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31
On LDPC codes over channels with memory
 IEEE Trans. Wireless Commun
, 2006
"... Abstract — The problem of detection and decoding of lowdensity paritycheck (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori proba ..."
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Abstract — The problem of detection and decoding of lowdensity paritycheck (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori probabilities of the information symbols, necessary to implement maximum a posteriori (MAP) symbol detection, are derived by using the sumproduct algorithm. With respect to the case of a LDPC code transmitted on a memoryless channel, the derived factor graphs have additional factor nodes taking into account the channel behavior and not the code constraints. It is shown that the function associated to the generic factor node modeling the channel is related to the basic branch metric used in the Viterbi algorithm when MAP sequence detection is applied or in the BCJR algorithm implementing MAP symbol detection. This fact suggests that all the previously proposed solutions for those algorithms can be systematically extended to LDPC codes and graphbased detection. When the sumproduct algorithm works on the derived factor graphs, the most demanding computation is in general that performed at factor nodes modeling the channel. In fact, the complexity of the computation at these factor nodes is in general exponential in a suitably defined channel memory parameter. In these cases, a technique for complexity reduction is illustrated. In some particular cases of practical relevance, the above mentioned complexity becomes linear in the channel memory. This does not happen in the same cases when detection is performed by using the Viterbi algorithm or the BCJR algorithm, suggesting that the use of factor graphs and the sumproduct algorithm might be computationally more appealing. As an example of application of the described framework, the cases of noncoherent and flat fading channels are considered. Index Terms — Factor graphs, sumproduct algorithm, channels with memory, phasenoise, flat fading, lowdensity paritycheck codes, iterative detection/decoding. I.
LMMSE turbo equalization based on factor graphs
 IEEE J. Sel. Areas Commun
, 2008
"... Abstract—This paper presents a factor graph approach to turbo equalization. Unlike the existing linear MMSE turbo equalization methods, which operate with truncated windows (sliding or extending window), the proposed is a fullwindow approach with low complexity. This approach supports a highspeed ..."
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Abstract—This paper presents a factor graph approach to turbo equalization. Unlike the existing linear MMSE turbo equalization methods, which operate with truncated windows (sliding or extending window), the proposed is a fullwindow approach with low complexity. This approach supports a highspeed parallel implementation technique, which makes it an attractive option in practice. I.
A unified framework for finitememory detection
 IEEE J. SAC
, 2005
"... In this paper, we present a general approach to finitememory detection. From a semitutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the wellknown Viterbi algorithm (VA), forwardbackward (FB), an ..."
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Cited by 10 (8 self)
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In this paper, we present a general approach to finitememory detection. From a semitutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the wellknown Viterbi algorithm (VA), forwardbackward (FB), and sumproduct (SP) algorithms, shows that a basic metric emerges naturally under very general causality and finitememory conditions. This result implies that detection solutions based on one algorithm can be systematically extended to other algorithms. For stochastic channels described by a suitable parametric model, a conditional Markov property is shown to imply this finitememory condition. Unfortunately, this property is seldom met in practice and optimality cannot be claimed. We show, however, that in the case of transmission over a linear channel characterized by a single timeinvariant stochastic parameter, a finitememory detection strategy is asymptotically optimal, regardless of the particular algorithm used (VA, FB, or SP). We consider, as examples, linear predictive and noncoherent detection schemes. The final conclusion is that while asymptotic optimality for increasing complexity can often be achieved, key issues in the design of detection algorithms are the computational efficiency and the performance for limited complexity. Index Terms MAP sequence/symbol detection, iterative detection, graphbased detection, adaptive detection, finitememory detection, Viterbi algorithm, forwardbackward algorithm, sumproduct algorithm.
LowComplexity Detection in LargeDimension MIMOISI Channels Using Graphical Models
"... Abstract—In this paper, we deal with lowcomplexity nearoptimal detection/equalization in largedimension multipleinput multipleoutput intersymbol interference (MIMOISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that nearoptimal pe ..."
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Cited by 10 (5 self)
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Abstract—In this paper, we deal with lowcomplexity nearoptimal detection/equalization in largedimension multipleinput multipleoutput intersymbol interference (MIMOISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that nearoptimal performance in MIMOISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMOISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)based graphical model with Gaussian approximation of interference (GAI). The persymbol complexities are ( 2 2) and ( ) for the MRF and the FG with GAI approaches, respectively, where and denote the number of channel uses per frame, and number of transmit antennas, respectively. These lowcomplexities are quite attractive for large dimensions, i.e., for large. From a performance perspective, these algorithms are even more interesting in largedimensions since they achieve increasingly closer to optimum detection performance for increasing. Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance ofQAM symbol detection. Index Terms—Factor graphs, graphical models, large dimensions, lowcomplexity detection, Markov random fields, multipleinput multipleoutput intersymbol interference (MIMOISI) channels, pairwise interaction, severe delay spreads. I.
Reducedcomplexity BCJR algorithm for turbo equalization
 IEEE Trans. Commun
, 2007
"... Abstract—We propose novel techniques to reduce the complexity of the wellknown Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is ..."
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Abstract—We propose novel techniques to reduce the complexity of the wellknown Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is more suitable than the original one for deriving reducedcomplexity techniques, we describe three reducedcomplexity algorithms, each of them particularly effective over one of the three different classes of channels affected by intersymbol interference (minimumphase, maximumphase, and mixedphase channels). The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques improving the effectiveness of the proposed solutions are described. Finally, we report the results of computer simulations showing the impressive performance of the proposed algorithms, and we compare them with other solutions in the literature. Index Terms—Complexity reduction, intersymbol interference (ISI), maximum a posteriori (MAP) symbol detection, turbo equalization. I.
Belief Propagation Based Decoding of Large NonOrthogonal STBCs
"... Abstract — In this paper, we present a belief propagation (BP) based algorithm for decoding nonorthogonal spacetime block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approach involves message passing on Markov random field (MRF) representation of the STBC ..."
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Abstract — In this paper, we present a belief propagation (BP) based algorithm for decoding nonorthogonal spacetime block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approach involves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode nonorthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BPbased decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves nearcapacity turbo coded BER performance; for e.g., with BP decoding of 24 × 24 STBC from CDA using BPSK (i.e., 576 real dimensions) and rate1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved. Keywords – Nonorthogonal STBCs, large dimensions, lowcomplexity decoding, belief propagation, Markov random fields, high spectral efficiencies. I.
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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Cited by 9 (0 self)
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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.
Iterative Detection for Channels With Memory
, 2007
"... In this paper, we present an overview on the design of algorithms for iterative detection over channels with memory. The starting point for all the algorithms is the implementation of softinput softouput maximum a posteriori (MAP) symbol detection strategies for transmissions over channels encom ..."
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Cited by 4 (1 self)
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In this paper, we present an overview on the design of algorithms for iterative detection over channels with memory. The starting point for all the algorithms is the implementation of softinput softouput maximum a posteriori (MAP) symbol detection strategies for transmissions over channels encompassing unknown parameters, either stochastic or deterministic. The proposed solutions represent effective ways to reach this goal. The described algorithms are grouped into three categories: i) we first introduce algorithms for adaptive iterative detection, where the unknown channel parameters are explicitly estimated; ii) then, we consider finitememory iterative detection algorithms, based on ad hoc truncation of the channel memory and often interpretable as based on an implicit estimation of the channel parameters; and iii) finally, we present a general detectiontheoretic approach to derive optimal detection algorithms with polynomial complexity. A few illustrative numerical results are also presented.
Bounds on the Information Rate for Sparse Channels with Long Memory and i.u.d. Inputs
"... Abstract — In this paper we propose new bounds on the achievable information rate for discretetime Gaussian channels with intersymbol interference (ISI) and independent and uniformly distributed (i.u.d.) channel input symbols drawn from finiteorder modulation alphabets. Specifically, we are intere ..."
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Cited by 3 (0 self)
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Abstract — In this paper we propose new bounds on the achievable information rate for discretetime Gaussian channels with intersymbol interference (ISI) and independent and uniformly distributed (i.u.d.) channel input symbols drawn from finiteorder modulation alphabets. Specifically, we are interested in developing new bounds on the achievable rates for sparse channels with long memory. We obtain a lower bound which can be achieved by practical receivers, based on MMSE channel shortening and suboptimal symbol detection for a reducedstate channel. An upper bound is given in the form of a semianalytical solution derived using basic information theoretic inequalities, by a grouping of the channel taps into several clusters resulting in a newly defined singleinput multipleoutput (SIMO) channel. We show that the so obtained timedispersive SIMO channel can be represented by an equivalent singleinput singleoutput (SISO) channel with a significantly shorter channel memory. The reduced computational complexity allows the use of the BCJR algorithm for the newly defined channel. The proposed bounds are illustrated through several sparse channel examples and i.u.d. input symbols, showing that the upper bound significantly outperforms existing bounds. Performance of our lower bound strongly depends on the channel structure, showing best results for minimumphase and maximumphase systems. Index Terms—Bounds, channel capacity, information rates, intersymbol interference, sparse channel. I.