DocumentCode :
1077567
Title :
Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels
Author :
Arikan, Erdal
Author_Institution :
Dept. of Electr.-Electron. Eng., Bilkent Univ., Ankara
Volume :
55
Issue :
7
fYear :
2009
fDate :
7/1/2009 12:00:00 AM
Firstpage :
3051
Lastpage :
3073
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 {WN(i)1 les i les N} such that, as N becomes large, the fraction of indices i for which I(WN(i)) is near 1 approaches I(W) and the fraction for which I(WN(i)) is near 0 approaches 1-I(W). The polarized channels {WN(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 {Cfrn;nges1} such that Cfrn has block-length N=2n , rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N logN) for each.
Keywords :
binary codes; channel capacity; channel coding; decoding; memoryless systems; probability; channel capacity; channel coding; channel polarization; code sequence; polar codes; probability; successive cancellation decoding algorithm; symmetric binary-input memoryless channel; Capacity planning; Channel capacity; Channel coding; Codes; Councils; Decoding; Information theory; Memoryless systems; Noise cancellation; Polarization; Capacity-achieving codes; Plotkin construction; Reed– Muller (RM) codes; channel capacity; channel polarization; polar codes; successive cancellation decoding;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2009.2021379
Filename :
5075875
Link To Document :
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