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Keywords = distributed joint source-channel coding

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19 pages, 3552 KB  
Article
U-Shaped Split Federated Learning with Compact Features for Deep Learning-Based Image Coding
by Qizheng Sun, Caili Guo, Meiyi Zhu and Yang Yang
Entropy 2026, 28(3), 331; https://doi.org/10.3390/e28030331 - 16 Mar 2026
Cited by 1 | Viewed by 661
Abstract
U-shaped Split Federated Learning (U-SFL) is a promising paradigm for distributed image coding, offering parallel training capabilities and privacy preservation while mitigating computational burdens on edge devices. However, the frequent bidirectional transmission of intermediate features between dual-split points incurs substantial communication overhead. To [...] Read more.
U-shaped Split Federated Learning (U-SFL) is a promising paradigm for distributed image coding, offering parallel training capabilities and privacy preservation while mitigating computational burdens on edge devices. However, the frequent bidirectional transmission of intermediate features between dual-split points incurs substantial communication overhead. To mitigate this issue, we propose a compact-feature U-shaped split federated learning framework (CoF U-SFL), which reduces communication overhead and improves training efficiency while maintaining low image distortion. We introduce a feature entropy estimation network to model the distribution of split-layer features, enabling effective compression during transmission. Furthermore, we formulate a joint optimization objective incorporating entropy constraints to guide the end-to-end training. Experimental results demonstrate that CoF U-SFL reduces communication overhead by 104.6 times while maintaining reconstruction performance. Full article
(This article belongs to the Special Issue Next-Generation Channel Coding: Theory and Applications)
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16 pages, 1190 KB  
Article
Distributed Images Transmission with Related Feature Assistance: A DeepJSCC Approach
by Cong Lin and Feng Liu
Electronics 2026, 15(5), 1103; https://doi.org/10.3390/electronics15051103 - 6 Mar 2026
Viewed by 614
Abstract
With the rapid development of emerging applications such as the Internet of Things (IoT) and distributed visual perception, massive amounts of correlated image data require efficient transmission under constrained bandwidth and noisy channel conditions. Although Shannon’s separation theorem provides a theoretically optimal basis [...] Read more.
With the rapid development of emerging applications such as the Internet of Things (IoT) and distributed visual perception, massive amounts of correlated image data require efficient transmission under constrained bandwidth and noisy channel conditions. Although Shannon’s separation theorem provides a theoretically optimal basis for independent source-channel design, end-to-end joint optimization methods demonstrate higher performance potential in finite block length scenarios. This paper addresses the distributed image transmission problem with source correlation by proposing a Deep Joint Source-Channel Coding (DeepJSCC)-based framework. The scheme introduces a correlation feature extraction module at the receiver to uncover similarities among multiple sources and assist image reconstruction. Experimental results demonstrate that this method significantly improves reconstruction quality across various signal-to-noise ratios (SNRs), particularly excelling under small bandwidth ratios. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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15 pages, 541 KB  
Article
Joint Optimization and Performance Analysis of Analog Shannon–Kotel’nikov Mapping for OFDM with Carrier Frequency Offset
by Jingwen Lin, Qiwang Chen, Yu Hua and Chen Chen
Entropy 2025, 27(8), 778; https://doi.org/10.3390/e27080778 - 23 Jul 2025
Cited by 1 | Viewed by 860
Abstract
An analog joint source-channel coding (AJSCC) based on Shannon–Kotel’nikov (S-K) mapping transmitting discrete-time encoded samples in orthogonal frequency division multiplexing (OFDM) systems over wireless channel has exhibited excellent performance. However, the phenomenon of carrier frequency offset (CFO) caused by the frequency mismatch between [...] Read more.
An analog joint source-channel coding (AJSCC) based on Shannon–Kotel’nikov (S-K) mapping transmitting discrete-time encoded samples in orthogonal frequency division multiplexing (OFDM) systems over wireless channel has exhibited excellent performance. However, the phenomenon of carrier frequency offset (CFO) caused by the frequency mismatch between the transmitter’s and receiver’s local oscillators often exists in actual scenarios; thus, in this paper the performance of AJSCC-OFDM with CFO is analyzed and the S-K mapping is optimized. A joint optimization strategy is developed to maximize the signal-to-distortion ratio (SDR) subject to CFO constraints. Considering that the optimized AJSCC-OFDM strategies will change the amplitude distribution of encoded symbol, the peak-to-average power ratio (PAPR) characteristics under different AJSCC parameters are also analyzed. Full article
(This article belongs to the Special Issue Next-Generation Channel Coding: Theory and Applications)
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23 pages, 8279 KB  
Article
Distributed Goppa-Coded Generalized Spatial Modulation: Optimized Design and Performance Study
by Chunli Zhao, Fengfan Yang, Daniel Kariuki Waweru, Chen Chen, Hongjun Xu and Lin Luo
Electronics 2023, 12(11), 2404; https://doi.org/10.3390/electronics12112404 - 25 May 2023
Cited by 2 | Viewed by 1662
Abstract
The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages such as the flexible codeword length, excellent code construction, and [...] Read more.
The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages such as the flexible codeword length, excellent code construction, and easy encoding and decoding complexity. At the relay, we select portions of the source information bits for further encoding. For each selection, the destination constructs a channel code. To obtain the best code in the destination, we propose the optimal information bit selection algorithm at the relay to choose the source information. However, Goppa codes with a large block length will impose high complexity on the optimal algorithm. Thus, the locally optimized selection algorithm is further proposed. At the destination, the joint decoding algorithm is adopted to recover the source information. Our simulated results indicate that the two selection algorithms proposed achieve better performance than the random selection method. This is because the optimized algorithms can generate the code with a larger minimum distance at the destination. Moreover, the proposed DGC-GSM scheme outperforms the non-cooperative system. Moreover, the DGC-GSM scheme can obtain the approximate performance with the distributed Goppa-coded spatial modulation (DGC-SM) scheme but has a significantly reduced transmit antenna number. Full article
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23 pages, 624 KB  
Article
On Decoder Ties for the Binary Symmetric Channel with Arbitrarily Distributed Input
by Ling-Hua Chang, Po-Ning Chen and Fady Alajaji
Entropy 2023, 25(4), 668; https://doi.org/10.3390/e25040668 - 16 Apr 2023
Viewed by 2352
Abstract
The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of the probability of MAP decoder [...] Read more.
The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of the probability of MAP decoder ties to the probability of error grows most linearly in blocklength when no MAP decoding ties occur, thus showing that decoder ties do not affect the code’s error exponent. This result generalizes a similar recent result shown for the case of block codes transmitted over the BSC under a uniform input distribution. Full article
(This article belongs to the Special Issue Advances in Information and Coding Theory)
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22 pages, 372 KB  
Article
Lossy State Communication over Fading Multiple Access Channels
by Viswanathan Ramachandran
Entropy 2023, 25(4), 588; https://doi.org/10.3390/e25040588 - 29 Mar 2023
Cited by 1 | Viewed by 2280
Abstract
Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, [...] Read more.
Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, an information-theoretic analysis of the absolute performance capabilities of joint sensing and communication systems that take into account practical limitations such as fading has not been addressed in the literature. Motivated by this, we undertake a network information-theoretic analysis of a typical joint communications and sensing system in this paper. Towards this end, we consider a state-dependent fading Gaussian multiple access channel (GMAC) setup with an additive state. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and non-causally available to all the transmitting nodes. The fading gains on the respective links are assumed to be stationary and ergodic and available only at the receiver. In this setting, with no knowledge of fading gains at the transmitters, we are interested in joint message communication and estimation of the state at the receiver to meet a target distortion in the mean-squared error sense. Our main contribution here is a complete characterization of the distortion-rate trade-off region between the communication rates and the state estimation distortion for a two-sender GMAC. Our results show that the optimal strategy is based on static power allocation and involves uncoded transmissions to amplify the state, along with the superposition of the digital message streams using appropriate Gaussian codebooks and dirty paper coding (DPC). This acts as a design directive for realistic systems using joint sensing and transmission in next-generation wireless standards and points to the relative benefits of uncoded communications and joint source-channel coding in such systems. Full article
(This article belongs to the Special Issue Advances in Multiuser Information Theory)
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33 pages, 752 KB  
Article
Distributed Hypothesis Testing over a Noisy Channel: Error-Exponents Trade-Off
by Sreejith Sreekumar and Deniz Gündüz
Entropy 2023, 25(2), 304; https://doi.org/10.3390/e25020304 - 6 Feb 2023
Cited by 1 | Viewed by 3647
Abstract
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to n independent and identically distributed samples, denoted by U and V, respectively. The observer communicates [...] Read more.
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to n independent and identically distributed samples, denoted by U and V, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of (U,V) based on V and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off. Full article
(This article belongs to the Special Issue Information Theory for Distributed Systems)
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18 pages, 2682 KB  
Article
Analysis and Design of Enhanced Distributed Fountain Codes in Multiple Access Networks with Cooperative Relay
by Hanqin Shao, Hongbo Zhu and Junwei Bao
Symmetry 2022, 14(10), 2026; https://doi.org/10.3390/sym14102026 - 27 Sep 2022
Cited by 2 | Viewed by 2878
Abstract
Distributed fountain coding plays an important role in rateless code research. The reliability and effectiveness of these coding schemes are increasingly challenged with the growing applications. In this paper, a novel multiple-access network with cooperative relay is presented, and a novel enhanced distributed [...] Read more.
Distributed fountain coding plays an important role in rateless code research. The reliability and effectiveness of these coding schemes are increasingly challenged with the growing applications. In this paper, a novel multiple-access network with cooperative relay is presented, and a novel enhanced distributed fountain coding scheme for this network is proposed. The overall degree distributions are derived, and the asymptotic decoding performance is analyzed theoretically by employing the And-Or tree method. On this basis, a design method using joint iterative optimization algorithms is proposed to optimize the degree distributions of the sources and relays. Simulation results show that the proposed enhanced distributed fountain codes outperform the existing generalized distributed fountain codes (GDFC) and have a good performance on both lossless and lossy channels. It reveals that the proposed codes can provide unequal error protection (UEP) property for different sources by introducing the extra cooperative relay. The performance improvement is not restricted to the sources connected to the cooperative relay but applies to all sources. With the additional relay, the proposed codes are able to overcome the effects of bad channel conditions caused by terrain, obstacles, and so on, to avoid communication interruptions and improve the reliability of the network. Full article
(This article belongs to the Special Issue Propagation Model Driven Spectrum Twin and Its Applications)
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12 pages, 14347 KB  
Article
Photon-Counting Underwater Optical Wireless Communication for Reliable Video Transmission Using Joint Source-Channel Coding Based on Distributed Compressive Sensing
by Zhu Hong, Qiurong Yan, Zihang Li, Ting Zhan and Yuhao Wang
Sensors 2019, 19(5), 1042; https://doi.org/10.3390/s19051042 - 1 Mar 2019
Cited by 20 | Viewed by 5844
Abstract
To achieve long-distance underwater optical wireless communication, a single photon detector with single photon limit sensitivity is used to detect the optical signal at the receiver. The communication signal is extracted from the discrete single photon pulses output from the detector. Due to [...] Read more.
To achieve long-distance underwater optical wireless communication, a single photon detector with single photon limit sensitivity is used to detect the optical signal at the receiver. The communication signal is extracted from the discrete single photon pulses output from the detector. Due to fluctuation of photon flux and quantum efficiency of photon detection, long-distance underwater optical wireless communication has the characteristics that the link is easily interrupted, the bit error rate is high, and the burst error is large. To achieve reliable video transmission, a joint source-channel coding scheme based on residual distributed compressive video sensing is proposed for the underwater photon counting communication system. Signal extraction from single photon pulses, data frame and data verification are specifically designed. This scheme greatly reduces the amount of data at the transmitter, transfers the computational complexity to the decoder in receiver, and enhances anti-channel error ability. The experimental results show that, when the baud rate was 100 kbps and the average number of photon pulses per bit was 20, the bit error rate (BER) was 0.0421 and video frame could still be restored clearly. Full article
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12 pages, 1307 KB  
Article
Distributed Joint Source-Channel Coding Using Quasi-Uniform Systematic Polar Codes
by Liqiang Jin and Hongwen Yang
Entropy 2018, 20(10), 806; https://doi.org/10.3390/e20100806 - 22 Oct 2018
Cited by 18 | Viewed by 3904
Abstract
This paper proposes a distributed joint source-channel coding (DJSCC) scheme using polar-like codes. In the proposed scheme, each distributed source encodes source message with a quasi-uniform systematic polar code (QSPC) or a punctured QSPC, and only transmits parity bits over its independent channel. [...] Read more.
This paper proposes a distributed joint source-channel coding (DJSCC) scheme using polar-like codes. In the proposed scheme, each distributed source encodes source message with a quasi-uniform systematic polar code (QSPC) or a punctured QSPC, and only transmits parity bits over its independent channel. These systematic codes play the role of both source compression and error protection. For the infinite code-length, we show that the proposed scheme approaches the information-theoretical limit by the technique of joint source-channel polarization with side information. For the finite code-length, the simulation results verify that the proposed scheme outperforms the distributed separate source-channel coding (DSSCC) scheme using polar codes and the DJSCC scheme using classic systematic polar codes. Full article
(This article belongs to the Special Issue Multiuser Information Theory II)
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33 pages, 1615 KB  
Article
Zero Delay Joint Source Channel Coding for Multivariate Gaussian Sources over Orthogonal Gaussian Channels
by Pål Anders Floor, Anna N. Kim, Tor A. Ramstad and Ilangko Balasingham
Entropy 2013, 15(6), 2129-2161; https://doi.org/10.3390/e15062129 - 31 May 2013
Cited by 10 | Viewed by 8089
Abstract
Communication of a multivariate Gaussian source transmitted over orthogonal additive white Gaussian noise channels using delay-free joint source channel codes (JSCC) is studied in this paper. Two scenarios are considered: (1) all components of the multivariate Gaussian are transmitted by one encoder as [...] Read more.
Communication of a multivariate Gaussian source transmitted over orthogonal additive white Gaussian noise channels using delay-free joint source channel codes (JSCC) is studied in this paper. Two scenarios are considered: (1) all components of the multivariate Gaussian are transmitted by one encoder as a vector or several ideally collaborating nodes in a network; (2) the multivariate Gaussian is transmitted through distributed nodes in a sensor network. In both scenarios, the goal is to recover all components of the multivariate Gaussian at the receiver. The paper investigates a subset of JSCC consisting of direct source-to-channel mappings that operate on a symbol-by-symbol basis to ensure zero coding delay. A theoretical analysis that helps explain and quantify distortion behavior for such JSCC is given. Relevant performance bounds for the network are also derived with no constraints on complexity and delay. Optimal linear schemes for both scenarios are presented. Results for Scenario 1 show that linear mappings perform well, except when correlation is high. In Scenario 2, linear mappings provide no gain from correlation when the channel signal-to-noise ratio (SNR) gets large. The gap to the performance upper bound is large for both scenarios, regardless of SNR, when the correlation is high. The main contribution of this paper is the investigation of nonlinear mappings for both scenarios. It is shown that nonlinear mappings can provide substantial gain compared to optimal linear schemes when correlation is high. Contrary to linear mappings for Scenario 2, carefully chosen nonlinear mappings provide a gain for all SNR, as long as the correlation is close to one. Both linear and nonlinear mappings are robust against variations in SNR. Full article
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17 pages, 192 KB  
Review
Distributed Joint Source-Channel Coding in Wireless Sensor Networks
by Xuqi Zhu, Yu Liu and Lin Zhang
Sensors 2009, 9(6), 4901-4917; https://doi.org/10.3390/s90604901 - 22 Jun 2009
Cited by 18 | Viewed by 18364
Abstract
Considering the fact that sensors are energy-limited and the wireless channel conditions in wireless sensor networks, there is an urgent need for a low-complexity coding method with high compression ratio and noise-resisted features. This paper reviews the progress made in distributed joint source-channel [...] Read more.
Considering the fact that sensors are energy-limited and the wireless channel conditions in wireless sensor networks, there is an urgent need for a low-complexity coding method with high compression ratio and noise-resisted features. This paper reviews the progress made in distributed joint source-channel coding which can address this issue. The main existing deployments, from the theory to practice, of distributed joint source-channel coding over the independent channels, the multiple access channels and the broadcast channels are introduced, respectively. To this end, we also present a practical scheme for compressing multiple correlated sources over the independent channels. The simulation results demonstrate the desired efficiency. Full article
(This article belongs to the Special Issue Wireless Sensor Technologies and Applications)
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