منابع مشابه
Relaxed Locally Correctable Codes
Locally decodable codes (LDCs) and locally correctable codes (LCCs) are error-correcting codes in which individual bits of the message and codeword, respectively, can be recovered by querying only few bits from a noisy codeword. These codes have found numerous applications both in theory and in practice. A natural relaxation of LDCs, introduced by Ben-Sasson et al. (SICOMP, 2006), allows the de...
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In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...
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Arikan’s Polar codes [1] attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper bounded by β < 1 2 . Since their discovery, many attempts have been made to improve the error exponent and the finite block-length performance, while keeping...
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In this note we offer a short summary of the content of the lecture on polar Grassmann codes given at the Indian Intitute of Technology, Mumbai, during the International Conference on Algebraic Geometry and Coding Theory in December 2013. More precisely, we consider the codes arising from the projective system determined by the image ε k (∆k) of the Grassmann embedding ε gr k of an orthogonal G...
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Introduction: Polar codes are a major breakthrough in coding theory [1]. They can achieve Shannon capacity with a simple encoder and a simple successive cancellation (SC) decoder, both with low complexity of the order of ( ) N N log O , where N is the code block size. But for short and moderate lengths, the error rate performance of polar codes with the SC decoding is not as good as LDPC or tur...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2017
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2017.2657691