Achieving Maximum Possible Speed on Constrained Block Transmission Systems
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Research Article Achieving Maximum Possible Speed on Constrained Block Transmission Systems Obianuju Ndili and Tokunbo Ogunfunmi Department of Electrical Engineering, Santa Clara University, Santa Clara, CA 95053, USA Received 20 May 2005; Revised 7 April 2006; Accepted 30 April 2006 Recommended by Vincent Poor 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 P 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 P 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. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
The performance of all digital modems is affected by the precision of analog-to-digital (A/D) and digital-to-analog (D/A) conversions. Quantization distortion which limits the performance of the system is introduced as a result of analog-todigital conversions. There are two different situations: one consists in designing a modem together with the A/D, D/A converters that interface a given analog channel and the other consists in designing a modem to face a channel which is part analog and part digital with a preexistent D/A and/or A/D conversion included. An example of this last case can be found in use when the modem sends or receives digital data across the public switched telephone network (PSTN). The core network of the PSTN today has evolved into an alldigital transport medium supported by optical communications. The access is mostly through twisted pairs of copper wires that are terminated by a PCM conversion. “Dial-up” is a technology that allows users to do this. In the uplink connection, the user’s data is converted to an appropriately band-limited analog signal by the user’s network interface hard
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