By Venkatesan Guruswami
Algorithmic leads to checklist interpreting introduces and motivates the matter of record deciphering, and discusses the relevant algorithmic result of the topic, culminating with the new effects on attaining "list deciphering capacity." the most technical concentration is on giving an entire presentation of the new algebraic effects reaching checklist deciphering skill, whereas tips or short descriptions are supplied for different works on checklist deciphering. Algorithmic ends up in checklist deciphering is meant for students and graduate scholars within the fields of theoretical computing device technology and data thought. the writer concludes via posing a few fascinating open questions and indicates instructions for destiny paintings.
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Additional resources for ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science)
Error-correction radius trade-oﬀ, however, is not optimized and is signiﬁcantly worse than what can be achieved with algebraic codes such as RS codes. The results of this chapter are not needed for Part II of the survey, so we will be content with stating the main results and deﬁnitions, and giving very high level descriptions of the central ideas. We will also provide pointers to the literature where further details on the proofs can be found. 2) plays a crucial role in the graph-based constructions.
For every integer 1, there exist R > 0, γ > 0, and a ﬁnite alphabet Σ for which there is an explicit family of codes of rate R( ) over alphabet Σ that are encodable as well as (γ , , )-listrecoverable in linear time. 1, one gets the following result of Guruswami and Indyk  on linear-time list-decodable codes for correcting any desired constant fraction of errors. 3. 2. Both expanders and the notion of list recovering play a prominent role throughout the construction and proof in . The construction (γ , , )-list recoverable codes proceeds recursively using a construction of (γ −1 , − 1, − 1)-list-recoverable codes (γ will recursively depend on γ −1 ).
2. A toy list recovering problem 155 decoding procedure consists of two cases. The ﬁrst case occurs when the set I has size at least n/10. In this case, we know at least 10% of symbols of c, and thus we can recover c using the linear-time erasuredecoding algorithm for the code C. It remains to consider the second case, when the size of the set I is smaller than n/10. Consider any i∈ / I. Observe that, for all (i, j) ∈ E, all sets L(i, j) must be equal to Ki . The set Ki contains two distinct symbols that are candidates for ci .
ALGORITHMIC RESULTS IN LIST DECODING (Foundations and Trends(R) in Theoretical Computer Science) by Venkatesan Guruswami