S. M. Aji, G. Horn, R. J. McEliece, and M. Xu. Iterative min-sum decoding of tail-biting codes. In Proc. IEEE Information Theory Workshop, Killarney Ireland, pages 68-69, June 1998. Home/Search Document Details and Download
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On the Theory of Linear Trellises - Koetter, Vardy (2002) (Correct)
....trellises. Numerous examples are known [2, 7, 11] where the complexity of a tailbiting trellis is much lower than the complexity of the best possible conventional trellis for the same code. Tail biting trellises for block codes were studied by several authors [2, 3, 11, 12] including McEliece [1]. However, such trellises are not yet well understood: we certainly know much less about tail biting trellises than about conventional trellises. McEliece [10] introduced in 1996 the class of simple linear trellises. He thus made an important distinction between trellis structures that possess ....
....C of length n over A if the set of all such n tuples is precisely the set of codewords of C . Tail biting trellises have been traditionally used as a means of terminating a convolutional code without incurring a rate loss. More recently, tail biting trellises for block codes were considered in [1, 2, 6, 11, 15] and other works. Such trellises may be viewed (cf. 2, 15] as a generalization of a conventional trellis to a circular time axis. Definition 2.2. A tail biting trellis T = V; E; A) of depth n is an edgelabeled directed graph with the following property: the vertex set V can be partitioned into ....
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S. Aji, G. Horn, R.J. McEliece, and M. Xu, "Iterative min-sum decoding of tail-biting codes," pp. 15--24 in Proc. Allerton Conference Comm., Control, and Computing, Monticello, IL, September 1998.
The Structure of Tail-Biting Trellises: Minimality and Basic.. - Koetter, Vardy (2002) (Correct)
....The recent development of iterative decoding techniques [35, 14] has led to a vivid interest in factor graphs. While the performance of iterative decoding on general graphs with cycles remains somewhat of a mystery, iterative decoding of tail biting trellises is by now reasonably well understood [1, 2, 7, 22, 25]. Thus the major remaining problem with tail biting trellises is that of ecient construction. Given a linear block code C over the nite eld F q , how can one construct a minimal tail biting trellis for C Although several examples of such trellises are known [3] the understanding of minimal ....
....(x 0 ; x 1 ; x 4 ) 01011) There are eight possible spans for x in a tail biting trellis, namely (1; 4] 3; 1] 0; 4] 1; 0] 2; 1] 3; 2] 4; 3] and [0; 4] I. Of these, only (1; 4] 0; 4] and [0; 4] are possible spans for x in a conventional trellis. 0 0 0 0 0 1 0 1 1 ] [ 0 1 0 1 1 ] [ 0 1 0 1 1 ] 0 1 0 1 1 ] 0 1 0 1 1 ] 0 1 0 1 1 ] 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 w w w 0 1 0 w c. 0 1 1 1 0 2 2 2 0 b. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ....
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S. Aji, G. Horn, R.J. McEliece, and M. Xu, \Iterative min-sum decoding of tail-biting codes," IEEE Workshop on Inform. Theory, Killarney, Ireland, pp. 68-69, June 1998.
Iterative Min-Sum Decoding of Tail-biting Codes - Aji, Horn, McEliece, Xu (1998) (3 citations) Self-citation (Aji Horn Mceliece Xu) (Correct)
....of a tail biting code will be effective if and only if the minimum pseudoweight of the code is strictly greater than its ordinary minimum weight. Closely related results were discovered independently by Wiberg in his thesis [15] and by Forney et al., in [10] This paper is an extension of [2]. Besides containing some new results on pseudoweights, this paper also includes results for the BSC as well. 2 Perron Frobenius Theorem for the min sum semiring In this section we will state without proof a Perron Frobenius theorem for the min sum semiring, which explains the behavior of the ....
S. M. Aji, G. B. Horn, R. J. McEliece, and M. Xu, "Iterative min-sum decoding of tail-biting codes," Proc. IEEE Information Theory Workshop, Killarney Ireland, June 1998. pp. 68-69.
Tree Consistency and Bounds on the Performance of the.. - Wainwright, Jaakkola, .. (2002) (4 citations) (Correct)
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S. M. Aji, G. Horn, R. J. McEliece, and M. Xu. Iterative min-sum decoding of tail-biting codes. In Proc. IEEE Information Theory Workshop, Killarney Ireland, pages 68-69, June 1998.
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