Browsing by Subject "Channel coding"

Now showing 1 - 10 of 10

Open Access
Application of guessing to sequential decoding of polarization-adjusted convolutional (PAC) codes
(Institute of Electrical and Electronics Engineers Inc., 2023-08-16) Moradi, Mohsen
Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.
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
(IEEE, 2008-07) Arıkan, Erdal
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 I(W) is the highest rate achievable subject to using the input letters of the channel equiprobably and equals the capacity C(W) if the channel has certain symmetry properties. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a different set of N binary-input channels such that the capacities of the latter set, except for a negligible fraction of them, are either near 1 or near 0. This second set of N channels are well-conditioned for channel coding: one need only send data at full rate through channels with capacity near 1 and at 0 rate through the others. The main coding theorem about polar coding states that, given any B-DMC W with I(W) > 0 and any fixed 0 < δ < I(W), there exist finite constants n1 (W, δ) and c(W, δ) such that for all n ≥ n1, there exist polar codes with block length N = 2n, rate R > I(W)-δ, and probability of block decoding error Pe ≤ cN-1/4. The codes with this performance can be encoded and decoded within complexity O(N log N). © 2008 IEEE.
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
Generalized approximate message-passing decoder for universal sparse superposition codes
(IEEE, 2017-06) Bıyık, Erdem; Barbier, J.; Dia, M.
Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense that they achieve capacity over any memoryless channel under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In this contribution we introduce the GAMP decoder for SS codes, we confirm empirically the universality of this communication scheme through its study on various channels and we provide the main analysis tools: state evolution and the potential. We also compare the performance of GAMP with the Bayes-optimal MMSE decoder. We empirically illustrate that despite the presence of a phase transition preventing GAMP to reach the optimal performance, spatial coupling allows to boost the performance that eventually tends to capacity in a proper limit. We also prove that, in contrast with the AWGNC case, SS codes for binary input channels have a vanishing error floor in the limit of large codewords. Moreover, the performance of Hadamard-based encoders is assessed for practical implementations. © 2017 IEEE.
Open Access
Large deviations of probability rank
(IEEE, 2000) Arıkan, Erdal
Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.
Open Access
Multi-input multi-output deletion channel
(Institute of Electrical and Electronics Engineers, 2012) Wang F.; Duman, T. M.
We describe a new channel model suitable in certain applications, namely the multi-input multi-output (MIMO) deletion channel. This channel models the scenarios where multiple transmitters and receivers suffering from synchronization errors are employed. We then consider a coding scheme over such channels based on a serial concatenation of a low-density parity check (LDPC) code, a marker code and a layered space-time code. We design two detectors operating at the bit level which jointly achieve synchronization for the deletion channel (with the help of the marker code) and detection for the MIMO channel. Utilizing the proposed detector together with an LDPC code with powerful error-correction capabilities, we demonstrate that reliable transmission over a MIMO deletion channel is feasible.
Open Access
A performance comparison of polar codes and reed-muller codes
(Institute of Electrical and Electronics Engineers, 2008) Arıkan, E.
Polar coding is a code construction method that can be used to construct capacity-achieving codes for binary-input channels with certain symmetries. Polar coding may be considered as a generalization of Reed-Muller (RM) coding. Here, we demonstrate the performance advantages of polar codes over RM codes under belief-propagation decoding.
Open Access
Polarization-adjusted convolutional (PAC) codes as a concatenation of inner cyclic and outer polar- and Reed-Muller-like codes
(Academic Press, 2023-10-23) Moradi, Mohsen
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this study, we show that PAC codes are equivalent to a new class of codes consisting of inner cyclic codes and outer polar- and Reed-Muller-like codes. We leverage the properties of cyclic codes to establish that PAC codes outperform polar- and Reed-Muller-like codes in terms of minimum distance.
Open Access
Special Issue on Advances in Channel Coding
(Korean Institute of Communication Sciences, 2015) Arikan, E.; Lentmaier, M.; Montorsi, G.
Since the invention of turbo codes in 1993 there has been an enormous interest and progress in the field of capacity approaching code constructions. Many classical constructions have been replaced by newer, better performing codes with feasible decoding complexity. Most of these modern code constructions, such as turbo codes, Gallager's low-density parity-check (LDPC) codes and their generalizations, can be modeled by sparse graphical models. Spatial coupling of sparse graphical models has in the last years attracted a lot of interest due to the threshold saturation phenomenon, which leads to capacity achieving performance with iterative message passing decoding. Polar codes are a recently discovered class of capacity achieving codes that are formed by an explicit construction based on a phenomenon called channel polarization. These codes, too, have various low-complexity decoding algorithms based on message passing on a sparse graph that has a recursive structure similar to that of fast transforms in signal processing.