scholarly journals Generalized Prolate Spheroidal Wave Functions: Spectral Analysis and Approximation of Almost Band-Limited Functions

2015 ◽  
Vol 22 (2) ◽  
pp. 383-412 ◽  
Author(s):  
Abderrazek Karoui ◽  
Ahmed Souabni
Keyword(s):  
Spectral Analysis ◽  
Wave Functions ◽  
Prolate Spheroidal ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Band Limited

scholarly journals Time-Limited Codewords over Band-Limited Channels: Data Rates and the Dimension of the W-T Space

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 924
Author(s):  
Youssef Jaffal ◽  
Ibrahim Abou-Faycal
Keyword(s):  
Degrees Of Freedom ◽  
Additive White Gaussian Noise ◽  
Wave Functions ◽  
Upper And Lower Bounds ◽  
Prolate Spheroidal ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Data Rates ◽  
Band Limited ◽  
Discrete Formulation

We consider a communication system whereby T-seconds time-limited codewords are transmitted over a W-Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as WT→∞, it is known that the maximal achievable rates with such a scheme converge to Shannon’s capacity with the presence of 2WT degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of WT. We use prolate spheroidal wave functions to obtain an information lossless equivalent discrete formulation and then we apply Polyanskiy’s results on coding in the finite block-length regime. We derive upper and lower bounds on the achievable rates and the corresponding degrees of freedom and we numerically evaluate them for sample values of 2WT. The bounds are asymptotically tight and numerical computations show the gap between them decreases as 2WT increases. Additionally, the possible decrease from 2WT in the available degrees of freedom is upper-bounded by a logarithmic function of 2WT.

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