On the rate of channel polarization

Arıkan, Erdal; Telatar, Emre

doi:10.1109/isit.2009.5205856

Cited by 423 publications

(575 citation statements)

References 4 publications

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“…In recent work [12], the following result has been obtained in this direction. This is a vast improvement over the bound proved in this paper.…”

Section: A Rate Of Polarizationmentioning

confidence: 79%

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Channel polarization: A method for constructing capacity-achieving codes

Arıkan

2008

2008 IEEE International Symposium on Information Theory

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135

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Abstract-A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W ) of any given binary-input discrete memoryless channel (B-DMC) W . The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W , a second set of N binary-input channels fW

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“…In recent work [12], the following result has been obtained in this direction. This is a vast improvement over the bound proved in this paper.…”

Section: A Rate Of Polarizationmentioning

confidence: 79%

“…in the order from to , where , are decision functions defined as if otherwise (12) for all . We will say that a decoder block error occurred if or equivalently if .…”

Section: ) -Coset Codesmentioning

confidence: 99%

Channel polarization: A method for constructing capacity-achieving codes

Arıkan

2008

2008 IEEE International Symposium on Information Theory

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135

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“…Subsequent to the derivation of channel polarization in [6] and the refined rate of polarization in [16], polarization methods have been extended to analyze multi-user information theory problems. In [10], a joint polarization method is proposed for muser MACs with connections to matroid theory.…”

Section: ) Polar Codes For Multi-user Settingsmentioning

confidence: 99%

Polar codes for broadcast channels

Goela

Abbé

Gastpar

2013

2013 IEEE International Symposium on Information Theory

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Abstract-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 constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Cover's superposition codes; ii) Marton's codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is O(n log n) where n is the block length. In addition, polar code sequences obtain a stretched-exponential decay of O(2 −n β ) of the average block error probability where 0 < β < 1 2 .

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“…In [15] authors improved the bound on the rate of polarization to O(2 −N β ) for β < 1/2, from O(N − 1 4 ) bound proved in [12]. Korada made most of the early contribution to the applicability of polar codes in his thesis [16].…”

Section: Polar Codesmentioning

confidence: 99%

Polar codes for distributed source coding

Onay

2013

Electron. lett.

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Polar codes were invented by Arıkan as the first "capacity achieving" codes for binary-input discrete memoryless symmetric channels with low encoding and decoding complexity. The "polarization phenomenon", which is the underlying principle of polar codes, can be applied to different source and channel coding problems both in single-user and multi-user settings. In this work, polar coding methods for multi-user distributed source coding problems are investigated. First, a restricted version of lossless distributed source coding problem, which is also referred to as the Slepian-Wolf problem, is considered. The restriction is on the distribution of correlated sources. It is shown that if the sources are "binary symmetric" then single-user polar codes can be used to achieve full capacity region without time sharing. Then, a method for two-user polar coding is considered which is used to solve the Slepian-Wolf problem with arbitrary source distributions. This method is also extended to cover multiple-access channel problem which is the dual of Slepian-Wolf problem.Next, two lossy source coding problems in distributed settings are investigated. The first problem is the distributed lossy source coding which is the lossy version of the Slepian-Wolf problem. Although the capacity region of this problem is not known in general, there is a good inner bound called the Berger-Tung inner bound. A polar coding method that can achieve the whole dominant face of the Berger-Tung region is devised. The second problem considered is the multiple description coding problem. The capacity region for this problem is also not known in general. El Gamal-Cover inner bound is the best known bound for this problem. A polar coding method that can achieve any point on the dominant face of El Gamal-Cover region is devised.

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On the rate of channel polarization

Cited by 423 publications

References 4 publications

Channel polarization: A method for constructing capacity-achieving codes

Channel polarization: A method for constructing capacity-achieving codes

Polar codes for broadcast channels

Polar codes for distributed source coding

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