On Convexity of Error Rates in Digital Communications

  title={On Convexity of Error Rates in Digital Communications},
  author={Sergey L. Loyka and Victoria Kostina and François Gagnon},
  journal={IEEE Transactions on Information Theory},
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… 

Figures and Tables from this paper

Convexity of error rates in digital communications under non-Gaussian noise
Under broad conditions, symbol error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way.
Universal Bounds on the Derivatives of the Symbol Error Rate for Arbitrary Constellations
  • B. Dulek
  • Computer Science
    IEEE Transactions on Signal Processing
  • 2014
The proposed bounds yield a better characterization of the symbol error rate (SER) for arbitrary two-dimensional constellations over the complete monotonicity property derived recently.
Distributionally Robust Relay Beamforming in Wireless Communications
This work forms a novel distributionally robust beamforming problem, in which the random channel coefficient follows a class of unimodal distribution with known first- and second-order moments, and shows that under mild conditions, the UDR model yields significant beamforming performance improvement over conventional robust models that merely rely on first-and-second- order moments of the channel distribution.
Distributionally Robust Collaborative Beamforming in D2D Relay Networks With Interference Constraints
This paper considers a device-to-device (D2D) network underlying a cellular system wherein the densely deployed D2D user devices can act as wireless relays for a distant transceiver pair and proposes a novel unimodal distributionally robust model to capture the channel uncertainties.
An encryption aware physical layer security system
Numerical results show that the proposed encryption-aware physical layer security system achieves a better power efficiency when compared to the classicalPhysical layer security approaches.


Error rates of capacity-achieving codes are convex
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.
Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications
Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels, and optimization of a unitary-precoded OFDM system.
Log-Concavity Property of the Error Probability With Application to Local Bounds for Wireless Communications
An analytical framework based on the log-concavity property of the EP is proposed which is proved for a wide family of multidimensional modulation formats in the presence of Gaussian disturbances and fading and construct a class of local bounds for the EP that improve known generic bounds in a given region of the SNR and are invertible, as well as easily tractable for further analysis.
Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications
Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied and universal bounds for the SER 1st and 2nd derivatives are obtained.
Bit Error Rate is Convex at High SNR
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
Convexity properties in binary detection problems
  • M. Azizoglu
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1996
The author investigates the convexity properties of error probability in the detection of binary-valued scalar signals corrupted by additive noise. It is shown that the error probability of the
Adaptive minimum bit-error rate equalization for binary signaling
This work proposes a simple stochastic adaptive algorithm that can provide a substantial reduction in BER with no increase in complexity and is compared to the least-mean-square algorithm.
Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial
Upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs and establish the goodness of linear Codes under optimal maximum-likelihood (ML) decoding.
Optimum detection of fading signals in impulsive noise
Results indicate that, for deep fading, the noise marginal distribution does not dramatically affect the error probability, nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions.
BER minimized OFDM systems with channel independent precoders
The BER performance of precoded OFDM systems with zero forcing and minimum mean squared error (MMSE) receivers is analyzed and it is shown that for quadrature phase shift keying (QPSK), there exists a class of optimal precoders that are channel independent.