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LDPC Codes for 2D Arrays

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Generalized Codes on Graphs and Applications in Content Distribution

Masoud Alipour Babaei

The contribution of this thesis is twofold. In the first part, we generalize and analyze two classes of error correcting codes: LDPC codes and product codes. We generalize graphical codes by considering checks being arbitrary codes instead of single pariti ...

EPFL2013

Irregular Product Codes

Mohammad Amin Shokrollahi, Ghid Maatouk, Seyed Omid Etesami, Masoud Alipour Babaei

We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that a ...

Ieee2012

Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC

Rüdiger Urbanke, Shrinivas Kudekar

Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed ...

2011

Array-Code Ensembles -or- Two-Dimensional LDPC Codes

Mohammad Amin Shokrollahi, Yuval Cassuto

Probabilistic construction of codes on two-dimensional arrays is proposed and analyzed. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic model of limiting the number of column fai ...

IEEE Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Universal Rateless Codes From Coupled LT Codes

Rüdiger Urbanke, Vahid Aref

It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We study the performanc ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Practical code design for compute-and-forward

Michael Christoph Gastpar

The Compute-and-Forward approach has been proven to be very beneficial for communication over Gaussian networks. While the theoretical results are promising, it is still not completely understood how to best apply this scheme in practice. The objective of ...

IEEE2011

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

Not Just for Errors: Codes for Fast and Secure Flash Storage

Yuval Cassuto

Error-correcting codes are normally employed in storage devices to guarantee the integrity of data in the presence of errors. This paper presents two schemes where error-correcting codes are used for entirely different purposes. In the first part of the pa ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC

Rüdiger Urbanke, Shrinivas Kudekar

Convolutional LDPC ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which s ...

IEEE2010

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