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Alfonso Martinez

Publications and source records attributed to Alfonso Martinez.

34 records · Page 2Linked to original sources
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↗
arXiv2014

A Derivation of the Source-Channel Error Exponent using Non-identical Product Distributions

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

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↗
arXiv2012

Extremes of Error Exponents

This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel. The proof technique also provides analogous extremes for other quantities related to Gallager's $E_0$ function, such as the cutoff rate, the Bhattacharyya parameter, and the channel dispersion.

cs.IT↗
arXiv2012

The Capacity Loss of Dense Constellations

We determine the loss in capacity incurred by using signal constellations with a bounded support over general complex-valued additive-noise channels for suitably high signal-to-noise ratio. Our expression for the capacity loss recovers the power loss of 1.53dB for square signal constellations.

cs.IT↗
arXiv2011

Microwave Photonics Parallel Quantum Key Distribution

The incorporation of multiplexing techniques used in Microwave Photonics to Quantum Key Distribution (QKD) systems bring important advantages enabling the simultaneous and parallel delivery of multiple keys between a central station and different end-users in the context of multipoint access and metropolitan networks, or by providing higher key distribution rates in point to point links by suitably linking the parallel distributed keys. It also allows the coexistence of classical information and quantum key distribution channels over a single optical fibre infrastructure. Here we show, for the first time to our knowledge, the successful operation of a two domain (subcarrier and wavelength division) multiplexed strong reference BB84 quantum key distribution system. A four independent channel QKD system featuring 10 kb/s/channel over an 11 km link with Quantum Bit Error Rate (QBER) < 2 % is reported. These results open the way for multi-quantum key distribution over optical fiber networks.

quant-ph↗
arXiv2010

Shaping Bits

The performance of bit-interleaved coded modulation (BICM) with bit shaping (i.e., non-equiprobable bit probabilities in the underlying binary code) is studied. For the Gaussian channel, the rates achievable with BICM and bit shaping are practically identical to those of coded modulation or multilevel coding. This identity holds for the whole range of values of signal-to-noise ratio. Moreover, the random coding error exponent of BICM significantly exceeds that of multilevel coding and is very close to that of coded modulation.

cs.IT↗
arXiv2008

Low-Signal-Energy Asymptotics of Capacity and Mutual Information for the Discrete-Time Poisson Channel

The first terms of the low-signal-energy asymptotics for the mutual information in the discrete-time Poisson channel are derived and compared to an asymptotic expression of the capacity. In the presence of non-zero additive noise (either Poisson or geometric), the mutual information is concave at zero signal-energy and the minimum energy per bit is not attained at zero capacity. Fixed signal constellations which scale with the signal energy do not attain the minimum energy per bit. The minimum energy per bit is zero when additive Poisson noise is present and $\ew\log 2$ when additive geometric noise of mean $\ew$ is present.

cs.IT↗
arXiv2008

Bit-Interleaved Coded Modulation Revisited: A Mismatched Decoding Perspective

We revisit the information-theoretic analysis of bit-interleaved coded modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The mismatched decoding model is well-defined for finite, yet arbitrary, block lengths, and naturally captures the channel memory among the bits belonging to the same symbol. We give two independent proofs of the achievability of the BICM capacity calculated by Caire et al. where BICM was modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. Our first achievability proof uses typical sequences, and shows that due to the random coding construction, the interleaver is not required. The second proof is based on the random coding error exponents with mismatched decoding, where the largest achievable rate is the generalized mutual information. We show that the generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity. We also show that the error exponent -and hence the cutoff rate- of the BICM mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite-interleaved model. We also consider the mutual information appearing in the analysis of iterative decoding of BICM with EXIT charts. We show that the corresponding symbol metric has knowledge of the transmitted symbol and the EXIT mutual information admits a representation as a pseudo-generalized mutual information, which is in general not achievable. A different symbol decoding metric, for which the extrinsic side information refers to the hypothesized symbol, induces a generalized mutual information lower than the coded modulation capacity.

cs.IT↗
arXiv2007

Bit-interleaved coded modulation in the wideband regime

The wideband regime of bit-interleaved coded modulation (BICM) in Gaussian channels is studied. The Taylor expansion of the coded modulation capacity for generic signal constellations at low signal-to-noise ratio (SNR) is derived and used to determine the corresponding expansion for the BICM capacity. Simple formulas for the minimum energy per bit and the wideband slope are given. BICM is found to be suboptimal in the sense that its minimum energy per bit can be larger than the corresponding value for coded modulation schemes. The minimum energy per bit using standard Gray mapping on M-PAM or M^2-QAM is given by a simple formula and shown to approach -0.34 dB as M increases. Using the low SNR expansion, a general trade-off between power and bandwidth in the wideband regime is used to show how a power loss can be traded off against a bandwidth gain.

cs.IT↗
arXiv2007

Derivative of BICM Mutual Information

In this letter we determine the derivative of the mutual information corresponding to bit-interleaved coded modulation systems. The derivative follows as a linear combination of minimum-mean-squared error functions of coded modulation sets. The result finds applications to the analysis of communications systems in the wideband regime and to the design of power allocation over parallel channels.

cs.IT↗
arXiv2007

Information Rate Loss due to Radiation Decoherence

The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.

quant-ph↗
arXiv2007

Baryon semileptonic decays: the Mexican contribution

We give a detailed account of the techniques to compute radiative corrections in baryon semileptonic decays developed over the years by Mexican collaborations. We explain how the method works by obtaining an expression for the Dalitz plot of semileptonic decays of polarized baryons including radiative corrections to order ${\mathcal O}(αq/πM_1)$, where $q$ is the four-momentum transfer and $M_1$ is the mass of the decaying baryon. From here we compute the totally integrated spin angular asymmetry coefficient of the emitted baryon and compare its value with other results.

hep-ph↗