Publications related to Using low density parity check codes in the McEliece cryptosystem

Polar codes for channel and source coding

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 ...

EPFL2009

On communication over discrete memoryless channels with noiseless feedback

Peter Allan Berlin

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 ...

EPFL2008

Decay of Correlations: An Application to Low-Density Parity Check codes

Nicolas Macris, Shrinivas Kudekar

Recently the decay of correlations between bits of low density generator matrix (LDGM) codes have been investigated by using high temperature expansions from statistical physics \cite{KuMa07}. In this work we apply these ideas to a special class of low den ...

IEEE2008

Exchange of Limits: Why Iterative Decoding Works

Rüdiger Urbanke, Satish Babu Korada

We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes under MP decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given by density e ...

2008

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

Nicolas Macris, Satish Babu Korada, Shrinivas Kudekar

We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...

2007

Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes

Nicolas Macris

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

Systems and processes for fast encoding of hamming codes

Mohammad Amin Shokrollahi

Decoding that uses an extended Hamming code in one of the primary stages of static encoding uses a calculation of the r+1 Hamming redundant symbols for k input symbols from which Hamming redundant symbols are calculated, where r satisfies 2.sup.r-1-r.ltore ...

2007

System and method for reliably communicating the content of a live data stream

Mohammad Amin Shokrollahi

A method for communicating the content of a live data stream to a receiver using a plurality of channels comprising two encoder channels used to encode the live data content prior to transmission. Initially a plurality of segments of a live data stream are ...

2007

Weight Distribution of Low-Density Parity-Check Codes

Rüdiger Urbanke, Changyan Di

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 ...

2006

Computational Hardness and Explicit Constructions of Error Correcting Codes

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

We outline a procedure for using pseudorandom generators to construct binary codes with good properties, assuming the existence of sufficiently hard functions. Specifically, we give a polynomial time algorithm, which for every integers

n

and

k

, constru ...

2006

Using low density parity check codes in the McEliece cryptosystem

Graph Chatbot

Chat with Graph Search

Polar codes for channel and source coding

On communication over discrete memoryless channels with noiseless feedback

Decay of Correlations: An Application to Low-Density Parity Check codes

Exchange of Limits: Why Iterative Decoding Works

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes

Systems and processes for fast encoding of hamming codes

System and method for reliably communicating the content of a live data stream

Weight Distribution of Low-Density Parity-Check Codes

Computational Hardness and Explicit Constructions of Error Correcting Codes

Weight Distribution of Low-Density Parity-Check Codes

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

On communication over discrete memoryless channels with noiseless feedback

Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes

Systems and processes for fast encoding of hamming codes

Decay of Correlations: An Application to Low-Density Parity Check codes

Exchange of Limits: Why Iterative Decoding Works

System and method for reliably communicating the content of a live data stream

Computational Hardness and Explicit Constructions of Error Correcting Codes

Polar codes for channel and source coding