arXiv subjects

Jonathan Scarlett

Publications and source records attributed to Jonathan Scarlett.

118 records · Page 7Linked to original sources

arXiv2015

A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csiszár-Körner, 1981), thus providing a counter-example to a previously reported converse result (Balakirsky, 1995). Both numerical evaluations and theoretical results are used in establishing this claim.

cs.IT↗

arXiv2015

Second-Order Asymptotics for the Discrete Memoryless MAC with Degraded Message Sets

This paper studies the second-order asymptotics of the discrete memoryless multiple-access channel with degraded message sets. For a fixed average error probability $ε\in(0,1)$ and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that point for codes that have asymptotic error probability no larger than $ε$, thus complementing an analogous result given previously for the Gaussian setting.

cs.IT↗

arXiv2014

Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's combinatorial central limit theorem, an inner bound on the set of locally achievable second-order coding rates is given for each point on the boundary of the capacity region. It is shown that the inner bound for constant-composition random coding includes that recovered by i.i.d. random coding, and that the inclusion may be strict. The inner bound is extended to the Gaussian multiple-access channel via an increasingly fine quantization of the inputs.

cs.IT↗

arXiv2014

Sparsistency of $\ell_1$-Regularized $M$-Estimators

We consider the model selection consistency or sparsistency of a broad set of $\ell_1$-regularized $M$-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSSC) on the loss function. We provide a general result giving deterministic sufficient conditions for sparsistency in terms of the regularization parameter, ambient dimension, sparsity level, and number of measurements. We show that several important statistical models have $M$-estimators that indeed satisfy the LSSC, and as a result, the sparsistency guarantees for the corresponding $\ell_1$-regularized $M$-estimators can be derived as simple applications of our main theorem.

math.ST↗

arXiv2014

Expurgated Random-Coding Ensembles: Exponents, Refinements and Connections

This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding which extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multi-letter exponent which extends immediately to channels with memory. Finally, a refined analysis expurgated i.i.d. random coding is shown to yield a O\big(\frac{1}{\sqrt{n}}\big) prefactor, thus improving on the standard O(1) prefactor. Moreover, the implied constant is explicitly characterized.

cs.IT↗

arXiv2014

The Saddlepoint Approximation: Unified Random Coding Asymptotics for Fixed and Varying Rates

This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently. Moreover, it is shown to be asymptotically tight for both fixed and varying rates, unifying existing achievability results in the regimes of error exponents, second-order coding rates, and moderate deviations. For fixed rates, novel exact-asymptotics expressions are specified to within a multiplicative 1+o(1) term. A numerical example is provided for which the approximation is remarkably accurate even at short block lengths.

cs.IT↗

arXiv2014

Mismatched Decoding: Error Exponents, Second-Order Rates and Saddlepoint Approximations

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For i.i.d. random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-order rates and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1+o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.

cs.IT↗

arXiv2013

On the Dispersions of the Gel'fand-Pinsker Channel and Dirty Paper Coding

This paper studies second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and by using a small fraction of the block to transmit the type of the state sequence. For error probabilities less than 1/2, it is shown that the second-order rate improves on an existing one based on i.i.d. random coding. In the Gaussian case (dirty paper coding) with an almost-sure power constraint, an achievability result is obtained used using random coding over the surface of a sphere, and using a small fraction of the block to transmit a quantized description of the state power. It is shown that the second-order asymptotics are identical to the single-user Gaussian channel of the same input power without a state.

cs.IT↗

arXiv2013

A Derivation of the Asymptotic Random-Coding Prefactor

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altuğ and Wagner is given, and the result is extended to the setting of mismatched decoding.

cs.IT↗

arXiv2011

On the Tradeoff Between Multiuser Diversity and Training Overhead in Multiple Access Channels

We consider a single antenna narrowband multiple access channel in which users send training sequences to the base station and scheduling is performed based on minimum mean square error (MMSE) channel estimates. In such a system, there is an inherent tradeoff between training overhead and the amount of multiuser diversity achieved. We analyze a block fading channel with independent Rayleigh distributed channel gains, where the parameters to be optimized are the number of users considered for transmission in each block and the corresponding time and power spent on training by each user. We derive closed form expressions for the optimal parameters in terms K and L, where K is the number of users considered for transmission in each block and L is the block length in symbols. Considering the behavior of the system as L grows large, we optimize K with respect to an approximate expression for the achievable rate, and obtain second order expressions for the resulting parameters in terms of L.

cs.IT↗