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List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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TL;DR: In this article, the authors show that the ability to trace with the IPP algorithm implies the ability of tracing with the TA algorithm when using an algebraic structure, and they also construct schemes with an algorithm that finds all possible traitor coalitions faster than the TA tracing algorithm.
Abstract: We use powerful new techniques for list decoding errorcorrecting codes to efficiently trace traitors. Although much work has focusedon constructing traceability schemes, the complexity of the tracing algorithm has receivedlittle attention. Because the TA tracing algorithm has a runtime of O(N) in general, where N is the number of users, it is inefficient for large populations.We produce schemes for which the TA algorithm is very fast. The IPP tracing algorithm, though less efficient, can list all coalitions capable of constructing a given pirate. We give evidence that when using an algebraic structure, the ability to trace with the IPP algorithm implies the ability to trace with the TA algorithm. We also construct schemes with an algorithm that finds all possible traitor coalitions faster than the IPP algorithm. Finally, we suggest uses for other decoding techniques in the presence of additional information about traitor behavior.
43 citations
TL;DR: It is shown that Reed-Solomon codes are twice better with respect to the number of locked positions than binary BCH codes; in fact, they are optimal.
Abstract: The use of syndrome coding in steganographic schemes tends to reduce distortion during embedding. The more complete model comes from the wet papers (J. Fridrich et al., 2005) and allow to lock positions which cannot be modified. Recently, binary BCH codes have been investigated and seem to be good candidates in this context (D. Schonfeld and A. Winkler, 2006). Here, we show that Reed-Solomon codes are twice better with respect to the number of locked positions; in fact, they are optimal. First, a simple and efficient scheme based on Lagrange interpolation is provided to achieve the optimal number of locked positions. We also consider a new and more general problem, mixing wet papers (locked positions) and simple syndrome coding (low number of changes) in order to face not only passive but also active wardens. Using list decoding techniques, we propose an efficient algorithm that enables an adaptive tradeoff between the number of locked positions and the number of changes.
42 citations
Journal Article•
TL;DR: This paper precisely characterize the region of all pairs (α β) for which one-sided unique decoding is possible in a way that Alice will output the correct answer, and suggests that in some error regimes, list-decoding is necessary for optimal unique decoding.
Abstract: In this paper, we extend the notion of list decoding to the setting of interactive communication and study its limits. In particular, we show that any protocol can be encoded, with a constant rate, into a list-decodable protocol which is resilient to a noise rate of up to $\frac{1}{2}-\varepsilon$, and that this is tight. Using our list-decodable construction, we study a more nuanced model of noise where the adversary can corrupt up to a fraction $\alpha$ of Alice's communication and up to a fraction $\beta$ of Bob's communication. We use list decoding to characterize fully the region $\mathcal{R}_U$ of pairs $(\alpha,\beta)$ for which unique decoding with a constant rate is possible. The region $\mathcal{R}_U$ turns out to be quite unusual in its shape. In particular, it is bounded by a piecewise-differentiable curve with infinitely many pieces. We show that outside this region the rate must be exponential. This suggests that in some error regimes, list decoding is necessary for optimal unique decoding. ...
42 citations
TL;DR: A new bounded-distance decoding algorithm is presented for the hexacode, which requires at most 34 real operations in the worst case, as compared to 57 such Operations in the best previously known decoder.
Abstract: We present a new bounded-distance decoding algorithm for the hexacode, which requires at most 34 real operations in the worst case, as compared to 57 such operations in the best previously known decoder. The new algorithm is then employed for bounded-distance decoding of the Leech lattice and the Golay code. The error-correction radius of the resulting decoders is equal to that of a maximum-likelihood decoder. The resulting decoding complexity is at most 331 real operations for the Leech lattice and at most 121 operations for the Golay code. For all the three codes-the hexacode, the Golay code, and the Leech lattice-the proposed decoders are considerably more efficient than any decoder presently known. >
42 citations
11 Aug 2014
TL;DR: A new family of protograph-based codes with no punctured variable nodes is presented, constructed by using differential evolution, partial brute force search, and the lengthening method introduced by Nguyen et al.
Abstract: A new family of protograph-based codes with no punctured variable nodes is presented. The codes are constructed by using differential evolution, partial brute force search, and the lengthening method introduced by Nguyen et al.. The protograph ensembles satisfy the linear minimum distance growth property and have the lowest iterative decoding thresholds yet reported in the literature among protograph codes without punctured variable nodes. Simulation results show that the new codes perform better than state-of-the-art protograph codes when the number of decoding iterations is small.
42 citations