Entropy

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12 pages, 610 KiB

Open AccessArticle

New Construction of Asynchronous Channel Hopping Sequences in Cognitive Radio Networks

by Yaoxuan Wang, Xianhua Niu, Chao Qi, Zhihang He and Bosen Zeng

Entropy 2023, 25(10), 1473; https://doi.org/10.3390/e25101473 - 22 Oct 2023

Viewed by 864

The channel-hopping-based rendezvous is essential to alleviate the problem of under-utilization and scarcity of the spectrum in cognitive radio networks. It dynamically allows unlicensed secondary users to schedule rendezvous channels using the assigned hopping sequence to guarantee the self-organization property in a limited [...] Read more.

The channel-hopping-based rendezvous is essential to alleviate the problem of under-utilization and scarcity of the spectrum in cognitive radio networks. It dynamically allows unlicensed secondary users to schedule rendezvous channels using the assigned hopping sequence to guarantee the self-organization property in a limited time. In this paper, we use the interleaving technique to cleverly construct a set of asynchronous channel-hopping sequences consisting of d sequences of period

x N^{2}

with flexible parameters, which can generate sequences of different lengths. By this advantage, the new designed CHSs can be used to adapt to the demands of various communication scenarios. Furthermore, we focus on the improved maximum-time-to-rendezvous and maximum-first-time-to-rendezvous performance of the new construction compared to the prior research at the same sequence length. The new channel-hopping sequences ensure that rendezvous occurs between any two sequences and the rendezvous times are random and unpredictable when using licensed channels under asynchronous access, although the full degree-of-rendezvous is not satisfied. Our simulation results show that the new construction is more balanced and unpredictable between the maximum-time-to-rendezvous and the mean and variance of time-to-rendezvous. Full article

(This article belongs to the Special Issue Coding and Entropy)

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25 pages, 354 KiB

Open AccessArticle

Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field

by Jiaxing Zhang

Entropy 2023, 25(10), 1445; https://doi.org/10.3390/e25101445 - 13 Oct 2023

Viewed by 836

Abstract

In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generalized Fisher information of a single space–time random field with respect [...] Read more.

In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generalized Fisher information of a single space–time random field with respect to time and space variables. Furthermore, we obtain the Jeffreys divergence between two space–time random fields obtained by different parameters under the same Fokker–Planck equations. Then, the identities between the partial derivatives of the Jeffreys divergence with respect to space–time variables and the generalized Fisher divergence are found, also known as the De Bruijn identities. Later, at the end of the paper, we present three examples of the Fokker–Planck equations on space–time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and their corresponding De Bruijn identities. Full article

(This article belongs to the Special Issue Coding and Entropy)

14 pages, 609 KiB

Open AccessArticle

Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback

by Haoheng Yuan, Guangfen Xie and Bin Dai

Entropy 2023, 25(9), 1339; https://doi.org/10.3390/e25091339 - 15 Sep 2023

Cited by 1 | Viewed by 615

Abstract

For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then [...] Read more.

For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key. By secret sharing, any capacity-achieving coding scheme for the AWGN channel without feedback can be secure by itself, which indicates that the capacity of the same model without the secrecy constraint also affords an achievable secrecy rate to the AWGN channel with an eavesdropper and feedback. Then it is natural to ask: is the secret key-based feedback scheme still the optimal scheme for the AWGN multiple-access channel (MAC) with an external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose the optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. This paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of an external eavesdropper and channel feedback. Full article

(This article belongs to the Special Issue Coding and Entropy)

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14 pages, 336 KiB

Open AccessArticle

Construction of Optimal Frequency Hopping Sequence Set with Low-Hit-Zone

by Xinyu Tian, Hongyu Han, Xianhua Niu and Xing Liu

Entropy 2023, 25(7), 1044; https://doi.org/10.3390/e25071044 - 11 Jul 2023

Viewed by 1039

Abstract

In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be [...] Read more.

In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be verified that they are optimal with respect to the Peng–Fan–Lee bound. Full article

(This article belongs to the Special Issue Coding and Entropy)

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17 pages, 510 KiB

Open AccessArticle

Channel Modeling and Quantization Design for 3D NAND Flash Memory

by Cheng Wang, Zhen Mei, Jun Li, Feng Shu, Xuan He and Lingjun Kong

Entropy 2023, 25(7), 965; https://doi.org/10.3390/e25070965 - 21 Jun 2023

Viewed by 1366

Abstract

As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new [...] Read more.

As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new sources of errors, which severely affects the reliability of the system. In this paper, for the first time, we derive the channel probability density function of 3D NAND flash memory by taking major sources of errors. Based on the derived channel probability density function, the mutual information (MI) for 3D flash memory with multiple layers is derived and used as a metric to design the quantization. Specifically, we propose a dynamic programming algorithm to jointly optimize read-voltage thresholds for all layers by maximizing the MI (MMI). To further reduce the complexity, we develop an MI derivative (MID)-based method to obtain read-voltage thresholds for hard-decision decoding (HDD) of error correction codes (ECCs). Simulation results show that the performance with jointly optimized read-voltage thresholds can closely approach that with read-voltage thresholds optimized for each layer, with much less read latency. Moreover, the MID-based MMI quantizer almost achieves the optimal performance for HDD of ECCs. Full article

(This article belongs to the Special Issue Coding and Entropy)

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13 pages, 887 KiB

Open AccessArticle

Windowed Joint Detection and Decoding with IR-HARQ for Asynchronous SCMA Systems

by Mengsheng Guan, Min Zhu and Baoming Bai

Entropy 2023, 25(6), 930; https://doi.org/10.3390/e25060930 - 13 Jun 2023

Viewed by 903

Abstract

To improve the decoding performance of asynchronous sparse code multiple access (SCMA) systems over additive white Gaussian noise (AWGN) channels, this paper proposes a novel windowed joint detection and decoding algorithm for a rate-compatible (RC), LDPC code-based, incremental redundancy (IR) hybrid automatic repeat [...] Read more.

To improve the decoding performance of asynchronous sparse code multiple access (SCMA) systems over additive white Gaussian noise (AWGN) channels, this paper proposes a novel windowed joint detection and decoding algorithm for a rate-compatible (RC), LDPC code-based, incremental redundancy (IR) hybrid automatic repeat quest (HARQ) scheme. Since incremental decoding can exchange information iteratively with the detections made at previous consecutive time units, we propose a windowed joint detection and decoding algorithm. The extrinsic information exchanging process is performed between the decoders and the previous w detectors at different consecutive time units. Simulation results show that the sliding-window IR-HARQ scheme for the SCMA system outperforms the original IR-HARQ scheme with a joint detection and decoding algorithm. The throughput of the SCMA system with the proposed IR-HARQ scheme is also improved. Full article

(This article belongs to the Special Issue Coding and Entropy)

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15 pages, 514 KiB

Open AccessArticle

Transformer-Based Detection for Highly Mobile Coded OFDM Systems

by Leijun Wang, Wenbo Zhou, Zian Tong, Xianxian Zeng, Jin Zhan, Jiawen Li and Rongjun Chen

Entropy 2023, 25(6), 852; https://doi.org/10.3390/e25060852 - 26 May 2023

Viewed by 1485

Abstract

This paper is concerned with mobile coded orthogonal frequency division multiplexing (OFDM) systems. In the high-speed railway wireless communication system, an equalizer or detector should be used to mitigate the intercarrier interference (ICI) and deliver the soft message to the decoder with the [...] Read more.

This paper is concerned with mobile coded orthogonal frequency division multiplexing (OFDM) systems. In the high-speed railway wireless communication system, an equalizer or detector should be used to mitigate the intercarrier interference (ICI) and deliver the soft message to the decoder with the soft demapper. In this paper, a Transformer-based detector/demapper is proposed to improve the error performance of the mobile coded OFDM system. The soft modulated symbol probabilities are computed by the Transformer network, and are then used to calculate the mutual information to allocate the code rate. Then, the network computes the codeword soft bit probabilities, which are delivered to the classical belief propagation (BP) decoder. For comparison, a deep neural network (DNN)-based system is also presented. Numerical results show that the Transformer-based coded OFDM system outperforms both the DNN-based and the conventional system. Full article

(This article belongs to the Special Issue Coding and Entropy)

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12 pages, 409 KiB

Open AccessArticle

Adaptive Bit-Labeling Design for Probabilistic Shaping Based on Residual Source Redundancy

by Chen Chen, Qiwang Chen, Sanya Liu and Lin Zhou

Entropy 2023, 25(4), 586; https://doi.org/10.3390/e25040586 - 29 Mar 2023

Cited by 1 | Viewed by 1016

Abstract

By using the residual source redundancy to achieve the shaping gain, a joint source-channel coded modulation (JSCCM) system has been proposed as a new solution for probabilistic amplitude shaping (PAS). However, the source and channel codes in the JSCCM system should be designed [...] Read more.

By using the residual source redundancy to achieve the shaping gain, a joint source-channel coded modulation (JSCCM) system has been proposed as a new solution for probabilistic amplitude shaping (PAS). However, the source and channel codes in the JSCCM system should be designed specifically for a given source probability to ensure optimal PAS performance, which is undesirable for systems with dynamically changing source probabilities. In this paper, we propose a new shaping scheme by optimizing the bit-labeling of the JSCCM system. Instead of the conventional fixed labeling, the proposed bit-labelings are adaptively designed according to the source probability and the source code. Since it is simple to switch between different labelings according to the source probability and the source code, the proposed design can be considered as a promising low complexity alternative to obtain the shaping gain for sources with different probabilities. Numerical results show that the proposed bit-labelings can significantly improve the bit-error rate (BER) performance of the JSCCM system. Full article

(This article belongs to the Special Issue Coding and Entropy)

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15 pages, 418 KiB

Open AccessEditor’s ChoiceArticle

Design and Analysis of Joint Group Shuffled Scheduling Decoding Algorithm for Double LDPC Codes System

by Qiwang Chen, Yanzhao Ren, Lin Zhou, Chen Chen and Sanya Liu

Entropy 2023, 25(2), 357; https://doi.org/10.3390/e25020357 - 15 Feb 2023

Cited by 3 | Viewed by 1304

Abstract

In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to [...] Read more.

In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to each group; the grouping relies on the types or the length of the variable nodes (VNs). By comparison, the conventional shuffled scheduling decoding algorithm can be regarded as a special case of this proposed algorithm. A novel joint extrinsic information transfer (JEXIT) algorithm for the D-LDPC codes system with the JGSSD algorithm is proposed, by which the source and channel decoding are calculated with different grouping strategies to analyze the effects of the grouping strategy. Simulation results and comparisons verify the superiority of the JGSSD algorithm, which can adaptively trade off the decoding performance, complexity and latency. Full article

(This article belongs to the Special Issue Coding and Entropy)

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