V. Guruswami. List Decoding of Error-correcting codes. PhD thesis, Massachusetts Institute of Technology, Boston, MA, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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Coding Theory: Tutorial Survey - Sudan (Correct)
....decoding. Notable omissions from this article are the non algebraic constructions, and the work on the side of highly ecient encoding. Applications of codes to theoretical computer science abound (cf. 90, Lecture 9] and new ones continue to emerge at a regular rate (see the thesis of Guruswami [40] for many recent connections) However we will not describe any here. 2 Bounds and constructions for codes 2.1 The random linear code Perhaps the most classical code is the random code and the random linear code. Hints that the random code are likely to be quite good in performance were ....
....of results revolving around list decoding is growing even as we write this article, shedding further light on its combinatorial signi cance, algorithmic capability, and use in theoretical computer science. A good starting point for further reading on this topic may be the thesis of Guruswami [40]. 4 Conclusions In summary we have hope to have introduced coding theory to a wide audience and convinced them that this eld contains a wealth of results, while also o ering the potential for new research problems. In particular some central algorithmic questions of coding theory, both in the ....
Venkatesan Guruswami. List decoding of Errorcorrecting codes. Ph.D. Thesis. Massachusetts Institute of Technology, 2001.
Reflections on "Improved Decoding of Reed-Solomon.. - Guruswami, Sudan (2002) Self-citation (Guruswami) (Correct)
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Venkatesan Guruswami. List Decoding of Error-Correcting Codes. PhD thesis, Massachusetts Institute of Technology, August 2001.
Limits to List Decodability of Linear Codes - Guruswami (2002) Self-citation (Guruswami) (Correct)
....positions. It thus permits recovery beyond d=2 errors. After a long hiatus since its introduction nearly four decades ago by Elias [2] and Wozencraft [21] list decoding has recently seen a spurt of activity, especially in the design of algorithms for list decoding important families of codes (see [6] for details and pointers about the recent work on list decoding) In order to eciently list decode a certain code C up to, say, e errors, it is important to have an a priori guarantee that every Hamming ball of radius e will have only a small (say, polynomial in block length) number of ....
Venkatesan Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
Combinatorial Bounds for List Decoding - Guruswami, Håstad, Sudan.. (2000) (1 citation) Self-citation (Guruswami) (Correct)
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V. Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
List Decoding from Erasures: Bounds and Code Constructions - Guruswami (2001) (1 citation) Self-citation (Guruswami) (Correct)
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V. Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
Decoding Concatenated Codes using Soft Information - Guruswami, Sudan (2001) Self-citation (Guruswami) (Correct)
.... (since a random received word will differ from each codeword in an expected fraction (1 1=q) of positions) In addition to their obvious relevance to coding theory, codes which correct such a large fraction of errors have also found use in several complexity theoretic applications (see [Sud00] or [Gur01, Chap. 12] for a discussion) Having fixed the desired error resilience of the code, the goal is to achieve good rate together with fast construction and decoding times. We first review the known results concerning this problem that appear in [GS00, GHSZ00] For the binary case, the construction ....
.... the code, the maximum bound up to which we are guaranteed to have a small number of codewords within distance R of r) Then we have X c2C maxf(R (r; c) 0 g 2 n 2 (2) Proof: The proof follows essentially the same approach as in the proof of the Johnson bound (see, for example, Gur01, Chap. 3] which gives an upper bound on the the number of codewords within a distance R from r. We now require an upper bound on the sum of squares of linear functions of the distance over all such codewords. We identify elements of [q] with vectors in R q by replacing the symbol i (1 i ....
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Venkatesan Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
Combinatorial Bounds for List Decoding - Guruswami, Håstad, Sudan.. (2000) (1 citation) Self-citation (Guruswami) (Correct)
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V. Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
Linear-time Codes to Correct a Maximum Possible Fraction of.. - Guruswami, Indyk (2001) Self-citation (Guruswami) (Correct)
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V. Guruswami. List Decoding of Error-Correcting Codes. PhD thesis, Massachusetts Institute of Technology, August 2001.
List Decoding from Erasures: Bounds and Code Constructions - Guruswami (2001) (1 citation) Self-citation (Guruswami) (Correct)
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V. Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
Multicast Authentication in Fully Adversarial Networks - Anna Lysyanskaya Roberto (Correct)
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V. Guruswami. List Decoding of Error-correcting codes. PhD thesis, Massachusetts Institute of Technology, Boston, MA, 2001.
Some Applications of Coding Theory in Computational Complexity - Trevisan (2004) (Correct)
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Venkatesan Guruswami. List Decoding of Error-Correcting Codes. PhD thesis, MIT, 2001.
SIGACT News Complexity Theory Column 38 - Lane Hemaspaandra Dept (Correct)
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V. Guruswami. List decoding of error-correcting codes. PhD thesis, M.I.T., 2001.
Near-Optimal Linear-Time Codes for Unique Decoding and New.. - Guruswami, Indyk (2002) (2 citations) (Correct)
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Venkatesan Guruswami. List Decoding of Error-Correcting Codes. Ph.D thesis, Massachusetts Institute of Technology, August 2001.
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