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Polar coding: a brief tour

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Polar coding schemes for the AWGN channel

Emmanuel Abbé

This paper investigates polar coding schemes achieving capacity for the AWGN channel. The approaches using a multiple access channel with a large number of binary-input users and a single-user channel with a large prime-cardinality input are compared with ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Polar Codes for Q-ary Source Coding

Emre Telatar, Mohammad Karzand

Polar coding is a recent channel coding technique invented by Arikan to achieve the 'symmetric capacity' of binary-input memoryless channels. Subsequently it was observed by Korada and Urbanke that such codes are also good for lossy channel coding, achievi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

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

Polar codes for channel and source coding

Satish Babu Korada

The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...

EPFL2009

Linear Universal Decoder for Compound Discrete Memoryless Channels

Rethnakaran Pulikkoonattu

Shannon in his seminal work \cite{paper:shannon} formalized the framework on the problem of digital communication of information and storage. He quantified the fundamental limits of compression and transmission rates. The quantity \textit{channel capacity} ...

2009

Polar codes: Characterization of exponent, bounds, and constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polar codes were recently introduced by Arikan. They achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

The Interference-Multiple-Access Channel

Emre Telatar, Suhas Diggavi, Etienne Perron

We introduce the interference-multiple-access channel, which is a discrete memoryless channel with two transmitters and two receivers, similar to the interference channel. One receiver is required to decode the information encoded at one transmitter, the o ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Concentration of Magnetization for Linear Block Codes

Nicolas Macris, Satish Babu Korada, Shrinivas Kudekar

We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...

2008

The case for structured random codes in network communication theorems

Michael Christoph Gastpar

In the Shannon-theoretic analysis of joint source-channel coding problems, achievability is usually established via a two-stage approach: The sources are compressed into bits' and these bits are reliably communicated across the noisy channels. Random codin ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

Delay and coding in multiple-user communications

Stéphane Musy

In multiple-user communications, the bursty nature of the packet arrival times cannot be divorced from the analysis of the transmission process. However, in traditional information theory the random arrival times are smoothed out by appropriated source cod ...

EPFL2007