List Decoding with Double Samplers
Autor: | Tali Kaufman, Inbal Livni Navon, Amnon Ta-Shma, Irit Dinur, Prahladh Harsha |
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Rok vydání: | 2019 |
Předmět: |
FOS: Computer and information sciences
General Computer Science Computer science General Mathematics Subroutine Pseudorandomness List decoding Data_CODINGANDINFORMATIONTHEORY 0102 computer and information sciences 02 engineering and technology High dimensional Computational Complexity (cs.CC) 01 natural sciences Computer Science - Data Structures and Algorithms 0202 electrical engineering electronic engineering information engineering Data Structures and Algorithms (cs.DS) Large distance Mathematics Discrete mathematics Pseudorandom number generator Base code 020206 networking & telecommunications Computer Science - Computational Complexity 010201 computation theory & mathematics Expander graph Algorithm Decoding methods Coding (social sciences) |
Zdroj: | Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms |
DOI: | 10.1137/1.9781611975482.129 |
Popis: | We strengthen the notion of "double samplers", first introduced by Dinur and Kaufman [Proc. 58th FOCS, 2017], which are samplers with additional combinatorial properties, and whose existence we prove using high dimensional expanders. The ABNNR code construction [IEEE Trans. Inform. Theory, 38(2):509--516, 1992] achieves large distance by starting with a base code $C$ with moderate distance, and then amplifying the distance using a sampler. We show that if the sampler is part of a larger double sampler then the construction has an efficient list-decoding algorithm. Our algorithm works even if the ABNNR construction is not applied to a base code $C$ but to any string. In this case the resulting code is approximate-list-decodable, i.e. the output list contains an approximation to the original input. Our list-decoding algorithm works as follows: it uses a local voting scheme from which it constructs a unique games constraint graph. The constraint graph is an expander, so we can solve unique games efficiently. These solutions are the output of the list decoder. This is a novel use of a unique games algorithm as a subroutine in a decoding procedure, as opposed to the more common situation in which unique games are used for demonstrating hardness results. Double samplers and high dimensional expanders are akin to pseudorandom objects in their utility, but they greatly exceed random objects in their combinatorial properties. We believe that these objects hold significant potential for coding theoretic constructions and view this work as demonstrating the power of double samplers in this context. |
Databáze: | OpenAIRE |
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