TY - GEN
T1 - LCC and LDC
T2 - 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
AU - Cohen, Gil
AU - Yankovitz, Tal
N1 - Publisher Copyright:
© Gil Cohen and Tal Yankovitz; licensed under Creative Commons License CC-BY 4.0
PY - 2022/7/1
Y1 - 2022/7/1
N2 - The Alon-Edmonds-Luby distance amplification procedure (FOCS 1995) is an algorithm that transforms a code with vanishing distance to a code with constant distance. AEL was invoked by Kopparty, Meir, Ron-Zewi, and Saraf (J. ACM 2017) for obtaining their state-of-the-art LDC, LCC and LTC. Cohen and Yankovitz (CCC 2021) devised a procedure that can amplify inverse-polynomial distances, exponentially extending the regime of distances that can be amplified by AEL. However, the improved procedure only works for LDC and assuming rate (Equation presented). 1 In this work we devise a distance amplification procedure for LCC with inverse-polynomial distances even for vanishing rate (Equation presented). For LDC, we obtain a more modest improvement and require rate (Equation presented). Thus, the tables have turned and it is now LCC that can be better amplified. Our key idea for accomplishing this, deviating from prior work, is to tailor the distance amplification procedure to the code at hand. Our second result concerns the relation between linear LDC and LCC. We prove the existence of linear LDC that are not LCC, qualitatively extending a separation by Kaufman and Viderman (RANDOM 2010).
AB - The Alon-Edmonds-Luby distance amplification procedure (FOCS 1995) is an algorithm that transforms a code with vanishing distance to a code with constant distance. AEL was invoked by Kopparty, Meir, Ron-Zewi, and Saraf (J. ACM 2017) for obtaining their state-of-the-art LDC, LCC and LTC. Cohen and Yankovitz (CCC 2021) devised a procedure that can amplify inverse-polynomial distances, exponentially extending the regime of distances that can be amplified by AEL. However, the improved procedure only works for LDC and assuming rate (Equation presented). 1 In this work we devise a distance amplification procedure for LCC with inverse-polynomial distances even for vanishing rate (Equation presented). For LDC, we obtain a more modest improvement and require rate (Equation presented). Thus, the tables have turned and it is now LCC that can be better amplified. Our key idea for accomplishing this, deviating from prior work, is to tailor the distance amplification procedure to the code at hand. Our second result concerns the relation between linear LDC and LCC. We prove the existence of linear LDC that are not LCC, qualitatively extending a separation by Kaufman and Viderman (RANDOM 2010).
KW - Distance Amplifications
KW - Locally Correctable Codes
KW - Locally Decodable Codes
UR - http://www.scopus.com/inward/record.url?scp=85133439013&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2022.44
DO - 10.4230/LIPIcs.ICALP.2022.44
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AN - SCOPUS:85133439013
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
A2 - Bojanczyk, Mikolaj
A2 - Merelli, Emanuela
A2 - Woodruff, David P.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Y2 - 4 July 2022 through 8 July 2022
ER -