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Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1791 (69 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sumproduct algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform algorithms.
Parallel Interleaving On Parallel Dsp Architectures
, 2002
"... Today's communications systems especially in the field of wireless communications rely on many different algorithms to provide applications with constantly increasing data rates and higher quality. This development combined with the wireless channel characteristics as well as the invention of t ..."
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Cited by 2 (2 self)
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Today's communications systems especially in the field of wireless communications rely on many different algorithms to provide applications with constantly increasing data rates and higher quality. This development combined with the wireless channel characteristics as well as the invention of turbo codes has particularly increased the importance of interleaver algorithms. In this paper we demonstrate the feasibility to exploit the hardware parallelism in order to accelerate the interleaving procedure. Based on a heuristic algorithm the possible speedup for different interleavers as a function of the degree of parallelism of the hardware is presented. The parallelization is generic in the sense that the assumed underlying hardware is based on a parallel datapath DSP architecture and therefore provides the flexibility of software solutions.
MULTIPATH EFFECT MITIGATION IN LPTVBASED MULTIPLE ACCESS SYSTEM
"... A multiple access system is developed in this paper by means of Linear Periodic Time Varying (LPTV) filters. We construct an LPTVbased Multiple Access (LPTVMA) system with complex modulators and matrix interleavers. This LPTVMA system has good spreading properties and small Multi User Interference ..."
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A multiple access system is developed in this paper by means of Linear Periodic Time Varying (LPTV) filters. We construct an LPTVbased Multiple Access (LPTVMA) system with complex modulators and matrix interleavers. This LPTVMA system has good spreading properties and small Multi User Interference (MUI). However, the equalization problem of such LPTV filters in stationary multipath channels remains unsolved. We show that, due to the presence of matrix interleavers, the received signal is affected by a time varying delay. By using a Zero Padding (ZP) technique, classical single user equalization techniques can be used. Further, when the users in the LPTVMA system are quasisynchronous, MUIfree transceivers can be achieved. Comparisons of the LPTVMA system with a Chip Interleaved Block Spread (CIBS) CDMA system are made in quasisynchronous and asynchronous scenarios. Simulations showed that the LPTVMA system has better performances in the asynchronous scenario than the CIBSCDMA system. 1.
Variance of the turbo code performance bound over the interleavers
 IEEE Trans. on Inform. Theory
, 2002
"... [11] D. Chase, “A class of algorithms for decoding block codes with channel measurement information, ” IEEE Trans. Inform. Theory, vol. IT18, pp. ..."
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Cited by 1 (0 self)
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[11] D. Chase, “A class of algorithms for decoding block codes with channel measurement information, ” IEEE Trans. Inform. Theory, vol. IT18, pp.
Pruned BitReversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures
, 2014
"... A mathematical characterization of seriallypruned permutations (SPPs) employed in variablelength permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct ..."
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A mathematical characterization of seriallypruned permutations (SPPs) employed in variablelength permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bitreversal permutations (BRPs) is presented, and closedform expressions for BRP statistics including descents/ascents, major index, excedances/descedances, inversions, and serial correlations are derived. It is shown that BRP sequences have weak correlation properties. Moreover, a new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardwareefficient architectures for the proposed algorithms are developed. Simulation results of interleavers employed in modern communication standards demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.
IMPROVED CLOSEDFORM BOUNDS ON THE PERFORMANCE OF CONVOLUTIONAL CODES WITH CORRELATED RAYLEIGH FADING
, 2008
"... Improved closedform bounds on the performance of convolutional codes with correlated Rayleigh fading ..."
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Improved closedform bounds on the performance of convolutional codes with correlated Rayleigh fading
HOW PERMUTATIONS DISPLACE POINTS AND STRETCH INTERVALS
"... Abstract. For pi ∈ Sn, let d(pi) be the arithmetic average of {i − pi(i); 1 ≤ i ≤ n}. Then 0 ≤ d(pi)/n ≤ 1/2, the expected value of d(pi)/n approaches 1/3 as n approaches infinity, and most permutations have d(pi)/n close to 1/3. We also describe all permutations with d(pi)/n = 1/2. Let s+(pi) and ..."
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Abstract. For pi ∈ Sn, let d(pi) be the arithmetic average of {i − pi(i); 1 ≤ i ≤ n}. Then 0 ≤ d(pi)/n ≤ 1/2, the expected value of d(pi)/n approaches 1/3 as n approaches infinity, and most permutations have d(pi)/n close to 1/3. We also describe all permutations with d(pi)/n = 1/2. Let s+(pi) and s∗(pi) be the arithmetic and geometric averages of {pi(i) − pi(i + 1); 1 ≤ i < n}, respectively. Let M+, M ∗ be the maxima of s+ and s ∗ over Sn, respectively. Then M+ = (2m2 − 1)/(2m − 1) when n = 2m, M+ = (2m2 + 2m − 1)/(2m) when n = 2m + 1, M ∗ = (mm(m + 1)m−1)1/(n−1) when n = 2m, and M ∗ = (mm(m + 1)(m + 2)m−1)1/(n−1) when n = 2m + 1> 1. We also describe all permutations pi, σ with s+(pi) =M+, s∗(σ) =M∗. 1. Motivation and