Browsing by Subject "Channel polarization"

Now showing 1 - 8 of 8

Open Access
Challenges and some new directions in channel coding
(Korean Institute of Communication Sciences, 2015) Arikan, E.; Ul Hassan, N.; Lentmaier, M.; Montorsi, G.; Sayir, J.
Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding.
Open Access
Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
(IEEE, 2009) Arikan, E.
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 ≤ i ≤ 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) and any target rate R < I(W), there exists a sequence of polar codes {Cn;n ≥ 1 such that Cn has block-length N = 2n, rate ≥ R, and probability of block error under successive cancellation decoding bounded as Pe (N, R) ≤ O(N-1/4 independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.
Open Access
A note on some inequalities used in channel polarization and polar coding
(Institute of Electrical and Electronics Engineers, 2018) Jayram, T. S.; Arıkan, Erdal
We give a unified treatment of some inequalities that are used in the proofs of channel polarization theorems involving a binary-input discrete memoryless channel.
Open Access
On the origin of polar coding
(Institute of Electrical and Electronics Engineers Inc., 2016) Arıkan, E.
Polar coding was conceived originally as a technique for boosting the cutoff rate of sequential decoding, along the lines of earlier schemes of Pinsker and Massey. The key idea in boosting the cutoff rate is to take a vector channel (either given or artificially built), split it into multiple correlated subchannels, and employ a separate sequential decoder on each subchannel. Polar coding was originally designed to be a low-complexity recursive channel combining and splitting operation of this type, to be used as the inner code in a concatenated scheme with outer convolutional coding and sequential decoding. However, the polar inner code turned out to be so effective that no outer code was actually needed to achieve the original aim of boosting the cutoff rate to channel capacity. This paper explains the cutoff rate considerations that motivated the development of polar coding.
Open Access
Polarization for arbitrary discrete memoryless channels
(IEEE, 2009) Şaşoǧlu, E.; Telatar, E.; Arıkan, Erdal
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization. This method can be extended to channels of composite input alphabet sizes by decomposing such channels into a set of channels with prime input alphabet sizes. It is also shown that all discrete memoryless channels can be polarized by randomized constructions. The introduction of randomness does not change the order of complexity of polar code construction, encoding, and decoding. A previous result on the error probability behavior of polar codes is also extended to the case of arbitrary discrete memoryless channels. The generalization of polarization to channels with arbitrary finite input alphabet sizes leads to polar-coding methods for approaching the true (as opposed to symmetric) channel capacity of arbitrary channels with discrete or continuous input alphabets.
Open Access
Source polarization
(IEEE, 2010) Arıkan, Erdal
The notion of source polarization is introduced and investigated. This complements the earlier work on channel polarization. An application to Slepian-Wolf coding is also considered. The paper is restricted to the case of binary alphabets. Extension of results to non-binary alphabets is discussed briefly.
Open Access
Strange attractor in density evolution
(IEEE Computer Society, 2019) Kahraman, Sinan
The strange attractor represents a complex pattern of behavior in dynamic systems. This paper introduces a strange attractor of channel polarization as a result of a geometric property of density evolution for code construction. In this way, we can define a subset of synthetic channels that are universally (channel independently) less reliable than the original channel. We show that the cardinality of the attractor set is the n + 2-th Fibonacci number for the block length N = 2 n . This can be accepted that it is a significantly large number for very long codes. Recently, it is known that polar codes can be constructed with sub-linear complexity by the use of partial orderings. In this study, we additionally define 1 + log 2 log 2 N universal operators. Finally, we show that these universal operators can be applied on the attractor set to increase the number of synthetic channels that are universally less reliable than the natural channel.
Open Access
A survey of Reed-Muller codes from polar coding perspective
(IEEE, 2010-01) Arıkan, Erdal
A survey of Reed-Muller (RM) coding is given with the goal of establishing a continuity between RM codes and polar codes. The focus is mainly on recursive decoding methods for RM codes and other ideas that are most relevant to polar coding.