Searching for authors named "Alexander Vardy" – sorted by Relevance.
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Full-rank Tilings of ... Do Not Exist
- We show that there are no full-rank tilings of F 2 , using a carefully designed exhaustive search. This solves an open problem posed in [5] and implies that a full-rank perfect binary code of length 15 with a kernel of dimension 7 does not exist.
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Decoding of Reed Solomon Codes for Additive Cost Functions
- this paper we investigate the case of arbitrary additive cost functions de ned on the product space Fq Y . Such a cost function includes both Hamming and generalized Hamming metric as well as log-likelihood based costs as special cases
- Cited by 4 (1 self) – Add To MetaCart
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A Complexity Reducing Transformation in Algebraic List Decoding of Reed-Solomon Codes
- The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of ReedSolomon codes are interpolation and factorization. A series of transformations is given for the interpolation problem that arises in these decoding algorithms. These transformations reduce the space
- Cited by 8 (3 self) – Add To MetaCart
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On the Theory of Linear Trellises
- Trellis linearity, first considered by McEliece in 1996, turns out to be crucial in the study of tail-biting trellises. In this chapter, basic structural properties of linear trellises are investigated. A rigorous definition of linearity is given for both conventional and tail-biting trellises.
- Cited by 9 (1 self) – Add To MetaCart
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The Structure of Tail-Biting Trellises: Minimality and Basic Principles
- Basic structural properties of tail-biting trellises are investigated. We start with rigorous definitions of various types of minimality for tail-biting trellises.
- Cited by 14 (1 self) – Add To MetaCart
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Soft decoding of Reed Solomon codes and optimal weight assignments
- A polynomial-time decoding algorithm for Reed-Solomon codes is developed in the context of interpolation based decoding algorithms. The developed algorithm maximizes the error correction capability of the code for a given additive cost function. A tight bound is given on the maximum additive error
- Cited by 2 (0 self) – Add To MetaCart
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Lexicographic Codes: Constructions Bounds, and Trellis Complexity
- We study lexicographic codes, which are generated by an iterative greedy construction. We analyze the relationship between successive iterations in this construction, and derive bounds on the parameters of the resulting codes that are tighter than the presently known bounds. Furthermore, we generali
- Cited by 1 (0 self) – Add To MetaCart
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Ordered Binary Decision Diagrams and Minimal Trellises
- Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a p
- Cited by 2 (1 self) – Add To MetaCart
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Maximum-likelihood decoding of Reed-Solomon codes is NP-hard
- Maximum-likelihood decoding is one of the central algorithmic problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether maximum-likelihood decoding remains hard for any specific fami
- Cited by 16 (2 self) – Add To MetaCart
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Algebraic Soft-Decision Decoding of Reed-Solomon Codes
- A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed.
- Cited by 68 (13 self) – Add To MetaCart

