On the rate of channel polarization

By E. Arıkan, Emre Telatar. 2009 IEEE International Symposium on Information Theory, 2008

513 citations recorded by the source corpus.

A bound is given on the rate of channel polarization. As a corollary, an earlier bound on the probability of error for polar coding is improved. Specifically, it is shown that, for any binary-input discrete memoryless channel W with symmetric capacity I(W) and any rate R ≪ I(W), the polar-coding block-error probability under successive cancellation decoding satisfies P<inf>e</inf>(N, R) ≤ 2<sup>−Nβ</sup> for any β ≪ 1/2 when the block-length N is large enough.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/27ba58c16e84d9c9887c2892e75b3691bc91184d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Electrical and Electronic Engineering

In Molecular Biology

Citations in the corpus

LLR-Based Successive Cancellation List Decoding of Polar Codes (2013, background): “SC decoding decays roughly like as a function of the block-length [14], they do not perform well at low-to-moderate block-lengths.”
Polar codes: Characterization of exponent, bounds, and constructions (2009, methodology): “Moreover, it is shown in [2] that when Zn approaches 0 it does so at a sufficiently fast rate: Theorem 8 ([2]): Given a B-DMC W , the matrix G2 and any β < 12 ,”
Source polarization (2010, methodology): “We omit the proof, which is covered by the results of [4].”
Polarization for arbitrary discrete memoryless channels (2009, background): “. The latter result was shown in [ 2 ]. The aim of this note is to extend these results of [1], [2] to”
Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes (2010, unknown): “Proposition10.”
CRC-Aided Decoding of Polar Codes (2012, methodology): “POLAR codes, proposed by Arıkan [1], [2], are proved to achieve the symmetric capacity of the binary-input discrete memoryless channels (B-DMCs) under a successive cancellation (SC) decoder.”
Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels (2008, background): “tate some open problems. A. Rate of polarization A major open problem suggested by this paper is to determine how fast a channel polarizes as a function of the blocklength parameter N. In recent work [12], the following result has been obtained in this direction. Proposition 18: Let W be a B-DMC. Fo”
Polar Codes for Channel and Source Coding (2009, background): “In [47] Arıkan and Telatar obtained the following result which yields a stretched-exponential bound on the block error probability.”
List decoding of polar codes (2011, background): “These remarkable properties of polar codes have generated an enormous interest, see [2], [3], [6], [8], [14], [15] and references therein.”