Theorems from Ensemble Weight Enumerators,” in preparation.
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© 1999 Springer-Verlag Berlin Heidelberg
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Jin, H., McEliece, R.J. (1999). RA Codes Achieve AWGN Channel Capacity. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_2
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DOI: https://doi.org/10.1007/3-540-46796-3_2
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