Error Rates of Capacity-Achieving Codes Are Convex
Abstract
Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also includes coding under maximum-likelihood decoding. Under this generic setting, the pairwise probability of error and bit error rate are shown to be convex functions of the SNR and noise power in the high SNR/low noise regime with explicitly-determined boundary. Any code, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates.
Additional Information
© 2010 Crown.Attached Files
Published - 05513337.pdf
Submitted - 1004.2683.pdf
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Additional details
- Eprint ID
- 49528
- Resolver ID
- CaltechAUTHORS:20140910-094918979
- Created
-
2014-09-10Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field
- Series Name
- IEEE International Symposium on Information Theory