arXiv subjects

Grigorii Trofimiuk

Publications and source records attributed to Grigorii Trofimiuk.

8 recordsLinked to original sources

arXiv2023

Fast Search Method for Large Polarization Kernels

A novel search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing the depth-first search combined with the computation of coset leaders weight tables and sufficient conditions of code non-equivalence. Using the proposed method, we improved all existing lower bounds on the maximum error exponent for kernels of size from 17 to 29. We also obtained kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results demonstrate the advantage of polar codes with the obtained kernels compared with shortened polar codes and polar codes with small kernels.

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

Shortened Polarization Kernels

A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick elimination of unsuitable shortening patterns. The proposed algorithm is applied to some kernels of sizes 16 and 32 to obtain shortened kernels of sizes from 9 to 31. These kernels are used in mixed-kernel polar codes of various lengths. Numerical results demonstrate the advantage of polar codes with shortened large kernels compared with shortened and punctured Arikan polar codes, and polar codes with small kernels.

cs.IT↗

arXiv2021

A Search Method for Large Polarization Kernels

A new search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing depth-first search combined with some methods which reduce the search space. Using the proposed method, we improved almost all existing lower bounds on the maximum rate of polarization for kernels of size from 17 to 27. We also obtained kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results demonstrate the advantage of polar codes with the proposed kernels compared with shortened polar codes and polar codes with small kernels.

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↗

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↗

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↗