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Varentropy Decreases Under the polar Transform

IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第6期62卷 3390-3400页

作者： Arikan, Erdal Bilkent Univ Dept Elect Elect Engn TR-06800 Ankara Turkey

We consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair (X, Y) consisting of a binary random variable X and an arbitrary side information random variable Y. The varentropy of (X, Y) is defined as the variance of the random variable - log (pX vertical bar Y) (X vertical bar Y). A polar transform of order two is a certain mapping that takes two independent BDEs and produces two new BDEs that are correlated with each other. It is shown that the sum of the varentropies at the output of the polar transform is less than or equal to the sum of the varentropies at the input, with equality if and only if at least one of the inputs has zero varentropy. This result is extended to polar transforms of higher orders and it is shown that the varentropy asymptotically decreases to zero when the BDEs at the input are independent and identically distributed.

关键词： polar coding varentropy dispersion

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polar-Coded OFDM With Index Modulation

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2024年第4期73卷 5335-5347页

作者： Zhang, Dexin Niu, Kai Beijing Univ Posts & Telecommun BUPT Minist Educ Key Lab Universal Wireless Commun Beijing 100876 Peoples R China

This paper studies the joint design of polar coding and orthogonal frequency division multiplexing with index modulation (OFDM-IM) to improve the system error performance. A three-stage channel transform is established based on cascaded signal-code polarization to decompose the raw OFDM-IM channel into polarized subchannels. Both multilevel coding (MLC) and bit-interleaved coded-modulation (BICM) based approaches are considered. For the transceiver implementation, a polar code construction method based on mutual information equivalence is first presented, followed by several well-designed index mapping lookup tables to ensure equal activation probabilities for each subcarrier. An index set partitioning (ISP) rule is further proposed to enhance the system polarization effect. Subsequently, the multi-stage collaborative receiver structure is described, along with a bit log-likelihood ratio (LLR) calculation method. Furthermore, the proposed polar-coded OFDM-IM framework can be extended to other OFDM-IM variants, such as OFDM-I/Q-IM. Simulation results demonstrate the superior error performance of the proposed schemes.

关键词： Encoding Symbols polar codes Transforms OFDM Reliability polar coding cascaded signal-code polarization orthogonal frequency division multiplexing (OFDM) index modulation (IM) index set partitioning (ISP)

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A Balanced Tree Approach to Construction of Length-Flexible polar Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第2期72卷 665-674页

作者： Yao, Xinyuanmeng Ma, Xiao Sun Yat sen Univ Sch Comp Sci & Engn Guangdong Prov Key Lab Informat Secur Technol Guangzhou 510006 Peoples R China

We propose a length-flexible coding scheme by defining a balanced tree. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either active bits or frozen bits, and a parent node is related to its child nodes by a length-adaptive $(U+V\mid V)$ operation. Both the encoding and the successive cancellation (SC)-based decoding can be implemented over the constructed coding tree. For code construction, we propose a signal-to-noise ratio (SNR)-dependent method and two SNR-independent methods, all of which evaluate the reliabilities of leaf nodes and then select the most reliable leaf nodes as the active nodes. Numerical results demonstrate that our proposed codes can have comparable performance to the 5G polar codes. To reduce the decoding latency, we propose a partitioned successive cancellation (PSC)-based decoding algorithm, which can be implemented over a sub-tree obtained by pruning the coding tree. Numerical results show that the PSC-based decoding can achieve similar performance to the conventional SC-based decoding.

关键词： Code construction coding tree length-flexible coding partitioned successive cancellation-based decoding polar coding

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polarization-Aided coding for Nonorthogonal Multiple Access

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IEEE INTERNET OF THINGS JOURNAL 2024年第17期11卷 27894-27903页

作者： Xie, Zhaopeng Chen, Pingping Fang, Yi Chen, Qiwang Fuzhou Univ Sch Adv Mfg Fuzhou 350108 Jinjiang Peoples R China Fuzhou Univ Coll Phys & Informat Engn Sch Adv Mfg Fuzhou 350108 Peoples R China Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Peoples R China Huaqiao Univ Sch Informat Sci & Engn Xiamen Peoples R China

In this article, we propose a polarization-aided polar coding scheme over nonorthogonal multiple access channels operated with physical-layer network coding (PN-NOMA), where $M$ users adopt polar coding for transmission. By exploiting the characteristic of physical-layer network coding and polar encoding, we found that the polar code at the users can be seen as nested codes and subcodeword of a larger polar code. It enables us to construct a single (virtual) polar code at the receiver, which has the length M times longer than that of the original user codes. In this way, we can decode all the user messages within this single polar code. The channel polarization effect as well as the decoding performance can be improved. We further propose a Monte Carlo-based code construction for the virtual polar code with user channel coefficients, and short nested user codes can be individually derived from this code. Simulation results show that the proposed PN-NOMA can achieve significant performance gains of more than 0.5 dB as compared to conventional polar-coded NOMA (PC-NOMA) over power-imbalanced channels, and this gain is more than 2 dB over Rayleigh fading channels.

关键词： Codes NOMA polar codes Receivers Encoding Decoding Gain Channel coefficients channel polarization effect nonorthogonal multiple access (NOMA) physical layer network coding polar coding

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FTN-GFDM Detection Based on Reduced-Complexity Soft Sphere Decoding Integrated with polar Codes

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JOURNAL OF COMMUNICATIONS AND NETWORKS 2024年第3期26卷 284-296页

作者： de Mello, Mariana Baracat Mendes, Luciano Leonel Silva, Daniely Gomes da Silva, Paulo Ricardo Branco Barbosa, Tiago Cardoso Inst Nacl Telecomunicacoes Inatel BR-37540000 Santa Rita Do Sapucai MG Brazil Ctr Pesquisa & Desenvolvimento Telecomunicacoes CP BR-13086902 Campinas SP Brazil

In remote rural areas, it is not possible to employ massive multiple-input multiple-output (MIMO), small cells, and ultra-dense networks (UDNs) with the aim of increasing throughput. A solution is to improve the waveform spectral efficiency, integrating faster than Nyquist (FTN) signaling with generalized frequency division multiplexing (GFDM). However, this presents high self-interference in the time and frequency domains, requiring dedicated detectors for performance loss mitigation. Hard decision detection schemes primarily designed for MIMO have been adapted to detect FTN-GFDM signals without degradation of the uncoded bit error rate (BER), but these schemes are suboptimal in terms of capacity as they do not provide all the information contained in log-likelihood ratios (LLRs). We design and evaluate in this paper a soft sphere detector (SD) algorithm for FTN-GFDM that can be integrated with state-of-the-art forward error control (FEC) decoders for good BER performance over mobile channels. The SD detector is combined with polar codes, and the BER and complexity are evaluated for different channel models. The results show that FTN-GFDM can provide high spectrum efficiency gains without significant coded BER losses and with affordable complexity on the receiver side, which makes this waveform an interesting candidate for mobile networks in remote areas.

关键词： Faster than Nyquist generalized frequency di- vision multiplexing polar coding single tree search algorithm soft sphere decoder

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An Improvement of Modified Successive-Cancellation Decoder for polar Codes

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IEEE COMMUNICATIONS LETTERS 2013年第12期17卷 2360-2363页

作者： Huang, Zhiliang Diao, Chunjuan Dai, Jianxin Duanmu, Chunjiang Wu, Xia Chen, Ming Zhejiang Normal Univ Sch Math Phys & Informat Engn Jinhua 321004 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China Nanjing Univ Posts & Telecommun Sch Sci Nanjing 210046 Jiangsu Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China

An improvement is introduced of the modified successive-cancellation (MSC) decoding for polar codes, in which local decoders at rate-other nodes are simplified. This improvement reduces the decoding latency and complexity of the MSC decoding with no sacrifice in error performance. Furthermore, in our method, the decoding latency decreases rapidly with increasing signal-to-noise ratio. Significant latency and complexity reductions are shown by simulation results.

关键词： polar codes polar coding successive cancellation decoding

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Shaped polar Codes for Higher Order Modulation

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IEEE COMMUNICATIONS LETTERS 2018年第2期22卷 252-255页

作者： Iscan, Onurcan Bohnke, Ronald Xu, Wen Huawei Technol Duesseldorf GmbH European Res Ctr D-80992 Munich Germany

A new polar coding scheme for higher order modulation is presented. An encoding method is proposed such that in combination with Gray labeled amplitude shift keying the channel input symbols have a desired non-uniform distribution, resulting in a shaping gain at the receiver compared with the conventional bit-interleaved coded modulation. The proposed scheme mainly affects the encoder, and the complexity increase at the receiver is negligible.

关键词： polar coding probabilistic shaping coded modulation

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Hardware Implementation of Fano Decoder for polarization-Adjusted Convolutional (PAC) Codes

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2022年第3期69卷 1632-1636页

作者： Mozammel, Amir Bilkent Univ Dept Elect Elect Engn TR-06800 Ankara Turkey

This brief proposes a hardware implementation architecture for Fano decoding of polarization-adjusted convolutional (PAC) codes. This architecture uses a novel branch metric unit specific to PAC codes. The proposed decoder is tested on FPGA, and its performance is evaluated on ASIC using TSMC 28 nm 0.72 V library. The decoder can be clocked at 500 MHz and reach an average information throughput of 38 Mb/s at 3.5 dB signal-to-noise ratio for a block length of 128 and a code rate of 1/2.

关键词： Decoding Picture archiving and communication systems Measurement Codes Hardware Convolution Encoding PAC codes sequential decoding Fano polar coding VLSI

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A New Two-User Binary polar Coded Multiple Access Scheme With Power and Rate Allocation

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IEEE WIRELESS COMMUNICATIONS LETTERS 2021年第10期10卷 2299-2303页

作者： Ng, Benjamin K. Lam, Chan-Tong Macao Polytech Inst Sch Appl Sci Macau Peoples R China

A new polar-code-based scheme with power and rate allocation is proposed to enhance the block error rate (BLER) performance in a two-user binary Gaussian multiple access channel (GMAC). Unlike previous works which mainly focused on the capacity-achieving capability of polar codes in the multiple access channel, we improve their finite-blocklength coding performance in the specific two-user channel. In our proposed scheme, each user employs two blocks of polar codes with unequal transmit power levels, and a notable feature of our approach is that the code construction and rate allocation of these two blocks as well as their power levels can be jointly optimized to give rise to performance improvement. We analytically derive the BLER upper bound of the proposed scheme using the information-theoretic coding performance approximation in the finite blocklength regime. We demonstrate the validity of our approach through simulations and show the performance advantages of the proposed scheme over the previously reported two-user LDPC-based and polar-coded GMAC of similar blocklength.

关键词： Decoding Resource management polar codes Encoding Complexity theory Upper bound Transmitters polar coding multiple access power allocation

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Performance Analysis of NR polar Codes at Short Information Blocks for Control Channels

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WIRELESS PERSONAL COMMUNICATIONS 2024年第2期138卷 879-890页

作者： Sinha, Tirthadip Bhaumik, Jaydeb Haldia Inst Technol Haldia India Jadavpur Univ Kolkata India

One important innovation in information and coding theory is polar code, which delivers capacity attaining error correction performance varying code rates and block lengths. In recent times, polar codes are preferred to offer channel coding in the physical control channels of the 5G (5th Generation) wireless standard by 3GPP (Third Generation Partnership Project) New Radio (NR) group. Being a part of the physical layer, Channel coding plays key role in deciding latency and reliability of a communication system. However, the error correction performance degrades with decreased message lengths. 5G NR requires channel codes with low rates, very low error floors with short message lengths and low latency in coding process. In this work, Distributed Cyclic Redundancy Check Aided polar (DCA-polar) code along with Cyclic Redundancy Check Aided polar (CA-polar) code, the two variant of polar codes have been proposed which provide significant error-correction performance in the regime of short block lengths and enable early termination of decoding processes. While CRC bits improve the performance of SCL (successive cancellation list) decoding by increasing distance properties, distributed CRC bits permit path trimming and early-termination of the decoding process. The design can reduce the decoding latency and energy consumption of hardware, which is crucial for mobile applications like 5G. The work also considers the performance analysis of NR polar codes over AWGN (Additive White Gaussian Noise) for short information block lengths at low code rates in the uplink and downlink control channels using SNR (Signal to Noise Ratio) and FAR (False Alarm Rate) as the performance measures. Simulation results illustrate different trade-offs between error-correction and detection performances comparing proposed NR polar coding schemes.

关键词： 5G NR SNR FAR Distributed CRC DCA-polar CA-polar polar coding List decoding Successive cancellation Blocklength AWGN PUCCH PDCCH

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