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Universal bounds on the scaling behavior of polar codes

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Coding for Communications and Secrecy

Mani Bastaniparizi

Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...

EPFL2017

Timely Updates over an Erasure Channel

Elie Najm, Emina Soljanin

Using an age of information (AoI) metric, we examine the transmission of coded updates through a binary erasure channel to a monitor/receiver. %Coded redundancy is employed to ensure the timely delivery of codupdate packets. We start by deriving the averag ...

2017

Status update through M/G/1/1 queues with HARQ

Elie Najm, Emina Soljanin

We consider a system where randomly generated updates are to be transmitted to a monitor, but only a single update can be in the transmission service at a time. Therefore, the source has to prioritize between the two possible transmission policies: preempt ...

2017

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

Optimization of LPN Solving Algorithms

Serge Vaudenay, Sonia Mihaela Bogos

In this article we focus on constructing an algorithm that automatizes the generation of LPN solving algorithms from the considered parameters. When searching for an algorithm to solve an LPN instance, we make use of the existing techniques and optimize th ...

Springer-Verlag Berlin2016

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

Polar Codes for Broadcast Channels

Michael Christoph Gastpar, Emmanuel Abbé, Naveen Goela

Polar codes are introduced for discrete memoryless broadcast channels. For m-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from m-independent messages to one codeword while satisfying broadcast constrai ...

Institute of Electrical and Electronics Engineers2015

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

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

LLR-Based Successive Cancellation List Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming

We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties that simplify the sorting step involved in su ...

Institute of Electrical and Electronics Engineers2015