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A Randomized Construction of Polar Subcodes [article]

Peter Trifonov, Grigorii Trofimiuk
2017 arXiv   pre-print
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  ...  CONCLUSIONS In this paper a randomized construction of polar subcodes was proposed.  ...  The proposed code construction algorithm Below we present a summary of the proposed method for construction of an (n, k) randomized polar subcode.  ... 
arXiv:1705.00202v2 fatcat:cdg7q7hgdve5rgnw3d4v7qylxy

Polar Coded Diversity on Block Fading Channels via Polar Spectrum [article]

Kai Niu, Yan Li
2020 arXiv   pre-print
In this paper, we establish a systematic framework to analyze the error performance of polar codes in the case of block mapping and random mapping.  ...  For arbitrary diversity order in the random mapping, with the help of uniform interleaving, we derive the approximate split polar spectrum by combining the polar spectrum and the probability of fading  ...  POLAR CODING BASED ON RANDOM MAPPING In this section, we consider the construction method of polar codes under the random mapping.  ... 
arXiv:2003.13320v1 fatcat:n7yitb5klbcgxig6emixoczdai

Randomized Nested Polar Subcode Constructions for Privacy, Secrecy, and Storage [article]

Onur Günlü, Peter Trifonov, Muah Kim, Rafael F. Schaefer, Vladimir Sidorenko
2020 arXiv   pre-print
A randomized nested PSC construction with a low-rate PSC and a high-rate PC, is proposed for list and sequential successive cancellation decoders.  ...  We consider polar subcodes (PSCs), which are polar codes (PCs) with dynamically-frozen symbols, to increase the minimum distance as compared to corresponding PCs.  ...  Polar Subcodes and Randomized Construction PSCs are a generalization of PCs, allowing some frozen symbols to be equal to linear combinations of other symbols [21] .  ... 
arXiv:2004.12091v3 fatcat:5qxcwgv36rbphn3hghoq6qk5te

Bit-permuted coded modulation for polar codes [article]

Saurabha R Tavildar
2016 arXiv   pre-print
When using polar codes designed for BPSK modulation, we show gains for BPCM over BICM with random interleaver of up to 0.2 dB, 0.7 dB and 1.4 dB for 4-ASK, 8-ASK, and 16-ASK respectively.  ...  The BPCM technique exploits a natural connection between MLC and polar codes. It involves applying bit permutations prior to mapping the polar code to a higher order modulation.  ...  For using BPSK codes with BICM technique, a random interleaver is used, and bit-channel capacities of the modulation with Gray labeling are used for the computation.  ... 
arXiv:1609.09786v1 fatcat:r6fngrp2ojgn3jlwkf7f5ps3my

A Search Method for Large Polarization Kernels [article]

Grigorii Trofimiuk
2021 arXiv   pre-print
A new search method for large polarization kernels is proposed.  ...  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 include the results for descending (DES) asymmetric construction with 16bit CRC [29] and improved hybrid design [30] of MK polar codes together with the performance of randomized chained polar  ... 
arXiv:2101.10269v4 fatcat:p7lds4azxvcyrlzwwob43dkfp4

Performance and Construction of Polar Codes: The Perspective of Bit Error Probability [article]

Bolin Wu, Kai Niu, Jincheng Dai
2022 arXiv   pre-print
In this paper, we establish a new framework to analyze the bit error probability of polar codes.  ...  Guided by the concept of polar subcode, we then derive an upper bound on the conditional bit error probability of each bit-channel, and accordingly, an upper bound on the bit error probability of polar  ...  Based on the weight distribution of polar subcode, a theoretical framework was established to analyze and construct polar codes.  ... 
arXiv:2204.07435v1 fatcat:j3hkhcxaanfn5cl22ppv6tn7vm

Polar Codes: Analysis and Construction Based on Polar Spectrum [article]

Kai Niu, Yan Li, Weiling Wu
2019 arXiv   pre-print
Thus we establish a systematic framework in term of the polar spectrum to analyze and construct polar codes.  ...  In this paper, by revisiting the error event of the polarized channel, a new concept, named polar spectrum, is introduced from the weight distribution of polar codes.  ...  Consequently, we set up a oneto-one mapping between the polarized channel and the polar subcode and introduce the weight distribution of the polar subcode, named polar spectrum, which is a set of the weight  ... 
arXiv:1908.05889v2 fatcat:lm3evlnq2rhjfie4urlhietzoe

Recursive Trellis Processing of Large Polarization Kernels [article]

Peter Trifonov
2021 arXiv   pre-print
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  ...  Polar subcodes were constructed using a mixture of kernels, as shown in the plot. It can be seen that polar subcodes provide almost the same performance as LDPC codes.  ... 
arXiv:2101.08081v2 fatcat:gx4lnh2zszdplewqedhdsj6pea

Successive Cancellation Inactivation Decoding for Modified Reed-Muller and eBCH Codes

Mustafa Cemil Coskun, Joachim Neu, Henry D. Pfister
2020 2020 IEEE International Symposium on Information Theory (ISIT)  
This decoder leverages the structure of the Hadamard matrix, but can be applied to any linear code by representing it as a polar code with dynamic frozen bits.  ...  A successive cancellation (SC) decoder with inactivations is proposed as an efficient implementation of SC list (SCL) decoding over the binary erasure channel.  ...  In [17] , the idea of dynamic frozen bits was used to define eBCH-polar subcodes. The construction of an (n, k) eBCHpolar subcode starts by choosing C to be an (n, k ) eBCH code with k < k .  ... 
doi:10.1109/isit44484.2020.9174226 dblp:conf/isit/CoskunNP20 fatcat:vj7zd654a5gdpbvjfhp4pmr2yu

Fast Sequential Decoding of Polar Codes [article]

Peter Trifonov, Vera Miloslavskaya, Ruslan Morozov
2018 arXiv   pre-print
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths.  ...  This enables significant complexity reduction with respect to the original stack algorithm at the expense of a negligible performance loss.  ...  The obtained codes are referred to as polar subcodes. Polar codes with CRC [2] can be considered as a special case of polar subcodes.  ... 
arXiv:1703.06592v2 fatcat:w7tckav65zavnmjlg5jjtub33a

Fast Block Sequential Decoding of Polar Codes [article]

Grigorii Trofimiuk, Nikolay Iakuba, Stanislav Rets, Kirill Ivanov, Peter Trifonov
2020 arXiv   pre-print
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  ...  Construction of such codewords is implemented by fast decoding algorithms, which are available for many codes arising in the decomposition of polar codes.  ...  Figure 4a illustrates the performance of the proposed BSDA. Simulations were run for the case of AWGN channel, BPSK modulation and randomized polar subcode [4] .  ... 
arXiv:1808.07268v2 fatcat:6u65wjx7zjd2vavoa3xgw2utny

Successive Cancellation Inactivation Decoding for Modified Reed-Muller and eBCH Codes [article]

Mustafa Cemil Coşkun, Joachim Neu, Henry D. Pfister
2020 arXiv   pre-print
This decoder leverages the structure of the Hadamard matrix, but can be applied to any linear code by representing it as a polar code with dynamic frozen bits.  ...  A successive cancellation (SC) decoder with inactivations is proposed as an efficient implementation of SC list (SCL) decoding over the binary erasure channel.  ...  In [17] , the idea of dynamic frozen bits was used to define eBCH-polar subcodes. The construction of an (n, k) eBCHpolar subcode starts by choosing C to be an (n, k ′ ) eBCH code with k < k ′ .  ... 
arXiv:2004.05969v1 fatcat:wbsllenl3bd7jci6nyehbwku3u

Adjacent-Bits-Swapped Polar codes: A new code construction to speed up polarization [article]

Guodong Li, Min Ye, Sihuang Hu
2022 arXiv   pre-print
We add a permutation layer after each polar transform layer in the construction of the ABS polar codes.  ...  The construction of polar codes with code length n=2^m involves m layers of polar transforms.  ...  MAIN IDEA OF THE NEW CODE CONSTRUCTION A. The polarization framework Let U 1 , U 2 , . . . , U n be n i.i.d. Bernoulli-1/2 random variables. Let G n be an n×n invertible matrix over the binary field.  ... 
arXiv:2202.04454v1 fatcat:kihuinncdne5xdc4f6as75hxt4

On Distance Properties of Convolutional Polar Codes [article]

Ruslan Morozov, Peter Trifonov
2019 arXiv   pre-print
Moreover, a construction of convolutional polar subcodes is proposed, which provides improved performance under successive cancellation list decoding.  ...  A lower bound on minimum distance of convolutional polar codes is provided.  ...  However, by generalizing the construction of randomized polar subcodes [10] to the case of CvPC, we obtain convolutional polar subcodes (CvPSs) with reduced error coefficient, which provide superior  ... 
arXiv:1901.06341v1 fatcat:ttblh3jyn5e65pk6mugtn7pvbu

An elementary description of polarization process [article]

Ilya Dumer
2020 arXiv   pre-print
This gives an elementary proof of polarization properties of SC decoding. We also derive a simple ordering of decoding channels with construction complexity of order nlog n.  ...  We analyze successive cancellation (SC) decoder by using two random functions.  ...  We also describe polarization as a set of random transformations of some angle θ, almost all of which lead θ to 0 or π/2. Section VII addresses fast polarization techniques.  ... 
arXiv:1706.06764v3 fatcat:gmeaegcy2vet3njplapj3dc6de
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