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Construction of polar codes for arbitrary discrete memoryless channels [article]

Talha Cihad Gulcu, Min Ye, Alexander Barg
2017 arXiv   pre-print
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity.  ...  Experimentation shows that the suggested construction algorithms can be used to construct long polar codes for alphabets of size q=16 and more with acceptable loss of the code rate for a variety of polarizing  ...  Let W : X → Y be a discrete memoryless channel and let y 1 , y 2 ∈ Y be two output symbols.  ... 
arXiv:1603.05736v2 fatcat:f3y6bym7v5e5bcnr7vjal5ehmy

Polarization for arbitrary discrete memoryless channels

Eren Sasoglu, Emre Telatar, Erdal Arikan
2009 2009 IEEE Information Theory Workshop  
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels.  ...  A previous result on the error probability behavior of polar codes is also extended to the case of arbitrary discrete memoryless channels.  ...  ACKNOWLEDGMENT The work of E.  ... 
doi:10.1109/itw.2009.5351487 fatcat:jongkvkxsre7dd4p54qrq2ctxa

On the optimality of polar codes for the deterministic wiretap channel

S. Ali. A. Fakoorian, A. Lee Swindlehurst
2013 2013 Asilomar Conference on Signals, Systems and Computers  
In this paper, we show that polar coding is an optimal coding scheme in achieving the secrecy capacity for the deterministic wiretap channel, where the channel between the transmitter and the intended  ...  While the secrecy capacity is achievable based upon a random-coding argument, constructing channel coding schemes that achieve the secrecy capacity of a general wiretap channel is still an open problem  ...  Berkeley for helpful discussions on [12] .  ... 
doi:10.1109/acssc.2013.6810675 dblp:conf/acssc/FakoorianS13 fatcat:vemnr6oltnhqdazd5te6falkzu

Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels [article]

Ryuhei Mori, Toshiyuki Tanaka
2009 arXiv   pre-print
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1].  ...  Furthermore, new upper and lower bounds of the block error probability of polar codes are derived for the BEC and the arbitrary symmetric B-MC, respectively.  ...  ACKNOWLEDGMENT TT acknowledges support of the Grant-in-Aid for Scientific Research on Priority Areas (No. 18079010), MEXT, Japan.  ... 
arXiv:0901.2207v2 fatcat:2hvxuylysvfsvmnyyxw7fipleu

Implementation of Polar Codes over AWGN and Binary Symmetric Channel

Navneet Kaur, Arvinder Pal Singh Kalsi
2016 Indian Journal of Science and Technology  
One such advancement in FEC is Polar Codes which has mathematically proved to attain the Shannon capacity for Binary Discrete Memoryless Channels using the phenomenon of channel polarization which states  ...  Applications: As polar codes are the first codes that achieve the Shannon capacity, so they seem to be the best solution for discrete memoryless channels which encounter packet failures and other noisy  ...  Polar Codes A new type of linear block codes which have proved to achieve the capacity of symmetric Binary Discrete Memoryless Channels like BEC and BSC 9 are known as polar codes.  ... 
doi:10.17485/ijst/2016/v9i19/91383 fatcat:4tyn7nzvlzhypa63mjz7oheqcu

Polar codes for magnetic recording channels

Aman Bhatia, Veeresh Taranalli, Paul H. Siegel, Shafa Dahandeh, Anantha Raman Krishnan, Patrick Lee, Dahua Qin, Moni Sharma, Teik Yeo
2015 2015 IEEE Information Theory Workshop (ITW)  
Polar codes provably achieve the capacity of binary memoryless symmetric (BMS) channels with low complexity encoding and decoding algorithms, and their finite-length performance on these channels, when  ...  However, magnetic recording channels are generally modeled as binary-input intersymbol interference (ISI) channels, and the design of polar coding schemes for these channels remains an important open problem  ...  ACKNOWLEDGEMENTS This research was supported in part by NSF Grants CCF-116739 and CCF-1405119, the Center for Magnetic Recording Research at UC San Diego, and Western Digital Corporation.  ... 
doi:10.1109/itw.2015.7133166 dblp:conf/itw/BhatiaTSDKLQSY15 fatcat:bil4iabiyvap5i52djdynzzlia

Polarization and Polar Codes

Eren Şaşoğlu
2011 Foundations and Trends in Communications and Information Theory  
We will begin in Section 4 by studying how discrete memoryless processes of arbitrary alphabet sizes, not just binary ones, can be polarized by recursive transforms.  ...  This performance guarantee is analytical, and is not only based on empirical evidence. • for symmetric channels, polar code construction is deterministic.  ... 
doi:10.1561/0100000041 fatcat:xv3q3vjszjcq3evcf3t4yxax2e

Polar coding schemes for the AWGN channel

Emmanuel Abbe, Andrew Barron
2011 2011 IEEE International Symposium on Information Theory Proceedings  
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 respect to complexity attributes  ...  POLAR CODES FOR LARGE INPUT ALPHABETS A. Prime alphabets Let P be a q-ary input discrete memoryless channel, where q is prime.  ... 
doi:10.1109/isit.2011.6033892 dblp:conf/isit/AbbeB11 fatcat:qlcwidwxfbe3tj2zkhcmxzsnna

Multilevel polarization of polar codes over arbitrary discrete memoryless channels

Aria G. Sahebi, S. Sandeep Pradhan
2011 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
It is shown that the original construction of polar codes suffices to achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes.  ...  It is also shown through an example that polar codes do not achieve the capacity of coset codes over arbitrary channels.  ...  INTRODUCTION Polar codes were originally proposed by Arikan in [1] for discrete memoryless channels with binary input.  ... 
doi:10.1109/allerton.2011.6120375 dblp:conf/allerton/SahebiP11 fatcat:wj5f76gwlfhbvlv65eos53rut4

Channel Polarization on q-ary Discrete Memoryless Channels by Arbitrary Kernels [article]

Ryuhei Mori, Toshiyuki Tanaka
2010 arXiv   pre-print
A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes.  ...  In the original work, binary input discrete memoryless channels are considered. A special case of q-ary channel polarization is considered by Sasoglu, Telatar, and Arikan.  ...  INTRODUCTION Channel polarization, proposed by Arıkan, is a method of constructing capacity achieving codes with low encoding and decoding complexities [1] .  ... 
arXiv:1001.2662v3 fatcat:pwhba7cnvzf5pn535c4qdiy3bi

Multilevel polar-coded modulation

Mathis Seidl, Andreas Schenk, Clemens Stierstorfer, Johannes B. Huber
2013 2013 IEEE International Symposium on Information Theory  
Based on a novel characterization of the channel polarization phenomenon, rules for the optimal choice of the bit labeling in this coded modulation scheme employing polar codes are developed.  ...  A framework is proposed that allows for a joint description and optimization of both binary polar coding and the multilevel coding (MLC) approach for 2^m-ary digital pulse-amplitude modulation (PAM).  ...  POLAR CODES Polar codes, as introduced by Arıkan [1] , have been shown to be a channel coding construction that provably achieves the symmetric capacity of arbitrary binary-input discrete memoryless channels  ... 
doi:10.1109/isit.2013.6620437 dblp:conf/isit/SeidlSSH13 fatcat:yfic4vuaybhbpnpzetrade3o5i

Implementation of Polar Codes in 5g

Dr. G. Indumathi
2017 International Journal for Research in Applied Science and Engineering Technology  
A new proposed method for constructing codes that achieves the symmetric capacity, (the capacity of the channel with the same probabilities for the inputs), I (W) , of any Binary Discrete Memoryless Channel  ...  Codes constructed on the basis of this idea are called polar codes.The block length while constructing the polar codes should be N= .  ...  by Arıkan which can achieve the symmetric capacity of any given binary-input discrete memoryless channel Polar coding is a linear block error correcting code.  ... 
doi:10.22214/ijraset.2017.4089 fatcat:de5yjkgahnae5hxffvlvplokui

Using concatenated algebraic geometry codes in channel polarization [article]

Abdulla Eid, Iwan Duursma
2013 arXiv   pre-print
Polar codes were introduced by Arikan in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity  ...  For binary polar codes (i.e. binary kernels) of a given length n, we compare numerically the use of short algebraic geometry codes over large fields versus long algebraic geometry codes over small fields  ...  We introduce now the polar codes and the channel polarization phenomenon for a q-ary input symmetric discrete memoryless channel W with input alphabet X and output alphabet Y.  ... 
arXiv:1310.7159v1 fatcat:msxdjyk6nrff3a6anp7yv6kupu

Alignment of Polarized Sets

Joseph M. Renes, David Sutter, S. Hamed Hassani
2016 IEEE Journal on Selected Areas in Communications  
Understanding the alignment of the polarized sets is important as it is directly related to universality properties of the induced polar codes, which are essential in particular for network coding problems  ...  Arıkan's polar coding technique is based on the idea of synthesizing n channels from the n instances of the physical channel by a simple linear encoding transformation.  ...  Third, knowledge of the structure and relation of polarized sets can be helpful in other aspects of polar coding, e.g. in the construction of polar codes (see [4, Chapter 5] ).  ... 
doi:10.1109/jsac.2015.2504271 fatcat:l3dy3cn6dvc5fiffkdngov4osq

Alignment of polarized sets

Joseph M. Renes, David Sutter, S. Hamed Hassani
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
Understanding the alignment of the polarized sets is important as it is directly related to universality properties of the induced polar codes, which are essential in particular for network coding problems  ...  Arıkan's polar coding technique is based on the idea of synthesizing n channels from the n instances of the physical channel by a simple linear encoding transformation.  ...  Third, knowledge of the structure and relation of polarized sets can be helpful in other aspects of polar coding, e.g. in the construction of polar codes (see [4, Chapter 5] ).  ... 
doi:10.1109/isit.2015.7282895 dblp:conf/isit/RenesSH15 fatcat:oeb7rvb2lzbtlhtiqgz5mcc4mq
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