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Error rates of capacity-achieving codes are convex.
| Content Provider | CiteSeerX |
|---|---|
| Author | Loyka, Sergey Gagnon, Francois Kostina, Victoria |
| Abstract | 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 explicitlydetermined 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. I. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Error Rate Capacity-achieving Code Convex Bit Error Rate Noise Power High Snr Low Noise Regime Wide-spread Use Hardened Noise Sphere Abstract Motivated Arbitrary Constellation Decision Region Maximum Likelihood Detector Operating Pairwise Probability Bit Mapping Generic Setting High Snr Requirement Convexity Property Capacity-achieving One Maximum-likelihood Decoding Convex Optimization Technique Convex Function Capacity-achieving Code Awgn Channel |
| Content Type | Text |
