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Achieving Maximum Possible Speed on Constrained Block Transmission Systems

Abstract

We develop a theoretical framework for achieving the maximum possible speed on constrained digital channels with a finite alphabet. A common inaccuracy that is made when computing the capacity of digital channels is to assume that the inputs and outputs of the channel are analog Gaussian random variables, and then based upon that assumption, invoke the Shannon capacity bound for an additive white Gaussian noise (AWGN) channel. In a channel utilizing a finite set of inputs and outputs, clearly the inputs are not Gaussian distributed and Shannon bound is not exact. We study the capacity of a block transmission AWGN channel with quantized inputs and outputs, given the simultaneous constraints that the channel is frequency selective, there exists an average power constraint at the transmitter and the inputs of the channel are quantized. The channel is assumed known at the transmitter. We obtain the capacity of the channel numerically, using a constrained Blahut-Arimoto algorithm which incorporates an average power constraint at the transmitter. Our simulations show that under certain conditions the capacity approaches very closely the Shannon bound. We also show the maximizing input distributions. The theoretical framework developed in this paper is applied to a practical example: the downlink channel of a dial-up PCM modem connection where the inputs to the channel are quantized and the outputs are real. We test how accurate is the bound 53.3 kbps for this channel. Our results show that this bound can be improved upon.

References

  1. 1.

    Ayanoglu E, Dagdeviren NR, Golden GD, Mazo JE: An equalizer design technique for the PCM modem: a new modem for the digital public switched network. IEEE Transactions on Communications 1998,46(6):763-774. 10.1109/26.681412

    Article  Google Scholar 

  2. 2.

    Rauschmayer DJ: ADSL/VDSL Principles : A Practical and Precise Study of Asymmetric Digital Subscriber Lines and Very High Speed Digital Subscriber Lines. Macmillan, New York, NY, USA; 1999.

    Google Scholar 

  3. 3.

    Lawyer DS: Modem-HOWTO. May 2003, https://doi.org/www.tldp.org/HOWTO/Modem-HOWTO-1.html

  4. 4.

    Shannon CE: A mathematical theory of communications. Bell Systems Technical Journal 1948, 27: 379–423 (pt I), 623–656 (pt II).

    MathSciNet  Article  Google Scholar 

  5. 5.

    Arimoto S: An algorithm for computing the capacity of arbitrary discrete memoryless channels. IEEE Transactions on Information Theory 1972,18(1):14-20. 10.1109/TIT.1972.1054753

    MathSciNet  Article  Google Scholar 

  6. 6.

    Blahut RE: Computation of channel capacity and rate-distortion functions. IEEE Transactions on Information Theory 1972,18(4):460-473. 10.1109/TIT.1972.1054855

    MathSciNet  Article  Google Scholar 

  7. 7.

    Kavcic A: On the capacity of Markov sources over noisy channels. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '01), November 2001, San Antonio, Tex, USA 5: 2997–3001.

    Article  Google Scholar 

  8. 8.

    Varnica N, Ma X, Kavcic A: Capacity of power constrained memoryless AWGN channels with fixed input constellations. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '02), November 2002, Taipei, Taiwan 2: 1339–1343.

    Google Scholar 

  9. 9.

    Honary B, Ali F, Darnell M: Information capacity of additive white Gaussian noise channel with practical constraints. IEE Proceedings, Part I: Communications, Speech and Vision 1990,137(5):295-301. 10.1049/ip-i-2.1990.0041

    Google Scholar 

  10. 10.

    Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1981,28(1):55-67.

    MathSciNet  Article  Google Scholar 

  11. 11.

    Ozarow LH, Wyner AD: On the capacity of the Gaussian channel with a finite number of input levels. IEEE Transactions on Information Theory 1990,36(6):1426-1428. 10.1109/18.59937

    MathSciNet  Article  Google Scholar 

  12. 12.

    Shamai (Shitz) S, Ozarow LH, Wyner AD: Information rates for a discrete-time Gaussian channel with intersymbol interference and stationary inputs. IEEE Transactions on Information Theory 1991,37(6):1527-1539. 10.1109/18.104314

    MathSciNet  Article  Google Scholar 

  13. 13.

    Varnica N, Ma X, Kavcic A: Power-constrained memoryless and intersymbol interference channels with finite input alphabets: capacities and concatenated code constructions. to appear in IEEE Transactions on Communications, https://doi.org/hrl.harvard.edu/~varnica/publications.htm to appear in IEEE Transactions on Communications,

  14. 14.

    Varnica N: Iteratively decodable codes for memoryless and intersymbol interference channels, Ph.D. dissertation. https://doi.org/hrl.harvard.edu/~varnica/pic/PhDThesis.pdf

  15. 15.

    Bellorado J, Ghassemzadeh S, Kavcic A: Approaching the capacity of the MIMO Rayleigh flat-fading channel with QAM constellations, independent across antennas and dimensions. to appear in IEEE Transactions on Wireless Communications, https://doi.org/people.deas.harvard.edu/~kavcic/recent.html to appear in IEEE Transactions on Wireless Communications,

  16. 16.

    Cover TM, Thomas JA: Elements of Information Theory. John Wiley & Sons, New York, NY, USA; 1991.

    Google Scholar 

  17. 17.

    Yeung RW: A First Course in Information Theory. Kluwer Academic/Plenum, New York, NY, USA; 2002.

    Google Scholar 

  18. 18.

    Csiszar I, Korner J: Information Theory: Coding Theorems for Discrete Memoryless Systems. Academic Press, London, UK; 1981.

    Google Scholar 

  19. 19.

    Vontobel PO: A generalized Blahut-Arimoto algorithm. Proceedings of the IEEE International Symposium on Information Theory, July 2003, Yokohama, Japan 53.

    Google Scholar 

  20. 20.

    Hamming RW: Numerical Methods for Scientists and Engineers. 2nd edition. Dover, New York, NY, USA; 1987.

    Google Scholar 

  21. 21.

    Gray RM, Neuhoff DL: Quantization. IEEE Transactions on Information Theory 1998,44(6):2325-2383. 10.1109/18.720541

    MathSciNet  Article  Google Scholar 

  22. 22.

    Bingham JAC: ADSL, VDSL, and Multicarrier Modulation, Wiley Series in Telecommunications and Signal Processing. John Wiley & Sons, New York, NY, USA; 2000.

    Google Scholar 

  23. 23.

    Caraballo LM: System level design and simulation of a PCM voiceband modem compliant with the ITU V.90 standard, M.S. thesis. Texas A&M University, Canyon, Tex, USA; 2000.

    Google Scholar 

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Correspondence to Obianuju Ndili.

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Ndili, O., Ogunfunmi, T. Achieving Maximum Possible Speed on Constrained Block Transmission Systems. EURASIP J. Adv. Signal Process. 2007, 035689 (2006). https://doi.org/10.1155/2007/35689

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Keywords

  • Information Technology
  • Gaussian Noise
  • Quantum Information
  • Average Power
  • White Gaussian Noise