arXiv subjects

Peter Trifonov

Publications and source records attributed to Peter Trifonov.

18 recordsLinked to original sources

arXiv2026

Efficient LLR-Domain Decoding of ABS+ Polar Codes

ABS+ polar codes are a generalization of Arikan polar codes that provides much faster polarization. We present an LLR-domain version of the SCL decoder of ABS+ polar codes. Furthermore, we optimize the SCL algorithm in order to reduce the complexity of LLR computation. In comparison with classical polar codes, the proposed approach requires less number of arithmetic operations in the SCL decoder to obtain the same frame error rate (FER) at high-SNR region.

cs.IT↗

arXiv2025

Polar subcodes for MIMO systems

Polar-coded multiple-input multiple-output systems are investigated. An advanced receiver implementing joint list decoding of polar codes and QR- and MMSE-based detectors is proposed. The approximate and exact path metrics are derived for joint list decoder of polar codes. A construction of polar subcodes for MIMO systems with cross-antenna dynamic freezing constraints is proposed. The obtained polar subcodes provide significant performance gain compared to LDPC-coded MIMO systems with the same rate allocation.

cs.IT↗

arXiv2023

Distributed Video Coding Based on Polar Codes

In this letter we present an improved distributed video coding (DVC) scheme based on polar coding techniques. Firstly, we adapt log-likelihood ratios (LLRs) for DVC with integer implementation of a discrete cosine transform (DCT). We propose a computationally efficient and numerically stable modification of these LLRs based on the simplified methods of polar codes decoding. We show that on average this approach provides 0.3 dB PSNR gain for DVC with LDPC accumulated (LDPCA) codes. Secondly, we introduce the nested shortened polar codes construction algorithm. We demonstrate that replacement of LDPCA by polar codes improves PSNR by 0.1 dB on average, whereas, for videos with relatively high motion level, the gain reaches up to 0.23, 0.39 and 0.55 dB for Group of Pictures (GOP) lengths 2, 4 and 8 frames, respectively. Finally, experimental results demonstrate that DVC with polar codes and Tal-Vardy list decoder operates up to two times faster than DVC with LDPCA code and belief propagation (BP) decoder.

cs.IT↗

arXiv2021

Window Processing of Binary Polarization Kernels

A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbols probabilities by computing the probabilities of several paths in Arikan successive cancellation (SC) decoder. In this paper we propose an improved version of WP, which has significantly lower arithmetic complexity and operates in log-likelihood ratios (LLRs) domain. The algorithm identifies and reuses common subexpressions arising in computation of Arikan SC path scores. The proposed algorithm is applied to kernels of size 16 and 32 with improved polarization properties. It enables polar (sub)codes with the considered kernels to simultaneously provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.

cs.IT↗

arXiv2021

Recursive Trellis Processing of Large Polarization Kernels

A reduced complexity algorithm is presented for computing the log-likelihood ratios arising in the successive cancellation decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits recursive trellis representation of the codes generated by submatrices of the polarization kernel, and enables codes based on large kernels to provide better performance compared to the codes based on Arikan kernel with the same decoding complexity.

cs.IT↗

arXiv2020

Performance and Complexity of the Sequential Successive Cancellation Decoding Algorithm

Simulation results illustrating the performance and complexity of the sequential successive cancellation decoding algorithm are presented for the case of polar subcodes with Arikan and large kernels, as well as for extended BCH\ codes. Performance comparison with Arikan PAC and LDPC codes is provided. Furthermore, complete description of the decoding algorithm is presented.

cs.IT↗

arXiv2020

Randomized Nested Polar Subcode Constructions for Privacy, Secrecy, and Storage

We consider polar subcodes (PSCs), which are polar codes (PCs) with dynamically-frozen symbols, to increase the minimum distance as compared to corresponding PCs. A randomized nested PSC construction with a low-rate PSC and a high-rate PC, is proposed for list and sequential successive cancellation decoders. This code construction aims to perform lossy compression with side information. Nested PSCs are used in the key agreement problem with physical identifiers. Gains in terms of the secret-key vs. storage rate ratio as compared to nested PCs with the same list size are illustrated to show that nested PSCs significantly improve on nested PCs. The performance of the nested PSCs is shown to improve with larger list sizes, which is not the case for nested PCs considered.

cs.IT↗

arXiv2020

Fast Block Sequential Decoding of Polar Codes

A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords of these codes in the descending order of their probability. Construction of such codewords is implemented by fast decoding algorithms, which are available for many codes arising in the decomposition of polar codes. Further complexity reduction is achieved by taking hard decisions of the intermediate LLRs, and avoiding decoding of some outer codes. Data structures for sequential decoding of polar codes are described. The proposed algorithm can be also used for decoding of polar codes with CRC and short extended BCH\ codes. It has lower average decoding complexity compared with the existing decoding algorithms for the corresponding codes. \end{abstract}

cs.IT↗

arXiv2020

Efficient decoding of polar codes with some 16$\times$16 kernels

A decoding algorithm for polar codes with binary 16$\times$16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the Arikan matrix to significantly reduce the decoding complexity without any performance loss. Simulation results show that polar (sub)codes with 16$\times$16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.

cs.IT↗

arXiv2019

On Distance Properties of Convolutional Polar Codes

A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of convolutional polar subcodes is proposed, which provides improved performance under successive cancellation list decoding. For sufficiently large list size, the decoding complexity of convolutional polar subcodes appears to be lower compared to Arikan polar subcodes with the same performance. The error probability of successive cancellation list decoding of convolutional polar subcodes is lower than that of Arikan polar subcodes with the same list size.

cs.IT↗

arXiv2018

Algebraic matching techniques for fast decoding of polar codes with Reed-Solomon kernel

We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft decoding of Reed-Solomon codes. Algebraic properties of the Reed-Solomon code are exploited to increase the reprocessing order. The obtained algorithm is used as a building block to obtain a decoder for polar codes with Reed-Solomon kernel.

cs.IT↗

arXiv2018

Chained Successive Cancellation Decoding of the Extended Golay code

The extended Golay code is shown to be representable as a chained polar subcode. This enables its decoding with the successive cancellation algorithm and its stack generalization. The decoder can be further simplified by employing fast Hadamard transform. The complexity of the obtained algorithm is comparable with that of the Vardy algorithm.

cs.IT↗

arXiv2018

Fast Sequential Decoding of Polar Codes

A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path. This enables significant complexity reduction with respect to the original stack algorithm at the expense of a negligible performance loss.

cs.IT↗

arXiv2017

A Randomized Construction of Polar Subcodes

A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are provided, which show that the obtained codes outperform LDPC and turbo codes.

cs.IT↗

arXiv2015

Polar Subcodes

An extension of polar codes is proposed, which allows some of the frozen symbols, called dynamic frozen symbols, to be data-dependent. A construction of polar codes with dynamic frozen symbols, being subcodes of extended BCH codes, is proposed. The proposed codes have higher minimum distance than classical polar codes, but still can be efficiently decoded using the successive cancellation algorithm and its extensions. The codes with Arikan, extended BCH and Reed-Solomon kernel are considered. The proposed codes are shown to outperform LDPC and turbo codes, as well as polar codes with CRC.

cs.IT↗

arXiv2013

Polar Codes with Dynamic Frozen Symbols and Their Decoding by Directed Search

A novel construction of polar codes with dynamic frozen symbols is proposed. The proposed codes are subcodes of extended BCH codes, which ensure sufficiently high minimum distance. Furthermore, a decoding algorithm is proposed, which employs estimates of the not-yet-processed bit channel error probabilities to perform directed search in code tree, reducing thus the total number of iterations.

cs.IT↗

arXiv2013

On the Root Finding Step in List Decoding of Folded Reed-Solomon Codes

The root finding step of the Guruswami-Rudra list decoding algorithm for folded Reed-Solomon codes is considered. It is shown that a multivariate generalization of the Roth-Ruckenstein algorithm can be used to implement it. This leads to an improved bound on the size of the list produced by the decoder, as well as enables one to relax the constraints on the parameters of folded codes. Furthermore, the class of time-domain folded Reed-Solomon codes is introduced, which can be efficiently list decoded with the Guruswami-Rudra algorithm, and provides greater flexibility in parameter selection than the classical (frequency-domain) folded codes.

cs.IT↗

arXiv2010

Efficient Interpolation in the Guruswami-Sudan Algorithm

A novel algorithm is proposed for the interpolation step of the Guruswami-Sudan list decoding algorithm. The proposed method is based on the binary exponentiation algorithm, and can be considered as an extension of the Lee-O'Sullivan algorithm. The algorithm is shown to achieve both asymptotical and practical performance gain compared to the case of iterative interpolation algorithm. Further complexity reduction is achieved by integrating the proposed method with re-encoding. The key contribution of the paper, which enables the complexity reduction, is a novel randomized ideal multiplication algorithm.

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