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Improved decoding of second-order Reed-Muller codes

Publications associées (64)

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Phase Transitions for Mutual Information

Mohammad Amin Shokrollahi, Krishna Kumar, Amir Hesam Salavati, Raj Kumar Krishna Kumar

We consider ensembles of binary linear error correcting codes, obtained by sampling each column of the generator matrix G or parity check matrix H independently from the set of all binary vectors of weight d (of appropriate dimension). We investigate the c ...

IEEE2010

Universal a posteriori metrics game

Emmanuel Abbé, Rethnakaran Pulikkoonattu

Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we address a similar qu ...

2010

Linear Universal Decoder for Compound Discrete Memoryless Channels

Rethnakaran Pulikkoonattu

Shannon in his seminal work \cite{paper:shannon} formalized the framework on the problem of digital communication of information and storage. He quantified the fundamental limits of compression and transmission rates. The quantity \textit{channel capacity} ...

2009

Source and channel coding using Fountain codes

Bertrand Ndzana Ndzana

The invention of Fountain codes is a major advance in the field of error correcting codes. The goal of this work is to study and develop algorithms for source and channel coding using a family of Fountain codes known as Raptor codes. From an asymptotic poi ...

EPFL2009

Non-binary LDPC codes and EXIT like functions

In the first part of this thesis we are interested in the asymptotic performance analysis of Non-Binary Low-Density Parity-Check (NBLDPC) codes over the Binary Erasure Channel (BEC) decoded via the suboptimal Belief Propagation (BP) decoder as well as the ...

EPFL2008

On the Power of Imperfect Information

Laurent Doyen

We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids su ...

2008

Cryptography based on error correcting codes

Lorenz Minder

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 ...

EPFL2007

Cooperative source coding with encoder breakdown

Etienne Perron, Dinkar Vasudevan

This paper provides an inner bound to the rate-distortion region of a source coding setup in which two encoders are allowed some collaboration to describe a pair of discrete memoryless sources. We further require some robustness in case one of the encoders ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

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

Finite-Length Scaling For Gallager A

Rüdiger Urbanke, Jérémie Ezri

We consider LDPC codes, transmission over the binary symmetric channel (BSC), and decoding using Gallager's algorithm A. For those ensembles whose threshold is determined by the behavior of the algorithm at the beginning of the decoding process we derive a ...

2006

Computational Hardness and Explicit Constructions of Error Correcting Codes

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

n

and

k

, constru ...

2006