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Optimal regular LDPC codes for the binary erasure channel

Publications associées (33)

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Extremal Channels of Gallager's E-0 Under the Basic Polarization Transformations

Mine Alsan

We study the extremality of the binary erasure channel and the binary symmetric channel for Gallager's reliability function E-0 of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarizat ...

Institute of Electrical and Electronics Engineers2014

Finite-Length Scaling for Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Consider a binary-input memoryless output-symmetric channel W. Such a channel has a capacity, call it I (W), and for any R < I (W) and strictly positive constant P-e we know that we can construct a coding scheme that allows transmission at rate R with an e ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Polarization Improves E-0

Emre Telatar, Mine Alsan

We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E-0 for binary input channels. In this sense, polarization creates E-0. This observation gives yet another justification as to w ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Scaling Exponent of List Decoders with Applications to Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Motivated by the significant performance gains which polar codes experience when they are decoded with successive cancellation list decoders, we study how the scaling exponent changes as a function of the list size L. In particular, we fix the block error ...

Ieee2013

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Vahid Aref

Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemb ...

2013

Displacement Convexity - A Useful Framework for the Study of Spatially Coupled Codes

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models under message passin ...

Ieee2013

Spatially coupled ensembles universally achieve capacity under belief propagation

Rüdiger Urbanke, Shrinivas Kudekar

We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a-priori threshold of the u ...

2012

Universal bounds on the scaling behavior of polar codes

Rüdiger Urbanke, Seyed Hamed Hassani, Ali Goli

We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the ...

2012

Polar Coding Theorems for Discrete Systems

Eren Sasoglu

Polar coding is a recently invented technique for communication over binary-input memoryless channels. This technique allows one to transmit data at rates close to the symmetric-capacity of such channels with arbitrarily high reliability, using low-complex ...

EPFL2011

On the scaling of polar codes: II. The behavior of un-polarized channels

Rüdiger Urbanke, Seyed Hamed Hassani

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bha ...

IEEE2010