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A generalization of the BlahutArimoto algorithm to finitestate channels
 IEEE Trans. Inf. Theory
, 2008
"... Abstract—The classical Blahut–Arimoto algorithm (BAA) is a wellknown algorithm that optimizes a discrete memoryless source (DMS) at the input of a discrete memoryless channel (DMC) in order to maximize the mutual information between channel input and output. This paper considers the problem of opti ..."
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Abstract—The classical Blahut–Arimoto algorithm (BAA) is a wellknown algorithm that optimizes a discrete memoryless source (DMS) at the input of a discrete memoryless channel (DMC) in order to maximize the mutual information between channel input and output. This paper considers the problem of optimizing finitestate machine sources (FSMSs) at the input of finitestate machine channels (FSMCs) in order to maximize the mutual information rate between channel input and output. Our main result is an algorithm that efficiently solves this problem numerically; thus, we call the proposed procedure the generalized BAA. It includes as special cases not only the classical BAA but also an algorithm that solves the problem of finding the capacityachieving input distribution for finitestate channels with no noise. While we present theorems that characterize the local behavior of the generalized BAA, there are still open questions
Information Geometric Formulation and Interpretation of Accelerated BlahutArimototype Algorithms
 IEEE International Workshop on Information Theory, 24–29 Oct
, 2004
"... Abstract — We propose two related classes of iterative algorithms for computing the capacity of discrete memoryless channels. The celebrated BlahutArimoto algorithm is a special case of our framework. The formulation of these algorithms is based on the natural gradient and proximal point methods. W ..."
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Abstract — We propose two related classes of iterative algorithms for computing the capacity of discrete memoryless channels. The celebrated BlahutArimoto algorithm is a special case of our framework. The formulation of these algorithms is based on the natural gradient and proximal point methods. We also provide interpretations in terms of notions from information geometry. A theoretical convergence analysis and simulation results demonstrate that our new algorithms have the potential to significantly outperform the BlahutArimoto algorithm in terms of convergence speed.
The Read Channel
, 2008
"... In this paper, we provide a survey of the novel read channel technologies that found their implementation in products over the past decade, and we outline possible technology directions for the future of read channels. Recently, magnetic recording read channels have undergone several changes. In ad ..."
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Cited by 8 (0 self)
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In this paper, we provide a survey of the novel read channel technologies that found their implementation in products over the past decade, and we outline possible technology directions for the future of read channels. Recently, magnetic recording read channels have undergone several changes. In addition to switching from longitudinal to perpendicular recording channels, detectors tuned to media noise sources are now readily implemented in read channel chips. Powerful numerical techniques have emerged to evaluate the capacity of the magnetic recording channel. Further, improved coding/decoding methods have surfaced both for the incumbent ReedSolomon codes and the promising lowdensity paritycheck (LDPC) codes. The paper is a tutoriallike survey of these emerging technologies with the aim to propel the reader to the forefront of research and development in the areas of signal processing and coding for magnetic recording channels.
The Capacity of Communication Channels with Memory
, 2004
"... For a state machine channel, a simple form of the feedbackcapacityachieving source distribution is revealed. A Markov source, whose memory length equals the channel memory length, achieves the feedback capacity. Given the posterior channelstate distribution, the optimal source Markov transition p ..."
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For a state machine channel, a simple form of the feedbackcapacityachieving source distribution is revealed. A Markov source, whose memory length equals the channel memory length, achieves the feedback capacity. Given the posterior channelstate distribution, the optimal source Markov transition probabilities become independent of the whole history of past channel outputs. Further, when the feedback is delayed, the delayed feedback capacity is achieved by a Markov source whose memory length equals the sum of the channel memory length and the feedback delay. The Markov source optimization is formulated as a standard stochastic control problem and is solved by dynamic programming. The (delayed) feedback capacity is an upperbound on the feedforward channel capacity, and this bound can be made tight by increasing the feedback delay. The linear Gaussian channel with an average input power constraint can be equivalently modelled as a state machine channel. When the channel has feedback, by following similar procedures as developed for the state machine channel, it is shown that GaussMarkov sources achieve the feedback capacity and a KalmanBucy filter is optimal for processing
1Computing the Channel Capacity and Ratedistortion Function with Twosided State Information
, 2004
"... We present iterative algorithms that numerically solve optimization problems of computing the capacitypower and ratedistortion functions for coding with twosided state information. Numerical examples are provided to demonstrate efficiency of our algorithms. Key words BlahutArimoto algorithm, co ..."
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We present iterative algorithms that numerically solve optimization problems of computing the capacitypower and ratedistortion functions for coding with twosided state information. Numerical examples are provided to demonstrate efficiency of our algorithms. Key words BlahutArimoto algorithm, coding with side information, Gel’fandPinsker problem, WynerZiv problem I.
Research Article Achieving Maximum Possible Speed on Constrained Block Transmission Systems
"... 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 vari ..."
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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 BlahutArimoto 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 dialup 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. 1.
1 Squeezing the ArimotoBlahut Algorithm for Faster Convergence
"... Abstract—The Arimoto–Blahut algorithm for computing the capacity of a discrete memoryless channel is revisited. A socalled “squeezing ” strategy is used to design algorithms that preserve its simplicity and monotonic convergence properties, but have provably better rates of convergence. Index Terms ..."
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Abstract—The Arimoto–Blahut algorithm for computing the capacity of a discrete memoryless channel is revisited. A socalled “squeezing ” strategy is used to design algorithms that preserve its simplicity and monotonic convergence properties, but have provably better rates of convergence. Index Terms—alternating minimization; channel capacity; discrete memoryless channel; rate of convergence. I.