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

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From Polar to Reed-Muller Codes

Marco Mondelli

The year 2016, in which I am writing these words, marks the centenary of Claude Shannon, the father of information theory. In his landmark 1948 paper "A Mathematical Theory of Communication", Shannon established the largest rate at which reliable communica ...

EPFL2016

Revisiting the Sanders-Bogolyubov-Ruzsa Theorem in F-p(n) and its Application to Non-malleable Codes

Divesh Aggarwal

Non-malleable codes (NMCs) protect sensitive data against degrees of corruption that prohibit error detection, ensuring instead that a corrupted codeword decodes correctly or to something that bears little relation to the original message. The split-state ...

Ieee2016

Re-proving Channel Polarization Theorems

Mine Alsan

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Arikan proved that this class of codes, ...

EPFL2015

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

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

Wave-Like Solutions of General 1-D Spatially Coupled Systems

Rüdiger Urbanke, Shrinivas Kudekar

We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a 1-D real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Linear Programming Decoding of Spatially Coupled Codes

Rüdiger Urbanke, Badih Ghazi

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

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

LDPC Codes for 2D Arrays

Mohammad Amin Shokrollahi, Yuval Cassuto

Binary codes over 2D arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper, we propose a new framework for probabilistic construction of codes on 2D arrays. Instead of a p ...

Institute of Electrical and Electronics Engineers2014

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smalle ...

2014