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Title: Explicit Time and Space Efficient Encoders Exist Only with Random Access
We give the first explicit constant rate, constant relative distance, linear codes with an encoder that runs in time n^{1 + o(1)} and space polylog(n) provided random access to the message. Prior to this work, the only such codes were non-explicit, for instance repeat accumulate codes [Divsalar et al., 1998] and the codes described in [Gál et al., 2013]. To construct our codes, we also give explicit, efficiently invertible, lossless condensers with constant entropy gap and polylogarithmic seed length. In contrast to encoders with random access to the message, we show that encoders with sequential access to the message can not run in almost linear time and polylogarithmic space. Our notion of sequential access is much stronger than streaming access.  more » « less
Award ID(s):
2200956
PAR ID:
10585119
Author(s) / Creator(s):
;
Editor(s):
Santhanam, Rahul
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
300
ISSN:
1868-8969
ISBN:
978-3-95977-331-7
Page Range / eLocation ID:
5:1-5:54
Subject(s) / Keyword(s):
Time-Space Trade Offs Error Correcting Codes Encoders Explicit Constructions Streaming Lower Bounds Sequential Access Time-Space Lower Bounds Lossless Condensers Invertible Condensers Condensers Theory of computation → Error-correcting codes Theory of computation → Expander graphs and randomness extractors Theory of computation → Streaming models Theory of computation → Lower bounds and information complexity
Format(s):
Medium: X Size: 54 pages; 1089147 bytes Other: application/pdf
Size(s):
54 pages 1089147 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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