Download ALGORITHMIC RESULTS IN LIST DECODING (Foundations and by Venkatesan Guruswami PDF

By Venkatesan Guruswami

Algorithmic ends up in record interpreting introduces and motivates the matter of record interpreting, and discusses the primary algorithmic result of the topic, culminating with the new effects on attaining "list interpreting capacity." the most technical concentration is on giving a whole presentation of the new algebraic effects attaining checklist deciphering potential, whereas tips or short descriptions are supplied for different works on record interpreting. Algorithmic leads to checklist deciphering is meant for students and graduate scholars within the fields of theoretical laptop technology and data concept. the writer concludes by means of posing a few attention-grabbing open questions and indicates instructions for destiny paintings.

Show description

Read Online or Download ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science) PDF

Best computers books

Graph-Theoretic Concepts in Computer Science: 15th International Workshop WG '89 Castle Rolduc, The Netherlands, June 14–16, 1989 Proceedings

The purpose of this workshop sequence is to give a contribution to integration in desktop technology by means of employing graph-theoretic suggestions. Commonalities among a variety of fields of specialization in computing device technology will be detected by way of employing graph-theoretic suggestions. The workshops are strange in that they mix theoretical elements with perform and functions.

Grid Services Engineering and Management: First International Conference, GSEM 2004, Erfurt, Germany, September 27-30, 2004. Proceedings

This ebook constitutes the refereed complaints of the 1st foreign convention on Grid providers Engineering and administration, GSEM 2004, held in Erfurt, Germany in September 2004. The eleven revised complete papers offered have been rigorously reviewed and chosen from 21 submissions. The papers are prepared in topical sections on grid provider structure, grid carrier composition, carrier safety, and grid carrier administration

Computer and intractability: a guide to the theory of NP-completeness

This book's creation includes a funny tale of a guy with a line of individuals in the back of him, who explains to his boss, "I cannot locate a good set of rules, yet neither can these kind of well-known humans. " This guy illustrates a huge caliber of a category of difficulties, specifically, the NP-complete difficulties: in the event you can turn out undefined challenge is during this classification, then it has no identified polynomial-time answer that's bound to paintings commonly.

Additional info for ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science)

Sample text

Distance trade-off, it was recently shown how to compute the required pre-processed information in polynomial time [36]. Even more generally, there is an abstract algebraic view of the decoding algorithm in the language of rings and ideals. The algorithms for RS codes, Chinese Remainder codes, and AG codes become just specific instantiations of this general algorithmic scheme for specific choices of the underlying ring and ideals. Details of the general algorithm for any “ideal-based” code that satisfies certain abstract axioms can be found in [28, Chapter 7] and [71].

Sn with each Si ⊆ Σ where all but βn of them have at most elements. In 1 of at most the first step, each i ∈ Y collects a set L2 (i, j) ⊆ Σd−1 possible symbols from the set Sj for each of its d2 neighbors, and then computes Ki = ∩(i,j)∈E2 L2 (i, j). If γ is chosen sufficiently small, for each candidate codeword that has to be output, most of the Ki s will for all i. Suppose that in fact have the correct symbol. Clearly |Ki | − 1. In this case, intuitively we at least βn of the Ki s satisfy |Ki | have made progress since the amount of “ambiguity” in those symbols has gone down from to − 1.

Proof. A polynomial Q(X, Y ) with (1, k)-weighted degree at most D can be expressed as D/k D−jk q jX Y j. 2) =0 The conditions Q(αi , yi ) = 0 for all i ∈ [n] give a system of n homogeneous linear equations in the unknowns q j . A nonzero solution to this system is guaranteed to exist if the number of unknowns, say U , exceeds the number n of equations (and if a nonzero solution exists, we can clearly find one in polynomial time by solving the above linear system). We turn to estimating U . D/k D−jk D/k (D − jk + 1) 1= U= j=0 =0 = (D + 1) j=0 D +1 k (D + 1)(D + 2) .

Download PDF sample

Rated 4.75 of 5 – based on 3 votes