Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels

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...

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Vydáno v:	IEEE transactions on information theory Ročník 55; číslo 7; s. 3051 - 3073
Hlavní autor:	Arikan, Erdal
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.07.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Applied sciences Binary system Blocking Cancellation Capacity planning Capacity-achieving codes Channel capacity Channel coding channel polarization Channels Codes Coding, codes Communication channels Construction Councils Decoding Encoders Exact sciences and technology Information theory Information, signal and communications theory Memoryless systems Noise cancellation Plotkin construction polar codes Polarization Reed- Muller (RM) codes Reproduction Signal and communications theory successive cancellation decoding Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Performance evaluation Binary channel Channel capacity Discrete channel successive cancellation decoding Information rate n channel Decoding Channel coding Information transmission Memoryless channel Codec Capacity-achieving codes Algorithm complexity Reed-Muller (RM) codes Plotkin construction polar codes channel polarization Reed Muller code
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	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 \{W_N^{(i)}:1\le i\le N\} such that, as N becomes large, the fraction of indices i for which I(W_N^{(i)}) is near 1 approaches I(W) and the fraction for which I(W_N^{(i)}) is near 0 approaches 1-I(W) . The polarized channels \{W_N^{(i)}\} are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W)> 0 and any target rate R ≪ I(W) , there exists a sequence of polar codes \{{\Fraktur {C}}_n;n\ge 1\} such that {\Fraktur {C}}_n has block-length N=2^n , rate \ge R , and probability of block error under successive cancellation decoding bounded as P_{e}(N,R) \le O(N^{-{1\over 4}}) independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2009.2021379