By Venkatesan Guruswami
Algorithmic ends up in checklist deciphering introduces and motivates the matter of record interpreting, and discusses the principal algorithmic result of the topic, culminating with the hot effects on reaching "list interpreting capacity." the most technical concentration is on giving an entire presentation of the hot algebraic effects attaining checklist interpreting means, whereas guidelines or short descriptions are supplied for different works on checklist interpreting. Algorithmic ends up in record interpreting is meant for students and graduate scholars within the fields of theoretical laptop technological know-how and knowledge conception. the writer concludes via posing a few attention-grabbing open questions and indicates instructions for destiny paintings.
Read Online or Download ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science) PDF
Similar computers books
2015 Reprint of 1956 Printing. complete facsimile of the unique variation. no longer reproduced with Optical reputation software program. Cybernetics is right here outlined as "the technology of regulate and conversation, within the animal and the machine"-in a observe, because the artwork of steersmanship; and this booklet will curiosity all who're attracted to cybernetics, communique concept and techniques for legislation and keep an eye on.
This ebook comprises chosen papers of the 1st overseas Workshop on Model-Based software program and knowledge Integration 2008, held in Berlin, Germany, in April 2008 as part of the Berlin software program Integration Week 2008. The nine revised complete papers offered including three invited lectures have been rigorously reviewed and chosen from quite a few submissions.
- Eurocal '87: European Conference on Computer Algebra Leipzig, GDR, June 2–5, 1987 Proceedings
- Illustrator CS4 For Dummies (For Dummies (Computer Tech))
- Brief Guide To Stata Commands
- Theory Is Forever: Essays Dedicated to Arto Salomaa on the Occasion of His 70th Birthday
Extra info for ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science)
The subgraph of HH that corresponds to the codeword c. In other words, V (c) contains the nodes in A that are compatible with c. The key fact, easily proved by induction, is that if (i, t) ∈ V (c), and (i , t ) ∈ A is reachable from (i, t) in HH, then (i , t ) ∈ V (c). Hence V (c) will be the union of the vertices in A that belong to some subset of connected components of HH. The fault-tolerance property of G can be shown to imply that one of these connected components must contain at least n/10 vertices.
It is also useful in decoding concatenated codes, where the inner decoder can provide weights along with the choices it outputs, which can then be used by a soft-decision decoder for the outer code. As mentioned in , the multiplicity based interpolation lends itself naturally to a soft-decision version, since the multiplicity required at a point can encode the importance of that point. Given weights wi,γ for positions i ∈ [n] and ﬁeld elements α ∈ F, we set the multiplicity of the point (αi , γ) to be proportional to wi,γ .
3. Let z ∈ (Fm )N and let y ∈ Fn be the unfolded version of z. Let Q(X, Y1 , Y2 ) be any nonzero polynomial over F of (1, k, k)weighted degree at D which has a zero of multiplicity r at (γ i , yi , yi+1 ) D . Then for i = 0, 1, . . , n − 1. Let t be an integer such that t > (m−1)r every polynomial f (X) ∈ F[X] of degree at most k whose encoding according to FRSF,γ,m,k agrees with z on at least t locations satisﬁes Q(X, f (X), f (γX)) ≡ 0. 3 motivate the following approach to list decoding the folded RS code FRSF,γ,m,k .
ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science) by Venkatesan Guruswami