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On Convexity of Error Rates in Digital Communications (2013)
| Content Provider | CiteSeerX |
|---|---|
| Author | Loyka, Sergey Kostina, Victoria Gagnon, Francois |
| Description | Convexity properties of error rates of a class of decoders, including the maximum-likelihood/min-distance one as a special case, are studied for arbitrary constellations, bit mapping, and coding. Earlier results obtained for the additive white Gaussian noise channel are extended to a wide class of noise densities, including unimodal and spherically invariant noise. Under these broad conditions, symbol and bit error rates are shown to be convex functions of the signal-to-noise ratio (SNR) in the high-SNR regime with an explicitly determined threshold, which depends only on the constellation dimension-ality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communi-cation systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case. The known high/low-SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general. The high-SNR bound fits closely into the channel coding theorem: all codes, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem), satisfy 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. Convexity prop-erties in signal amplitude and noise power are also investigated. Some applications of the results are discussed. In particular, it is shown that fading is convexity-preserving and is never good in low dimensions under spherically invariant noise, which may also include any linear diversity combining. |
| File Format | |
| Language | English |
| Publisher Date | 2013-01-01 |
| Publisher Institution | AVAILABLE AT HTTP://ARXIV.ORG/ABS/1304.8102). 2013 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY45 |
| Access Restriction | Open |
| Subject Keyword | Arbitrary Constellation Linear Diversity Powerful Tool Signal Amplitude Index Term Bit Error Rate Capacity-achieving Code Noise Density High-snr Bound Convexity Concavity Low Dimension Additive White Gaussian Noise Channel High-snr Requirement Convex Function Decision Region Boundary Signal-to-noise Ratio General Case Known High Low-snr Bound Digital Communication Convexity Prop-erties Bit Mapping Decreasing Nature Bit Error Rate Rigorous Way Invariant Noise Symbol Error Rate Digital Communi-cation System High-snr Regime Wide Class Error Rate Broad Condition Special Case Noise Power Density Maximum-likelihood Min-distance Convexity Concavity Region Noise Power Decision Region Minimum Distance Abstract Convexity Property Convex Optimization Constellation Dimension-ality Unimodal Noise Capacity-achieving One Hardened Noise Sphere |
| Content Type | Text |
| Resource Type | Article |
