Saddlepoint Approximations for Short-Packet Wireless Communications

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