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Re-proving Channel Polarization Theorems

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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

Polar Codes are Optimal for Lossy Source Coding

Rüdiger Urbanke, Satish Babu Korada

We consider lossy source compression of a binary symmetric source using polar codes and the low-complexity successive encoding algorithm. It was recently shown by Arikan that polar codes achieve the capacity of arbitrary symmetric binary-input discrete mem ...

Institute of Electrical and Electronics Engineers2010

Lossless Source Coding with Polar Codes

Satish Babu Korada, Harm Cronie

In this paper lossless compression with polar codes is considered. A polar encoding algorithm is developed and a method to design the code and compute the average compression rate for finite lengths is given. It is shown that the scheme achieves the optima ...

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

Rateless Codes for AVC Models

Michael Christoph Gastpar

The arbitrarily varying channel (AVC) is a channel model whose state is selected maliciously by an adversary. Fixed-blocklength coding assumes a worst-case bound on the adversary's capabilities, which leads to pessimistic results. This paper defines a vari ...

2010

Polar coding: a brief tour

Emre Telatar

Arikan's 'polar coding' is a technique to achieve the symmetric capacity of binary input memoryless channels. In this talk I will attempt to describe this technique, and briefly discuss its extensions to q-ary input channels, multiple access channels and r ...

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

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 capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...

2010

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

Symmetric LDPC codes are not necessarily locally testable

Ghid Maatouk

Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be loca ...

2010

Applications of Derandomization Theory in Coding

Mahdi Cheraghchi Bashi Astaneh

Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate ...

EPFL2010

A 15.8 pJ/bit/iter quasi-cyclic LDPC decoder for IEEE 802.11n in 90 nm CMOS

Andreas Peter Burg, Pascal Andreas Meinerzhagen, Christoph Studer

We present a low-power quasi-cyclic (QC) low density parity check (LDPC) decoder that meets the throughput requirements of the highest-rate (600 Mbps) modes of the IEEE 802.11n WLAN standard. The design is based on the layered offset-min-sum algorithm and ...

IEEE2010