Using time-limited pulses in a combined PAM-OMM system over band-limited channels

Jaffal, Youssef; Abou-Faycal, Ibrahim

doi:10.1109/wcnc.2019.8885512

Cited by 1 publication

(2 citation statements)

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“…Recently, in [ 10 , 11 ], we studied the use of T -seconds time-limited pulses over W -Hz real band-limited Gaussian channels, and derived the channel capacity by allowing the time duration of the codewords to grow towards infinity. In [ 10 ], we considered a pulse amplitude modulation (PAM) system and we studied optimal signaling; we showed that one can approach Shannon’s capacity by signaling at faster than the Nyquist rate.…”

Section: Introductionmentioning

confidence: 99%

“…In [ 10 ], we considered a pulse amplitude modulation (PAM) system and we studied optimal signaling; we showed that one can approach Shannon’s capacity by signaling at faster than the Nyquist rate. In [ 11 ], we considered a combined PAM-orthogonal multi-pulse modulation scheme (PAM-OMM) and derived the achievable rates and evaluated them numerically. We showed that these rates can be made arbitrarily close to the Shannon’s capacity by using a finite number of parallel filters.…”

Section: Introductionmentioning

confidence: 99%

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

Jaffal

Abou-Faycal

2020

Entropy

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%