Browsing by Subject "Polar codes"

Now showing 1 - 20 of 35

Open Access
A slotted pilot-based unsourced random access scheme with a multiple-antenna receiver
(Institute of Electrical and Electronics Engineers, 2023-08-30) Özateş, Mert; Kazemi, Mohammad; Duman, Tolga Mete
We consider unsourced random access over fading channels with a massive number of antennas at the base station, and propose a simple, yet energy-efficient solution by dividing the transmission frame into slots. We utilize non-orthogonal pilot sequences followed by a polar codeword for transmission in each slot. At the receiver side, we first detect the transmitted pilot sequences by employing a generalized orthogonal matching pursuit algorithm and utilize a linear minimum mean square error solution to estimate the channel vectors. We then perform an iterative decoding based on maximal ratio combining, single-user polar decoding, and successive interference cancellation with re-estimation of the channel vectors to recover the data bits. We also analyze the performance of the proposed scheme using normal approximations and provide a detailed complexity analysis. Numerical examples demonstrate that the proposed scheme either outperforms the existing schemes in the literature or has a competitive performance with a lower complexity. Furthermore, it is suitable for fast-fading scenarios due to its excellent performance in the short blocklength regime.
Open Access
A tree pruning technique for decoding complexity reduction of polar codes and PAC codes
(Institute of Electrical and Electronics Engineers , 2023-05-18) Moradi, Mohsen; Mozammel, Amir
Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without visible degradation in the code’s error correction performance. In an SCL decoding with an optimum metric function we show that, on average, the correct branch’s bit-metric value must be equal to the bit-channel capacity, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.
Open Access
Bit-flipping for stack decoding of polarization-adjusted convolutional (PAC) codes
(Institute of Electrical and Electronics Engineers, 2022-09-06) Moradi, Mohsen
While sequential decoding of polarization-adjusted convolutional (PAC) codes constructed using polar rate profile has low computational complexity, their error-correction per-formance falls far short of the theoretical bounds for finite blocklength codes. In this paper, we use the bit-flipping technique in the stack decoding algorithm of PAC codes in order to improve their error-correction performance. This technique maintains the low memory requirements of stack decoding and polar demapper. Additionally, at high SNR values, the number of visits at each level of the decoding tree is almost one. Numerical findings indicate that this approach is capable of outperforming the stack decoding algorithm.
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
Design of low complexity unsourced random access schemes over wireless channels
(2023-11) Özateş, Mert
The Sixth Generation and Beyond communication systems are expected to enable communications of a massive number of machine-type devices. The traffic generated by some of these devices will significantly deviate from those in conventional communication scenarios. For instance, for applications where a massive number of cheap sensors communicate with a base station (BS), the devices will only be sporadically active and there will be no coordination among them or with the BS. For such systems requiring massive random access solutions, a new paradigm called unsourced random access (URA) has recently been proposed. In URA, all the users employ the same codebook and there is no user identity. The destination is only interested in the list of messages being sent from the set of active users. While there are many interesting URA schemes developed in the recent literature, many significant challenges remain, in particular in designing low-complexity and energy-efficient solutions. With the motivation of addressing the current challenges in URA, we develop practical solutions for several scenarios. First, we propose and study URA over frequency-selective channels via orthogonal frequency division multiplexing to mitigate the fading effects. The decoder employs a joint activity detection and channel estimation algorithm coupled with treating interference as noise and successive interference cancellation (SIC). Our results show that the pro-posed scheme offers competitive performance with grant-based frequency division multiple-access while the performance loss due to the estimated channel state information is limited. We then examine the scenario for which the receiver is equipped with a massive number of antennas and develop a simple yet energy-efficient solution by dividing the transmission frame into slots where each active user utilizes a non-orthogonal pilot sequence followed by its polar encoded codeword. At the receiver, we first detect the transmitted pilot sequences by a generalized orthogonal matching pursuit algorithm and utilize a linear minimum mean square error (LMMSE) solution to estimate the channel vectors. We then perform iterative decoding based on maximal ratio combining and single-user decoding followed by SIC. Numerical examples and analysis results demonstrate that the proposed scheme either outperforms the existing approaches in the lit-erature or has a competitive performance with lower complexity. We then adapt our solution to the scenarios with residual hardware impairments (HWIs) at the BS and the user equipment sides by developing a hardware-impairment aware LMMSE solution for channel estimation using the HWI statistics and observe that the newly proposed solution improves the energy efficiency and increases the number of supported active users. Finally, we study on-off division multiple access in the context of URA where each active user utilizes a small fraction of the transmission frame and show that the new approach is superior to the existing ones in terms of performance or complexity.
Open Access
An FPGA implementation architecture for decoding of polar codes
(IEEE, 2011) Pamuk, Alptekin
Polar codes are a class of codes versatile enough to achieve the Shannon bound in a large array of source and channel coding problems. For that reason it is important to have efficient implementation architectures for polar codes in hardware. Motivated by this fact we propose a belief propagation (BP) decoder architecture for an increasingly popular hardware platform; Field Programmable Gate Array (FPGA). The proposed architecture supports any code rate and is quite flexible in terms of hardware complexity and throughput. The architecture can also be extended to support multiple block lengths without increasing the hardware complexity a lot. Moreover various schedulers can be adapted into the proposed architecture so that list decoding techniques can be used with a single block. Finally the proposed architecture is compared with a convolutional turbo code (CTC) decoder for WiMAX taken from a Xilinx Product Specification and seen that polar codes are superior to CTC codes both in hardware complexity and throughput. © 2011 IEEE.
Open Access
An fpga implementation of successive cancellation list decoding for polar codes
(2016-01) Süral, Altuğ
Polar Codes are the rst asymptotically provably capacity achieving error correction codes under low complexity successive cancellation (SC) decoding for binary discrete memoryless symmetric channels. Although SC is a low complexity algorithm, it does not provide as good performance as a maximum-likelihood (ML) decoder, unless su ciently large code block is used. SC is a soft decision decoding algorithm such that it employs depth- rst searching method with a divide and conquer approach to nd a su ciently perfect estimate of decision vector. Using SC with a list (SCL) improves the performance of SC decoder such that it provides near ML performance. SCL decoder employs beam search method as a greedy algorithm to achieve ML performance without considering all possible codewords. The ML performance of polar codes is not good enough due to the minimum hamming distance of possible codewords. For the purpose of increasing the minimum distance, cyclic redundancy check aided (CRC-SCL) decoding algorithm can be used. This algorithm makes polar codes competitive with state of the art codes by exchanging complexity with performance. In this thesis, we present an FPGA implementation of an adaptive list decoder; consisting of SC, SCL and CRC decoders to meet with the tradeo between performance and complexity.
Open Access
High throughput decoding methods and architectures for polar codes with high energy-efficiency and low latency
(2017-11) Dizdar, Onur
Polar coding is a low-complexity channel coding method that can provably achieve Shannon’s channel capacity for any binary-input discrete memoryless channels (B-DMC). Apart from the theoretical interest in the subject, polar codes have attracted attention for their potential applications. We propose high throughput and energy-efficient decoders for polar codes using combinational logic targeting, but not limited to, next generation communication services such as optical communications, Massive Machine-Type Communications (mMTC) and Terahertz communications. First, we propose a fully combinational logic architecture for Successive-Cancellation (SC) decoding, which is the basic decoding method for polar codes. The advantages of this architecture are high throughput, high energy-efficiency and flexibility. The proposed combinational SC decoder operates at very low clock frequencies compared to synchronous (sequential logic) decoders, but takes advantage of the high degree of parallelism inherent in such architectures to provide a higher throughput and higher energy-efficiency compared to synchronous implementations. We provide ASIC and FPGA implementation results to present the characteristics of the proposed architecture and show that the decoder achieves approximately 2.5 Gb/s throughput with a power consumption of 190 mW with 90 nm 1.3 V technology and block length of 1024. We also provide analytical estimates for complexity and combinational delay of such decoders. We explain the use of pipelining with combinational decoders and introduce pipelined combinational SC decoders. At longer block lengths, we propose a hybrid-logic SC decoder that combines the advantageous aspects of the combinational and synchronous decoders. In order to improve the throughput further, we use weighted majority-logic decoding for polar codes. Unlike SC decoding, majority-logic decoding fails to achieve channel capacity, but offers better throughput due its parallelizable schedule. We give a novel recursive description for weighted majority-logic decoding for bit-reversed polar codes and use the proposed definition for implementations without determining the check-sums individually as done in conventional majoritylogic decoding. We demonstrate by analytical estimates that the complexity and latency of the proposed architecture are O(Nlog2 3) and O(log2 2 N), respectively. Then, we validate the calculated estimates by a fully combinational logic implementation on ASIC. For a block length of 256, the implemented decoders achieve 17 Gb/s throughput with 90 nm 1.3 V technology. In order to compensate the error performance penalty of the majority-logic decoding, we propose novel hybrid decoders that combine SC and weighted majority-logic decoding algorithms. We demonstrate that very high latency gains can be obtained by such decoders with small error performance degradation with respect to SC decoding.
Open Access
A high-throughput energy-efficient implementation of successive cancellation decoder for polar codes using combinational logic
(Institute of Electrical and Electronics Engineers Inc., 2016) Dizdar, O.; Arıkan, E.
This paper proposes a high-throughput energy-efficient Successive Cancellation (SC) decoder architecture for polar codes based on combinational logic. The proposed combinational architecture operates at relatively low clock frequencies compared to sequential circuits, but takes advantage of the high degree of parallelism inherent in such architectures to provide a favorable tradeoff between throughput and energy efficiency at short to medium block lengths. At longer block lengths, the paper proposes a hybrid-logic SC decoder that combines the advantageous aspects of the combinational decoder with the low-complexity nature of sequential-logic decoders. Performance characteristics on ASIC and FPGA are presented with a detailed power consumption analysis for combinational decoders. Finally, the paper presents an analysis of the complexity and delay of combinational decoders, and of the throughput gains obtained by hybrid-logic decoders with respect to purely synchronous architectures.
Open Access
Kutupsal kodlar ile asimetrik ve asimetrik olmayan Slepian-Wolf kodlama
(IEEE, 2012) Önay, Saygun
Bu bildiride, düzgün marjinal dağılıma sahip kaynaklar için Slepian–Wolf (SW) hız egrisindeki herhangi bir noktaya ulaşabilen Gehrig tarafından bulunmuş bir asimetrik olmayan dağıtık kaynak kodlama (DKK) tasarımını ele alıyor ve kutupsal kodlamanın bu yöntem içerisinde nasıl kullanılabileceğini gösteriyoruz. Daha sonra önerilen yöntemin simülasyon sonuçlarıyla performansını sunuyoruz.
Open Access
Learning and inference for wireless communications applications using in-memory analog computing
(2024-07) Ali, Muhammad Atif
The exponential growth of wireless communication technologies has created a crucial need for more efficient and intelligent signal processing in decentralized devices and systems. Traditional digital computing architectures increasingly struggle to meet these rising computational demands, leading to performance bottlenecks and energy inefficiencies. The problem becomes more significant on edge devices with limited computing capabilities and severe energy limitations. Integrating machine learning algorithms with in-memory analog computing, specifically memristor-based architectures, provides a non-traditional computing paradigm and can potentially enhance the energy efficiency of edge devices. By leveraging the properties of memristors, which can perform both storage and computation, this research investigates ways to potentially reduce latency and power consumption in signal-processing tasks for wireless communications. This study examines memristor-based analog computing for deep learning and inference in three areas of (wireless) communications: cellular network traffic prediction, multi-sensor over-the-air inference for internet-of-things devices, and neural successive cancellation decoding for polar codes. The research includes the development of robust training techniques for memristive neural networks to cater for degraded performance due to noise in analog computations and offer acceptable prediction accuracy with reduced computational overhead for network traffic management. It explores in-memory computing for an Lp-norm inspired sensor fusion method with analog sensors and enables more efficient multi-sensor data fusion. Also, it investigates the incorporation of analog memristive computing in neural successive cancellation decoders for polar codes, which could lead to more energy-efficient decoding algorithms. The findings of the thesis suggest potential improvements in energy efficiency and provide insights into the benefits and limitations of using in-memory computing for wireless communication applications.
Open Access
Lossless data compression with polar codes
(2013) Çaycı, Semih
In this study, lossless polar compression schemes are proposed for finite source alphabets in the noiseless setting. In the first part, lossless polar source coding scheme for binary memoryless sources introduced by Arıkan is extended to general prime-size alphabets. In addition to the conventional successive cancellation decoding (SC-D), successive cancellation list decoding (SCL-D) is utilized for improved performance at practical block-lengths. For code construction, greedy approximation method for density evolution, proposed by Tal and Vardy, is adapted to non-binary alphabets. In the second part, a variable-length, zero-error polar compression scheme for prime-size alphabets based on the work of Cronie and Korada is developed. It is shown numerically that this scheme provides rates close to minimum source coding rate at practical block-lengths under SC-D, while achieving the minimum source coding rate asymptotically in the block-length. For improved performance at practical block-lengths, a scheme based on SCL-D is developed. The proposed schemes are generalized to arbitrary finite source alphabets by using a multi-level approach. For practical applications, robustness of the zero-error source coding scheme with respect to uncertainty in source distribution is investigated. Based on this robustness investigation, it is shown that a class of prebuilt information sets can be used at practical block-lengths instead of constructing a specific information set for every source distribution. Since the compression schemes proposed in this thesis are not universal, probability distribution of a source must be known at the receiver for reconstruction. In the presence of source uncertainty, this requires the transmitter to inform the receiver about the source distribution. As a solution to this problem, a sequential quantization with scaling algorithm is proposed to transmit the probability distribution of the source together with the compressed word in an efficient way.
Open Access
On polarization adjusted convolutional codes over fading and additive white Gaussian noise channels
(2022-05) Seyedmasoumian Charandabi, Seyed Sadra
Ultra-reliable and low-latency communications (URLLC), which focuses on delay sensitive applications and services, is one of the three main pillars of 5G New Radio (NR) network architecture. URLLC's physical layer design is challenging since it must meet two contradictory requirements: ultra-low latency and ultra-high reliability. Short packets are used to minimize latency but at the cost of a significant loss of coding gain. Alternatively, system bandwidth can be increased, which is not always practical, particularly for some URLLC applications in industrial control that use unlicensed spectrum. In order to improve reliability, we must utilize robust channel codes in conjunction with retransmission techniques. Therefore, the construction of block codes with short blocklengths (e.g., a thousand or less information bits) is receiving significant attention with emerging wireless communications applications. In this thesis, we review existing channel coding bounds with short blocklengths for both additive white Gaussian noise (AWGN) and block fading channels. Furthermore, we investigate the performances of tail-biting convolutional, polar, and polarization adjusted convolutional (PAC) codes. With the motivation of reducing the decoding complexity of PAC decoders, we implement an alternative sequential decoding algorithm, namely, creeper algorithm, and describe a simplified list decoding approach. We also conduct an investigation on the performance of PAC codes and channel coding limits for block fading channels. Furthermore, we derive a method for computing approximate weight distribution of PAC codes, which can be used for an accurate performance bound; and, employing this approximation, we design PAC codes utilizing simulated annealing for optimization of the rate profiles. The results show that the newly designed PAC code rate profiles offer superior performance.
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
Performance and computational analysis of polarization-adjusted convolutional (PAC) codes
(2022-06) Moradi, Mohsen
We study the performance of sequential decoding of polarization-adjusted con- volutional (PAC) codes. We present a metric function that employs bit-channel mutual information and cutoff rate values as the bias values and significantly re- duces the computational complexity while retaining the excellent error-correction performance of PAC codes. With the proposed metric function, the computa- tional complexity of sequential decoding of PAC codes is equivalent to that of conventional convolutional codes. Our results indicate that the upper bound on the sequential decoding compu- tational complexity of PAC codes follows a Pareto distribution. We also employ guessing technique to derive a lower bound on the computational complexity of sequential decoding of PAC codes. To reduce the PAC sequential decoder’s worst-case latency, we restrict the number of searches executed by the sequential decoder. We introduce an improvement to the successive-cancellation list (SCL) decod- ing for polarized channels that reduces the number of sorting operations without degrading the code’s error-correction performance. In an SCL decoding with an optimum metric function, we show that, on average, the correct branch’s bit- metric value must be equal to the bit-channel capacity. On the other hand, the average bit-metric value of a wrong branch can be at most 0. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. This enables the decoder to identify incorrect branches and exclude them from the list of metrics to be sorted. We employ a similar technique to the stack algorithm, resulting in a considerable reduction in the stack size. Additionally, we propose a technique for constructing a rate profile for PAC codes of arbitrary length and rate which is capable of balancing the error- correction performance and decoding complexity of PAC codes. For signal-to- noise ratio (SNR) values larger than a target SNR value, the proposed approach can significantly enhance the error-correction performance of PAC codes while retaining a low mean sequential decoding complexity. Finally, we examine the weight distribution of PAC codes with the goal of providing a new demonstration that PAC codes surpass polar codes in terms of weight distribution.
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
Polar code construction for non-binary source alphabets
(IEEE, 2012) Çaycı, Semih; Arıkan, Orhan; Arıkan, Erdal
In this paper, approximation methods for binary polar code construction proposed by Tal and Vardy are extended to non-binary source alphabets. Additionally, a new approximation method that enables accurate polar code construction with less usage of computational resources is proposed. Efficiency and accuracy of proposed methods are supported analytically and numerically. © 2012 IEEE.
Open Access
Polar codes for distributed source coding
(2014) Önay, Saygun
Polar codes were invented by Arıkan as the first “capacity achieving” codes for binary-input discrete memoryless symmetric channels with low encoding and decoding complexity. The “polarization phenomenon”, which is the underlying principle of polar codes, can be applied to different source and channel coding problems both in single-user and multi-user settings. In this work, polar coding methods for multi-user distributed source coding problems are investigated. First, a restricted version of lossless distributed source coding problem, which is also referred to as the Slepian-Wolf problem, is considered. The restriction is on the distribution of correlated sources. It is shown that if the sources are “binary symmetric” then single-user polar codes can be used to achieve full capacity region without time sharing. Then, a method for two-user polar coding is considered which is used to solve the Slepian-Wolf problem with arbitrary source distributions. This method is also extended to cover multiple-access channel problem which is the dual of Slepian-Wolf problem. Next, two lossy source coding problems in distributed settings are investigated. The first problem is the distributed lossy source coding which is the lossy version of the Slepian-Wolf problem. Although the capacity region of this problem is not known in general, there is a good inner bound called the Berger-Tung inner bound. A polar coding method that can achieve the whole dominant face of the Berger-Tung region is devised. The second problem considered is the multiple description coding problem. The capacity region for this problem is also not known in general. El Gamal-Cover inner bound is the best known bound for this problem. A polar coding method that can achieve any point on the dominant face of El Gamal-Cover region is devised.
Open Access
Polar codes for distributed source coding
(The Institution of Engineering and Technology, 2013) Önay, S.
A polar coding method to construct a distributed source coding scheme which can achieve any point on the dominant face of the Slepian-Wolf rate region for sources with uniform marginals is proposed. Source encoding and decoding operations are performed using efficient algorithms which makes practical implementation feasible. Simulation results are given to exhibit the performance of the presented method. © The Institution of Engineering and Technology 2013.