S. M. Aji, G. B. Horn, and R. J. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," in Proceedings of IEEE International Symposium on Information Theory, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....applicable. It is well known that the resulting algorithm may not converge; moreover, when it does converge, the quality of the resulting approximations varies substantially. Recent work has yielded some insight into the dynamics and convergence properties of BP. For example, several researchers [5, 1, 30, 48] have analyzed the single cycle case, where belief propagation can be reformulated as a matrix powering method. For Gaussian processes on arbitrary graphs, two groups [49, 42] using independent methods, have shown that when BP converges, then the conditional means are exact but the error ....

S. M. Aji, G. Horn, and R. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings IEEE Intl. Symp. on Information Theory, page 276, Cambridge, MA, 1998.

....agreement in the coding community that these codes represent a genuine, and perhaps historic, breakthrough [17] a theoretical understanding of their performance has yet to be achieved. Progress in the analysis of loopy belief propagation has been made for the case of networks with a single loop [23, 24, 6, 2]. For these networks, it can be shown that: ffl Unless all the compatibilities are deterministic, loopy belief propagation will converge. ffl An analytic expression relates the correct marginals to the loopy marginals. The approximation error is related to the convergence rate of the messages ....

S.M. Aji, G.B. Horn, and R.J. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998.

....applicable. It is well known that the resulting algorithm may not converge; moreover, when it does converge, the quality of the resulting approximations varies substantially. Recent work has yielded some insight into the dynamics and convergence properties of BP. For example, several researchers [5, 1, 28, 48] have analyzed the single loop case, where belief propagation can be reformulated as a matrix powering method. For Gaussian processes on arbitrary graphs, two groups [49, 43] using independent methods, have shown that when BP converges, then the conditional means are exact but the error ....

S. Aji, G. Horn, and R. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings IEEE Intl. Symp. on Information Theory, page 276, Cambridge, MA, 1998.

....can be quite good. However, for other graphs, especially those with many relatively short cycles, the approximations of BP can be very poor. 2.3.1 Previous results on belief propagation Theoretical results on BP are available for certain special kinds of loopy graphs. A number of researchers [6, 1, 30, 47] have analyzed the single loop case, where belief propagation can be reformulated as a matrix powering method. As a result, the xed points of the message updates correspond to eigenvectors of a certain transition matrix. For Gaussian processes de ned on arbitrary graphs, two groups [49, 44] ....

S. Aji, G. Horn, and R. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings IEEE Intl. Symp. on Information Theory, page 276, Cambridge, MA, 1998.

....is known about the convergence properties of iterative probability propagation. Probability propagation in networks containing a single cycle has been successfully analyzed by Weiss (1999) and Smyth et al. 1997) and in the case of so called tail biting trellises by Forney et al. 1998) and Aji et al. 1998). However, results for networks containing many cycles are much less revealing (Wiberg 1996; Richardson 1998; Frey, Koetter and Vardy 1998; MacKay 1999) We show that iterative probability propagation converges to the correct answer within a few iterations in random factor analysis networks and ....

Aji, S. M., Horn, G. B., and McEliece, R. J. 1998. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings of IEEE International Symposium on Information Theory.

....primarily to understand loopy belief propagation in general, with single loop networks being the simplest special case. Independent of our work, several groups working in the context of errorcorrecting codes have recently obtained results on probability propagation in networks with a single loop. Aji, Horn, and McEliece (1998) have shown that iterative decoding (equivalent to belief update) of a single loop code will converge to a correct decoding for binary nodes. They also showed that the messages will converge to the principal eigenvectors of a matrix analogous to our matrix C 21 . Forney, Kschischang, and Marcus ....

Aji, S., Horn, G., & McEliece, R. (1998). On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT.

....low density parity check codes further strengthens these results [24] Another line of analytical work has aimed at understanding the behavior of belief propagation in general graphs with cycles. As a starting point, several researchers have studied the case involving a graph with a single cycle [2, 8, 28]. This case is not useful in its own right, since exact inference is tractable in the presence of a single cycle. However, the study of this case has lead to concise results that enhance our state of understanding. In particular, results pertaining to the case of a single cycle include: 1. Belief ....

S. M. Aji, G. B. Horn, and R. J. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," Proc. CISS 1998, Princeton, N.J., March 1998.

.... with coding or decoding will show that in some sense belief propagation converges with high probability to a near optimum value of the desired belief on a class of loopy DAGs [10] Progress in the analysis of loopy belief propagation has been made for the case of networks with a single loop [18, 19, 2, 1]. For the sum product (or belief update ) version it can be shown that: ffl Unless all the conditional probabilities are deterministic, belief propagation will converge. ffl There is an analytic expression relating the correct marginals to the loopy marginals. The approximation error is related ....

S.M. Aji, G.B. Horn, and R.J. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT, 1998.

....in the coding community that these codes represent a genuine, and perhaps historic, breakthrough [16] a theoretical understanding of their performance has yet to be achieved. Progress in the analysis of loopy belief propagation has been made for the case of networks with a single loop [22, 23, 6, 2]. For these networks, it can be shown that: ffl Unless all the compatibilities are deterministic, loopy belief propagation will converge. ffl An analytic expression relates the correct marginals to the loopy marginals. The approximation error is related to the convergence rate of the messages ....

S.M. Aji, G.B. Horn, and R.J. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT, 1998.

....agreement in the coding community that these codes represent a genuine, and perhaps historic, breakthrough [17] a theoretical understanding of their performance has yet to be achieved. Progress in the analysis of loopy belief propagation has been made for the case of networks with a single loop [23, 24, 6, 2]. For these networks, it can be shown that: ffl Unless all the compatibilities are deterministic, loopy belief propagation will converge. ffl An analytic expression relates the correct marginals to the loopy marginals. The approximation error is related to the convergence rate of the messages ....

S.M. Aji, G.B. Horn, and R.J. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT, 1998.

.... do with coding or decoding will show that in some sense belief propagation converges with high probability to a near optimum value of the desired belief on a class of loopy DAGs [10] Progress in the analysis of loopy belief propagation has been made for the case of networks with a single loop [18, 19, 1]. For the sum product (or belief update ) version it can be shown that: ffl Unless all the conditional probabilities are deterministic, belief propagation will converge. ffl There is an analytic expression relating the correct marginals to the loopy marginals. The approximation error is related ....

S.M. Aji, G.B. Horn, and R.J. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT, 1998.

.... 7 8 are equivalent to the Kalman filter and optimal smoothing (Gelb, 1974) In error correcting codes, both belief revision and belief update can be thought of as special cases of a general class of decoding algorithms for codes defined on graphs (Kschischang and Frey, 1998; Forney, 1997; Aji and McEliece, 1998). In nearly all the contexts surveyed above, belief propagation has only been analyzed for singly connected graphs. Note, however, that these procedures are perfectly well defined for any pairwise Markov network. This raises questions including: ffl How far is the steady state belief from the ....

....to understand loopy belief propagation in general, with single loop networks being the simplest special case. Independently of our work, several groups working in the context of error correcting codes have recently obtained results on probability propagation in networks with a single loop. Aji et al. 1998) have shown that iterative decoding (equivalent to belief update) of a single loop code will converge to a correct decoding for binary nodes. They also showed that the messages will converge to the principal eigenvectors of a matrix analogous to our matrix C 21 . Forney et al. 1998) have also ....

Aji, S., Horn, G., and McEliece, R. (1998). On the convergence of iterative decoding on graphs with a single cycle. In Proc. 1998 ISIT.

....is 1 or more than 1. IV. Iterative Decoding of Tail biting Codes The iterative min sum decoding algorithm for tail biting codes is discussed explicitly in [3, 6, 8] Our view is that it is an application of the Generalized Distributive Law [2] as applied to a junction graph with just one cycle [1]. In any case, if y is the received noisy codeword, after a finite number of iterations, the decoder will lock on to the pseudocodeword nearest to y, which is called the dominant pseudocodeword in [6] This follows from the minsum Perron Frobenius theorem (alternatively see [8] or [6] Here the ....

S. M. Aji, G. B. Horn, and R. J. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," Proc. CISS 1998 (Princeton, N.J., March 1998).

....more segments. 4 Iterative Decoding of Tail biting Codes The iterative min sum decoding algorithm for tail biting codes is discussed explicitly in [13, 5, 9, 14] Our view is that it is an application of the Generalized Distributive Law [4, 1] as applied to a junction graph with just one cycle [3]. In any case, if y is the received noisy codeword, after a finite number of iterations, the decoder will lock on to the pseudocodeword nearest to y, which is called the dominant pseudocodeword in [9] This follows from the min sum Perron Frobenius theorem (alternatively see [14] or [9] Here ....

S. M. Aji, G. B. Horn, and R. J. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," Proc. CISS 1998(Princeton, N.J., March 1998).

No context found.

S. M. Aji, G. B. Horn, and R. J. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," in Proceedings of IEEE International Symposium on Information Theory, 1998.

No context found.

S. Aji, G. Horn, and R. McEliece. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings IEEE Intl. Symp. on Information Theory, page 276, Cambridge, MA, 1998.

No context found.

S. M. Aji, G. Horn, and R. McEliece, "On the convergence of iterative decoding on graphs with a single cycle," in Proc. IEEE Intl. Symp. Information Theory, Cambridge, MA, Aug. 1998, p. 276.

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