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FiniteState Markov Modeling of Fading Channels—A Survey of Principles and Applications
 IEEE Sign. Process. Mag
"... [A survey of principles and applications] © MASTER SERIES In late 1950s and early 1960s, Gilbert and Elliott at Bell Labs were modeling burstnoise telephone circuits with a very simple twostate channel model with memory. This simple model allowed them to evaluate channel capacity and error rate pe ..."
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[A survey of principles and applications] © MASTER SERIES In late 1950s and early 1960s, Gilbert and Elliott at Bell Labs were modeling burstnoise telephone circuits with a very simple twostate channel model with memory. This simple model allowed them to evaluate channel capacity and error rate performance through bursty wireline telephone circuits. However, it took another 30 years for the socalled GilbertElliott channel (GEC) and its generalized finitestate Markov channel (FSMC) to be applied in the design of secondgeneration (2G) wireless communication systems. Since the mid 1990s, the GEC and FSMC models have been widely used for modeling wireless flatfading channels in a variety of applications, ranging from modeling channel error bursts to decoding at the receiver. FSMC models are versatile, and with suitable choices of model parameters, can capture the essence of timevarying fading channels. This article’s goal is to provide an indepth understanding of the principles of FSMC modeling of fading channels with its applications in wireless communication systems. Digital Object Identifier 10.1109/MSP.2008.926683 10535888/08/$25.00©2008IEEE IEEE SIGNAL PROCESSING MAGAZINE [57] SEPTEMBER 2008While the emphasis is on frequency nonselective or flatfading channels, this understanding will be useful for future generalizations of FSMC models for frequencyselective fading channels. The target audience of this article include both theory and practiceoriented researchers who would like to design accurate channel models for evaluating the performance of wireless communication systems in the physical or media access control layers, or those who would like to develop more efficient and reliable transceivers that take advantage of the inherent memory in fading channels. Both FSMC models and flatfading channels will be formally introduced. However, a background in timevarying fading communication channels is beneficial.
Determining and approaching achievable rates of binary intersymbol interference channels using multistage decoding
 IEEE Trans. Information Theory
, 2007
"... Abstract—By examining the achievable rates of a multistage decoding system on stationary ergodic channels, we derive lower bounds on the mutual information rate corresponding to independent and uniformly distributed (i.u.d.) inputs, also referred to as the i.u.d. information rate. For binary intersy ..."
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Abstract—By examining the achievable rates of a multistage decoding system on stationary ergodic channels, we derive lower bounds on the mutual information rate corresponding to independent and uniformly distributed (i.u.d.) inputs, also referred to as the i.u.d. information rate. For binary intersymbol interference (ISI) channels, we show that these bounds become tight as the number of decoding stages increases. Our analysis, which focuses on the marginal conditional output densities at each stage of decoding, provides an information rate corresponding to each stage. These rates underlie the design of multilevel coding schemes, based upon lowdensity paritycheck (LDPC) codes and message passing, that in combination with multistage decoding approach the i.u.d. information rate for binary ISI channels. We give example constructions for channel models that have been commonly used in magnetic recording. These examples demonstrate that the technique is very effective even for a small number of decoding stages. Index Terms—Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm, coset codes, density evolution, finitestate channels, information rates, intersymbol interference (ISI) channels, lowdensity paritycheck (LDPC) codes, magnetic recording, multilevel coding, multistage decoding. I.
Upper bounds on the capacities of noncontrollable finitestate channles using dynamic programming methods
 in Proc. International Symposium on Information Theory, Seoul, South Korea
, 2009
"... Noncontrollable finitestate channels (FSCs) are finitestate channels in which the user cannot control the channel state, i.e., the state evolves freely in time. Thus far, good upper bounds on the capacities as well as computable capacities of general noncontrollable FSCs with/without feedback ar ..."
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Noncontrollable finitestate channels (FSCs) are finitestate channels in which the user cannot control the channel state, i.e., the state evolves freely in time. Thus far, good upper bounds on the capacities as well as computable capacities of general noncontrollable FSCs with/without feedback are unknown. Here we consider the delayed channel state as part of the channel input and then mathematically define the directed information between the new channel input (including the source and the delayed channel state) and the channel output. With this technique, computable upper bounds on the capacities of noncontrollable FSCs with/without feedback are developed. The upper bounds are achieved by conditional Markov sources, conditioned on the delayed feedback and the delayed state information. A dynamic programming method is proposed to optimize conditional Markov sources and the bounds are numerically computed by Monte Carlo techniques.
Asymptotics of the inputconstrained binary symmetric channel capacity
 Annals of Applied Probability
, 2009
"... We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop ..."
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We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117–122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this result, we establish an asymptotic formula for the capacity of a BSC with input process supported on an irreducible finite type constraint, as the noise parameter tends to zero. 1. Introduction and background. Let X,Y be discrete random variables with alphabet X,Y and joint probability mass function pX,Y (x,y) △ = P(X = x,Y = y), x ∈ X,y ∈ Y [for notational simplicity, we will write p(x,y) rather than pX,Y (x,y), similarly p(x),p(y) rather than pX(x),pY (y), resp., when it
Shitz), “On the achievable information rates of finitestate input twodimensional channels with memory
 Proc. 2005 IEEE Int. Symp. on Information Theory
"... Abstract — The achievable information rate of finitestate input twodimensional (2D) channels with memory is an open problem, which is relevant, e.g., for intersymbolinterference (ISI) channels and cellular multipleaccess channels. We propose a method for simulationbased computation of such in ..."
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Abstract — The achievable information rate of finitestate input twodimensional (2D) channels with memory is an open problem, which is relevant, e.g., for intersymbolinterference (ISI) channels and cellular multipleaccess channels. We propose a method for simulationbased computation of such information rates. We first draw a connection between the Shannontheoretic information rate and the statistical mechanics notion of free energy. Since the free energy of such systems is intractable, we approximate it using the cluster variation method, implemented via generalized belief propagation. The derived, fully tractable, algorithm is shown to provide a practically accurate estimate of the information rate. In our experimental study we calculate the information rates of 2D ISI channels and of hexagonal Wyner cellular networks with binary inputs, for which formerly only bounds were known. Submitted to ISIT 2005 I.
Joint Iterative Decoding of LDPC Codes and Channels with Memory
, 2003
"... This paper considers the joint iterative decoding of irregular lowdensity paritycheck (LDPC) codes and channels with memory. It begins by introducing a new class of erasure channels with memory, known as generalizederasure channels. For these channels, a single parameter recursion for the density ..."
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This paper considers the joint iterative decoding of irregular lowdensity paritycheck (LDPC) codes and channels with memory. It begins by introducing a new class of erasure channels with memory, known as generalizederasure channels. For these channels, a single parameter recursion for the density evolution of the joint iterative decoder is derived. This provides a necessary and sucient condition for decoder convergence, and allows the algebraic construction of sequences of LDPC degree distributions. Under certain conditions, these sequences can achieve the symmetric information rate (SIR) of the channel using only iterative decoding. Example code sequences are given for two channels, and it is conjectured that they each achieve the respective SIR. Keywords: joint iterative decoding, erasure channel, capacityachieving, LDPC codes 1.
A Pragmatic Approach to Coded ContinuousPhase Modulation
"... Abstract — In this paper, we show that a “pragmatic ” approach to coded CPM schemes suffers from a significant capacity loss. This loss can be greatly reduced by choosing an appropriate mapping different from natural or Gray, adopted so far. We propose to add to the CPM modulator a linear feedback, ..."
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Abstract — In this paper, we show that a “pragmatic ” approach to coded CPM schemes suffers from a significant capacity loss. This loss can be greatly reduced by choosing an appropriate mapping different from natural or Gray, adopted so far. We propose to add to the CPM modulator a linear feedback, optimized through capacity arguments, that permits to achieve performance within 1 dB from the CPM capacity. I.
Noisy Constrained Capacity
 In Information Theory Symposium, volume IEEE
, 2006
"... Abstract — We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose input is a sequence from a constrained set. As stated in [4] “... while calculation of the noisefree capacity of constrained sequences is we ..."
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Cited by 4 (2 self)
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Abstract — We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose input is a sequence from a constrained set. As stated in [4] “... while calculation of the noisefree capacity of constrained sequences is well known, the computation of the capacity of a constraint in the presence of noise... has been an unsolved problem in the halfcentury since Shannon’s landmark paper.... ” We express the constrained capacity of a binary symmetric channel with (d, k)constrained input as a limit of the top Lyapunov exponents of certain matrix random processes. We compute asymptotic approximations of the noisy constrained capacity for cases where the noise parameter ε is small. In particular, we show that when k≤2d, the error term with respect to the constraint capacity is O(ε), whereas it is O(ε log ε) when k> 2d. In both cases, we compute the
Informationtheoretic limits of twodimensional optical recording channels
"... During the past five years, advances in the informationtheoretic analysis of “onedimensional (1D) ” recording channels have clarified the limits on linear densities that can be achieved by trackoriented magnetic and optical storage technologies. Channel architectures incorporating powerful codes, ..."
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During the past five years, advances in the informationtheoretic analysis of “onedimensional (1D) ” recording channels have clarified the limits on linear densities that can be achieved by trackoriented magnetic and optical storage technologies. Channel architectures incorporating powerful codes, such as turbo codes and lowdensity paritycheck codes, have been shown to achieve performance very close to the informationtheoretic limits. As 1D trackoriented data storage technologies reach maturity, there is increasing interest in “twodimensional (2D) ” recording technologies, such as twodimensional optical storage (TwoDOS) and holographic storage. This paper provides an overview of some recently developed techniques for determining analytical bounds and simulationbased estimates for achievable densities of such 2D recording channels, as well as some recently proposed signal processing and coding methods that can move system performance closer to the informationtheoretic limits.
Coherent ContinuousPhase FrequencyShift Keying: Parameter Optimization and Code Design
"... Abstract—The symmetric information rate of a modulationconstrained transmission system is the informationtheoretic limit on performance under the assumption that the inputs are independent and uniformly distributed. The symmetric information rate for continuousphase frequencyshift keying (CPFSK) ..."
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Abstract—The symmetric information rate of a modulationconstrained transmission system is the informationtheoretic limit on performance under the assumption that the inputs are independent and uniformly distributed. The symmetric information rate for continuousphase frequencyshift keying (CPFSK) over an AWGN channel may be estimated by considering the system to be a finitestate Markov channel and executing a BCJRlike algorithm. In this paper, the estimated symmetric information rate is used along with the exact expression for the 99% power bandwidth to determine the informationtheoretic tradeoff between energy and spectral efficiency for CPFSK modulation. Using this tradeoff, the code rate and modulation index are jointly optimized for a particular spectral efficiency and alphabet size. Codes are then designed for the optimized system. The codes are comprised of variable nodes (which represent irregular repetition codes), check nodes (which represent single paritycheck codes), and an interleaver connecting the variable and check nodes. The degree distributions of the code are optimized from the system’s EXIT chart by using linear programming. Additional details of the code design, including labeling and interleaver design, are also discussed. Simulation results show that the optimized coded systems achieve bit error rates within 0.4 dB of the informationtheoretic limits at BER = 10 −5.