177 research outputs found
On the Rate of Channel Polarization
It is shown that for any binary-input discrete memoryless channel with
symmetric capacity and any rate , the probability of block
decoding error for polar coding under successive cancellation decoding
satisfies for any when the block-length
is large enough.Comment: Some minor correction
Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis
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, Ar{\i}kan proved
that this class of codes, called polar codes, achieve the symmetric capacity
--- the mutual information evaluated at the uniform input distribution ---of
any stationary binary discrete memoryless channel with low complexity encoders
and decoders requiring in the order of operations in the
block-length . This discovery settled the long standing open problem left by
Shannon of finding low complexity codes achieving the channel capacity.
Polar coding settled an open problem in information theory, yet opened plenty
of challenging problems that need to be addressed. A significant part of this
thesis is dedicated to advancing the knowledge about this technique in two
directions. The first one provides a better understanding of polar coding by
generalizing some of the existing results and discussing their implications,
and the second one studies the robustness of the theory over communication
models introducing various forms of uncertainty or variations into the
probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version,
see http://people.epfl.ch/mine.alsan/publication
An entropy inequality for q-ary random variables and its application to channel polarization
It is shown that given two copies of a q-ary input channel , where q is
prime, it is possible to create two channels and whose symmetric
capacities satisfy , where the inequalities are
strict except in trivial cases. This leads to a simple proof of channel
polarization in the q-ary case.Comment: To be presented at the IEEE 2010 International Symposium on
Information Theor
Polarization as a novel architecture to boost the classical mismatched capacity of B-DMCs
We show that the mismatched capacity of binary discrete memoryless channels
can be improved by channel combining and splitting via Ar{\i}kan's polar
transformations. We also show that the improvement is possible even if the
transformed channels are decoded with a mismatched polar decoder.Comment: Submitted to ISIT 201
Properties and Construction of Polar Codes
Recently, Ar{\i}kan introduced the method of channel polarization on which
one can construct efficient capacity-achieving codes, called polar codes, for
any binary discrete memoryless channel. In the thesis, we show that decoding
algorithm of polar codes, called successive cancellation decoding, can be
regarded as belief propagation decoding, which has been used for decoding of
low-density parity-check codes, on a tree graph. On the basis of the
observation, we show an efficient construction method of polar codes using
density evolution, which has been used for evaluation of the error probability
of belief propagation decoding on a tree graph. We further show that channel
polarization phenomenon and polar codes can be generalized to non-binary
discrete memoryless channels. Asymptotic performances of non-binary polar
codes, which use non-binary matrices called the Reed-Solomon matrices, are
better than asymptotic performances of the best explicitly known binary polar
code. We also find that the Reed-Solomon matrices are considered to be natural
generalization of the original binary channel polarization introduced by
Ar{\i}kan.Comment: Master thesis. The supervisor is Toshiyuki Tanaka. 24 pages, 3
figure
Universal Polar Decoding with Channel Knowledge at the Encoder
Polar coding over a class of binary discrete memoryless channels with channel
knowledge at the encoder is studied. It is shown that polar codes achieve the
capacity of convex and one-sided classes of symmetric channels
Source Polarization
The notion of source polarization is introduced and investigated. This
complements the earlier work on channel polarization. An application to
Slepian-Wolf coding is also considered. The paper is restricted to the case of
binary alphabets. Extension of results to non-binary alphabets is discussed
briefly.Comment: To be presented at the IEEE 2010 International Symposium on
Information Theory
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