Publications associées à Universal bounds on the scaling behavior of polar codes

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A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

Rüdiger Urbanke

Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially ...

Institute of Electrical and Electronics Engineers2015

A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

Jonathan Mark Scarlett, Albert Guillén i Fàbregas

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the Csiszar-Korner-Hui rate, thus providing a counter-example to a p ...

Institute of Electrical and Electronics Engineers2015

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

Universal Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless outputsymmetric channel. Further, both the encoding and the decoding can be accomplished in O(N log(N)) real operations, where N is the blocklength. O ...

Ieee2014

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

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

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

Rüdiger Urbanke, Seyed Hamed Hassani

We consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel W. In particular, we study the asymptotics of the cumulative distribution, P(Z(n ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Windowed Decoding of Spatially Coupled Codes

Rüdiger Urbanke

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as fo ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Universal bounds on the scaling behavior of polar codes

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A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

Finite-Length Scaling for Polar Codes

Universal Polar Codes

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

Scaling Exponent of List Decoders with Applications to Polar Codes

Polarization Theorems for Arbitrary DMCs

Generalized Codes on Graphs and Applications in Content Distribution

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

Windowed Decoding of Spatially Coupled Codes

Generalized Codes on Graphs and Applications in Content Distribution

Windowed Decoding of Spatially Coupled Codes

A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

Finite-Length Scaling for Polar Codes

Universal Polar Codes

Scaling Exponent of List Decoders with Applications to Polar Codes

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

Polarization Theorems for Arbitrary DMCs

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