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Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval

Vajha, Myna and Ramkumar, Vinayak and Kumar, P Vijay (2017) Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval. In: IEEE International Symposium on Information Theory (ISIT), JUN 25-30, 2017, Aachen, GERMANY, pp. 2648-2652.

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Official URL: http://dx.doi.org/ 10.1109/ISIT.2017.8007009

Abstract

The notion of a Private Information Retrieval (PIR) code was recently introduced by Fazeli, Vardy and Yaakobi 1] who showed that this class of codes permit PIR at reduced levels of storage overhead in comparison with rephcated-server PIR. In the present paper, the construction of an (n, k) tau-server binary linear PIR code having parameters n = Sigma (l)(i=0) ((m)(i)), k = ((m)(l)) and tau = 2(l) for any integer m >= l >= 0 is presented. These codes are obtained through homogeneous-polynomial evaluation and correspond to the binary. Projective Reed Muller (PRM) code. The construction can be extended to yield PIR codes for any tau is an element of{2(l), 2(l) - 1 vertical bar l is an element of Z, l >= 0} and any value of k, through a combination of single-symbol puncturing and shortening of the PRM code. Each of these code constructions above, have smaller storage overhead in comparison with known short block length codes in 1]. For the particular case of tau = 3,4, we show that the codes constructed here are optimal, systematic PIR codes by providing an improved lower bound on the block length n(k, tau) of a systematic PIR code. It follows from a result by Vardy and Yaakobi 2], that these codes also yield optimal, systematic primitive multi-set (n, k, tau)(B) batch codes for tau = 3,4. The PIR code constructions presented here also yield upper bounds on the generahzed Hamming weights of binary PRM codes.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belong to IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 18 May 2018 15:59
Last Modified: 18 May 2018 15:59
URI: http://eprints.iisc.ac.in/id/eprint/59904

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