Decoding of the extended Golay code by the simplified successive-cancellation list decoder adapted to multi-kernel polar codes (original) (raw)

A method to enhance the performance of successive cancellation decoding in polar codes

2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), 2016

Polar codes are regarded as a major breakthrough in modern channel coding since they are capacity-achieving using simple successive cancellation (SC) decoding. However, this is only possible with significantly large code lengths which may not be applicable for many systems. In this paper, we focus on short length polar codes and present a method which can enhance the performance of the successive cancellation decoder. For the purpose of analysis, we discuss the SC code tree and show how the proposed method can improve the performance by increasing the computational nodes in the code tree. The results quantify the achieved performance improvement over the conventional SC decoder.

Recursive Descriptions of Decoding Algorithms and Hardware Architectures for Polar Codes

2012

Abstract: Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. This description allows an easy development of the first two algorithms for arbitrary polarizing kernels. Hardware architectures for these decoding algorithms are also described in a recursive way, both for Arikan's standard polar codes and for arbitrary polarizing kernels.

Fast Successive-Cancellation-Based Decoders of Polar Codes

IEEE Transactions on Communications, 2019

The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.

Generalized Fast Decoding of Polar Codes

2018 IEEE Global Communications Conference (GLOBECOM), 2018

Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have been selected as one of the coding schemes in the 5 th generation wireless standard (5G). Over the years various polar code decoding algorithms, like SC-list (SCL), have been proposed to improve the mediocre performance of the successive cancellation (SC) decoding algorithm for finite code lengths; however, like SC, they suffer from long decoding latency. Fast decoding of polar codes tries to overcome this problem by identifying particular subcodes in the polar code and decoding them with efficient decoders. In this work, we introduce a generalized approach to fast decoding of polar codes to further reduce SC-based decoding latency. We propose three multi-node polar code subcodes whose identification patterns include most of the existing subcodes, extending them to SCL decoding, and allow to apply fast decoding to larger subsets of bits. Without any error-correction performance degradation, the proposed technique shows up to 23.6% and 29.2% decoding latency gain with respect to fast SC and SCL decoding algorithms, respectively, and up to 63.6% and 49.8% if a performance loss is accepted, whose amount depends on code and decoding algorithm parameters, along with the desired speedup.

A low-complexity improved successive cancellation decoder for polar codes

2014 48th Asilomar Conference on Signals, Systems and Computers, 2014

Under successive cancellation (SC) decoding, polar codes are inferior to other codes of similar blocklength in terms of frame error rate. While more sophisticated decoding algorithms such as list-or stack-decoding partially mitigate this performance loss, they suffer from an increase in complexity. In this paper, we describe a new flavor of the SC decoder, called the SC flip decoder. Our algorithm preserves the low memory requirements of the basic SC decoder and adjusts the required decoding effort to the signal quality. In the waterfall region, its average computational complexity is almost as low as that of the SC decoder.

An Optimized Method for Polar Code Construction

International Journal of Advanced Computer Science and Applications, 2023

Polar codes are traditionally constructed by calculating the reliability of channels, then sorting them by intensive calculations to select the most reliable channels. However, these operations can be complicated especially when, the polar code length, N becomes great. This paper proposes a new low-complexity procedure for polar codes construction over binary erasure and additive white Gaussian noise (AWGN) channels. Using the proposed algorithm, the code construction complexity is reduced from O(Nlog N) to O(N), where N=2 n (n≥1). The proposed approach involves storing the classification of channels by reliabilities in a vector of length L, and then deriving the classification of M channels for every M where M<=L. The proposed method is consistent with Bhattacharya parameter based Construction and Density Evolution with Gaussian Approximation (DEGA) based construction. In this paper, the Successive Cancellation Decoding algorithm (SCDA) is used. Thanks to its low complexity and its high error-correction capability.

Multi-Kernel Polar Codes: Concept and Design Principles

IEEE Transactions on Communications, 2020

In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar code allows for more flexibility in terms of the code length, moreover allowing for various new design principles. We describe in detail encoding as well as successive cancellation (SC) decoding and SC list (SCL) decoding, and we provide a novel design method for the frozen set that allows to optimise the performance under list decoding, as opposed to original relability-based code design. Finally, we numerically demonstrate the advantage of multi-kernel polar codes under the new design principles compared to punctured and shortened polar codes.

LLR-Based Successive Cancellation List Decoding of Polar Codes

IEEE Transactions on Signal Processing, 2015

We present an LLR-based implementation of the successive cancellation list (SCL) decoder. To this end, we associate each decoding path with a metric which (i) is a monotone function of the path's likelihood and (ii) can be computed efficiently from the channel LLRs. The LLR-based formulation leads to a more efficient hardware implementation of the decoder compared to the known log-likelihood based implementation. Synthesis results for an SCL decoder with block-length of N = 1024 and list sizes of L = 2 and L = 4 confirm that the LLR-based decoder has considerable area and operating frequency advantages in the orders of 50% and 30%, respectively.

Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes

The capacity-achieving property of polar codes has garnered much recent research attention resulting in low-complexity and high-throughput hardware and software decoders. It would be desirable to implement flexible hardware for polar encoders and decoders that can implement polar codes of different lengths and rates, however this topic has not been studied in depth yet. Flexibility is of significant importance as it enables the communications system to adapt to varying channel conditions and is mandated in most communication standards. In this work, we describe a low-complexity and flexible systematic-encoding algorithm, prove its correctness, and use it as basis for encoder implementations capable of encoding any polar code up to a maximum length. We also investigate hardware and software implementations of decoders, describing how to implement flexible decoders that can decode any polar code up to a given length with little overhead and minor impact on decoding latency compared to...

Folded successive cancelation decoding of polar codes

2014 Australian Communications Theory Workshop (AusCTW), 2014

Polar codes are the first explicit class of codes that are provably capacity-achieving under the successive cancelation (SC) decoding. As a suboptimal decoder, SC has quasi-linear complexity N (1 + log N) in the code length N. In this paper, we propose a new non-binary SC decoder with reduced complexity N 2 (1 + log N 2) based on the folding operation, which was first proposed in [11] to implement folded tree maximum-likelihood decoding of polar codes. Simulation results for the additive white Gaussian noise channel show that folded SC decoders can achieve the same error performance of standard SC by suitable selecting the folding of the polar code.