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Rüdiger Urbanke

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Related publications (84)

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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

Exchange of Limits: Why Iterative Decoding Works

Rüdiger Urbanke

We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes under MP decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given by density e ...

2008

Achieving Marton's Region for Broadcast Channels Using Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

This paper presents polar coding schemes for the two-user discrete memoryless broadcast channel (DM-BC) which achieve Marton's region with both common and private messages. This is the best achievable rate region known to date, and it is tight for all clas ...

Ieee-Inst Electrical Electronics Engineers Inc2015

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

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

Query Complexity of Adversarial Attacks

Rüdiger Urbanke, Grzegorz Adam Gluch

There are two main attack models considered in the adversarial robustness literature: black-box and white-box. We consider these threat models as two ends of a fine-grained spectrum, indexed by the number of queries the adversary can ask. Using this point ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

How to Prove the Maxwell Conjecture Via Spatial Coupling - A Proof of Concept

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...

Ieee2012

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels

Rüdiger Urbanke, Seyed Hamed Hassani, Shrinivas Kudekar

Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...

IEEE2018

On the Universality of Low-Density Parity-Check Block Codes

Rüdiger Urbanke, Wei Liu

An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this pape ...

IEEE2020

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 under successive cancellation list decoding, their scaling exponent is studied as a function of the list size. In particular, the error probability is fixed, and the tradeoff betwe ...

Ieee-Inst Electrical Electronics Engineers Inc2015

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

Lossy source coding via spatially coupled LDGM ensembles

Rüdiger Urbanke, Nicolas Macris, Marc Vuffray, Vahid Aref

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generatormatrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of ...

Ieee2012

Finite-Length Scaling For Gallager A

Rüdiger Urbanke

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

Linear Programming Decoding of Spatially Coupled Codes

Rüdiger Urbanke

For a given family of spatially coupled codes, we prove that the linear programming (LP) threshold on the binary-symmetric channel (BSC) of the tail-biting graph cover ensemble is the same as the LP threshold on the BSC of the derived spatially coupled ens ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Improved decoding of second-order Reed-Muller codes

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...

IEEE2019

A Generalization of the Finite-Length Scaling Approach Beyond the BEC

Rüdiger Urbanke

We want to extend the approximation of the error probability via a scaling approach from the BEC to general binary-input memoryless output-symmetric (BMS) channels. In particular, we consider such scaling laws for regular LDPC ensembles and message-passing ...

2007

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

On the Efficiency of Polar-Like Decoding for Symmetric Codes

Rüdiger Urbanke, Kirill Ivanov

The recently introduced polar codes constitute a breakthrough in coding theory due to their capacity-achieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures based on the Plo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Physics-Inspired Methods for Networking and Communications

Rüdiger Urbanke

Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior int ...

Ieee-Inst Electrical Electronics Engineers Inc2014

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