In Shannon's paper [1], where the sphere packing bound is introduced, it is outlined how to calculate the finite block length capacity for a Gaussian channel if the required parameters are known. However, the transmit waveform is allowed to have infinite duration. We want to examine what happens when we introduce constraints on the energy concentration of the waveform, i.e., most of its energy is concentrated in a time interval T and a bandwidth W. The problem of the maximal energy concentration was solved in [2]. We want to find upper and lower bound for the finite block length capacity with these constraints.

[1] C. Shannon, "Probability of error for optimal codes in a Gaussian channel", The Bell System Technical Journal, 1959

[2] D. Slepian, H. O. Pollack, H. J. Landau, "Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty I-V", The Bell System Technical Journal, 1961-1978

Prerequisites

Digital Communications, Digital Communications II

Information Theory

Python/MATLAB

Contact

delcho.donev@tum.de

Supervisor:

Delcho Donev

Forschungspraxis or MSCE Internships

Capacity Bounds for Time and Bandwidth Constraint Transmissions

In Shannon's paper [1], where the sphere packing bound is introduced, it is outlined how to calculate the finite block length capacity for a Gaussian channel if the required parameters are known. However, the transmit waveform is allowed to have infinite duration. We want to examine what happens when we introduce constraints on the energy concentration of the waveform, i.e., most of its energy is concentrated in a time interval T and a bandwidth W. The problem of the maximal energy concentration was solved in [2]. We want to find upper and lower bound for the finite block length capacity with these constraints.

[1] C. Shannon, "Probability of error for optimal codes in a Gaussian channel", The Bell System Technical Journal, 1959

[2] D. Slepian, H. O. Pollack, H. J. Landau, "Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty I-V", The Bell System Technical Journal, 1961-1978

Coşkun, M. C.; Donev, D.; Kramer, G.: Efficient Coding and Modulation for Satellite Links with Severe Delay Constraints. Munich Aerospace Summer School, Jul 2019 more…

Donev, D.; Kramer, G.: Lower Bounds on the Out of Time Constraint Finite Blocklength Transmissions. 2019 European School of Information Theory, Apr 2019 more…

Donev, D.; Kramer, G.: Lower Bounds on the Out of Time Constraint Finite Blocklength Transmissions. 19th Joint Workshop on Communications and Coding (JWCC), Mar 2019 more…

2018

Donev, D.; Böcherer, G.: Polar-Coded Pulse Position Modulation for the Poisson Channel. 9th Advanced Satellite Multimedia Systems Conference, Sep 2018 more…

Donev, D.: The Prolate Spheroidal Wave Functions in Finite Block Length Communications. TUM CoC COM PhD Workshop 2018: Ultra Reliable Low Latency Communications and Applications for 5G, Jul 2018 more…

Donev, D.; Kramer, G.: Surface and Intersection Area of Spherical Caps on a n-dimensional Hypersphere. 2018 Munich Doctoral Seminar on Communications (MSC), Jul 2018 more…

Donev, D.: The Prolate Spheroidal Wave Functions in Finite Block Length Communications. 2018 IEEE European School of Information Theory, May 2018 more…

2017

Donev, D.: Prolate Spheroidal Wave Functions. 18th Joint Workshop on Communications and Coding (JWCC), Mar 2017 more…

2016

Donev, D.; Böcherer, G.: Polar Codes with Pulse Position Modulation. Internal LNT Workshop , 2016 more…