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The nonnegativity of relative entropy implies that the differential entropy of a random vector X with probability density function (pdf) f is upper-bounded by -E[log g(X)]for any arbitrary pdf g. Using this inequality with a cleverly chosen g, we derive a lower bound on the asymptotic excess rate of entropy-constrained vector quantization for d-dimensional sources and rth-power distortion, where the asymptotic excess rate is defined as the difference between the smallest output entropy of a vector quantizer satisfying the distortion constraint and the rate-distortion function in the limit as the distortion tends to zero. Specialized to the one-dimensional case, this lower bound coincides with the asymptotic excess rate achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal as the allowed distortion tends to zero. Furthermore, in the one-dimensional case, the derivation of the lower bound reveals a necessary condition for a sequence of quantizers to be asymptotically optimal. This condition implies that any sequence of asymptotically optimal almost-regular quantizers must converge to a uniform quantizer as the distortion tends to zero. While the obtained lower bound itself is not novel, to the best of our knowledge, we present the first rigorous derivation that follows the direct approach by Gish and Pierce without resorting to heuristic high-resolution approximations commonly found in the quantization literature. Furthermore, our derivation holds for all d-dimensional sources having finite differential entropy and whose integer part has finite entropy. In contrast to Gish and Pierce, we do not require additional constraints on the continuity or decay of the source pdf. ; This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Ministerio de Economía y Competitividad of Spain under Grants TEC2013-41718-R, RYC-2014-16332, IJCI-2015-27020, TEC2015-69648-REDC, and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845. The material in this paper was presented in part at the 2016 IEEE International Symposium on Information Theory, Barcelona, Spain, July 2016.

Proceeding of: 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 21-26 June 2020 ; The channel capacity of wireless networks Is often studied under the assumption that the communicating nodes have perfect channel-state information and that interference is always present. In this paper, we study the channel capacity of a wireless network without these assumptions, i.e., a bursty noncoherent wireless network where the users are grouped in cells and the base-station features several receive antennas. We demonstrate that the channel capacity is bounded in the signal-to-noise ratio (SNR) when the number of receive antennas is finite and the probability of presence of interference is strictly positive. ; This work has been supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161), and by the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU).

Proceeding of: 53rd Asilomar Conference on Signals, Systems, and Computers (ACSSC 2019), 3-6 Nov. 2019, Pacific Grove, CA, USA ; Several emerging wireless communication services and applications have stringent latency requirements, necessitating the transmission of short packets. To obtain performance benchmarks for short-packet wireless communications, it is crucial to study the maximum coding rate as a function of the blocklength, commonly called finite-blocklength analysis. A finiteblocklength analysis can be performed via nonasymptotic bounds or via refined asymptotic approximations. This paper reviews finite-blocklength approximations for the noncoherent Rayleigh block-fading channel. These approximations have negligible computational cost compared to the nonasymptotic bounds and are shown to be accurate for error probabilities as small as 10-8 [super index] and SNRs down to 0 dB. ; A. Lancho has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161) and from the Swedish Research Council under grant 2016-03293. J. O¨ stman has been supported by the Swedish Research Council under grants 2014-6066 and 2016-03293. T. Koch has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161) and from the Spanish Ministerio de Economía y Competitividad under grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU). G. Vazquez-Vilar has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161) and from the Spanish Ministerio de Economía y Competitividad under grant TEC2016- 78434-C3-3-R (AEI/FEDER, EU).

This article was presented in part at the 2019 IEEE International Symposium on Information Theory, Paris, France, July 2019, and in part at the 2019 53rd Annual Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, November 2019. ; In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more. ; The work of Alejandro Lancho was supported in part by European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme under Grant 714161, and in part by the Wallenberg AI, Autonomous Systems, and Software Program. The work of Johan Östman and Giuseppe Durisi was supported by the Swedish Research Council under Grant 2014-6066 and Grant 2016-03293. The work of Tobias Koch was supported in part by the European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme under Grant 714161 and in part by the Spanish Ministerio de Economía y Competitividad (AEI/FEDER, EU) under Grant RYC-2014-16332 and Grant TEC2016-78434-C3-3-R. The work of Gonzalo Vazquez-Vilar was supported in part by the European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme Under Grant 71416 and in part by the Spanish Ministerio de Economía y Competitividad (AEI/FEDER, EU) under Grant TEC2016-78434-C3-3-R.

Proceeding of: 2019 IEEE International Symposium on Information Theory (ISIT), 7-12 July 2019, Paris, France ; This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB, blocklengths of 168 channel uses or more, and when the channel's coherence interval is not smaller than two. It is demonstrated that the derived approximations recover both the normal approximation and the reliability function of the channel. ; A. Lancho, G. Vázquez-Vilar and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (714161), the Spanish Ministerio de Economía y Competitividad (RYC-2014-16332, TEC2016-78434-C3-3-R (AEI/FEDER, EU) and IJCI2015-27020), the Spanish Ministerio de Educación, Cultura y Deporte (FPU014/01274), and the Comunidad de Madrid (S2103/ICE-2845). G. Durisi and J. Östman have been supported by the Swedish Research Council under Grants 2016-03293 and 2014-6066.

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. ; This work has been funded in part by the European Research Council (ERC) under grant agreement 259663; by the European Union under the 7th Framework Programme, grants FP7-PEOPLE-2009-IEF no. 252663, FP7-PEOPLE-2011-CIG no. 303633, FP7-PEOPLE-2012-CIG no. 333680, FP7- PEOPLE-2013-IEF no. 329837; and by the Spanish Ministry of Economy and Competitiveness under grants CSD2008-00010, TEC2009-14504-C02- 01, TEC2012-38800-C03-01, TEC2012-38800-C03-03 and RYC-2011-08150. A. Tauste Campo acknowledges funding from an EPSRC (Engineering and Physical Sciences Research Council, UK) Doctoral Prize Award.