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

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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

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

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

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

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

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

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

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

Finite-Length Scaling for Polar Codes

Polarization Improves E-0

Scaling Exponent of List Decoders with Applications to Polar Codes

On the Convergence Speed of Spatially Coupled LDPC Ensembles

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

Universal bounds on the scaling behavior of polar codes

Polar Coding Theorems for Discrete Systems

Phase Transitions for Mutual Information

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

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

Universal bounds on the scaling behavior of polar codes

Finite-Length Scaling for Polar Codes

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

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

Phase Transitions for Mutual Information

Polarization Improves E-0

Scaling Exponent of List Decoders with Applications to Polar Codes

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Polar Coding Theorems for Discrete Systems