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The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...
It is shown that a correlation inequality of statistical mechanics can be applied to linear low-density parity-check codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular low-density parity-check (LDPC ...
Institute of Electrical and Electronics Engineers2007
We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns ...
We generalize the results about how to compute iterative decoding thresholds over the binary erasure channel of non-binary LDPC code ensembles of [16] to non-binary TLDPC codes [2], [3]. We show in this case how density evolution can be performed in order ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007
The fabrication of crossbar memories with sublithographic features is expected to be feasible within several emerging technologies; in all of them, the nanowire (NW) decoder is a critical part since it bridges the sublithographic wires to the outer circuit ...
The idea to use error-correcting codes in order to construct public key cryptosystems was published in 1978 by McEliece [ME1978]. In his original construction, McEliece used Goppa codes, but various later publications suggested the use of different familie ...
LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We w ...
Erasure coded storage provides a cheap and space efficient way to tolerate failures through the use of networked commodity servers. Erasure coded data is kept on n different servers out of which f can fail. By combining encoded blocks from n-f servers, the ...
The addition of a feedback link to a discrete memoryless channel does not increase its capacity, but it does bring with it other benefits. One of these benefits is an increase to the best achievable error exponent. In the first part of this thesis we revis ...
In this paper we describe some practical aspects of the design process of good Raptor codes for finite block lengths over arbitrary binary input symmetric channels. In particular we introduce a simple model for the finite-length convergence behavior of the ...
