Satellite edge computing offers promising solutions for extending the coverage of terrestrial networks, particularly in remote and harsh environments. By offloading ground data to satellites for processing, this paradigm enables real-time data handling in non-terrestrial networks (NTNs). However, due to limited onboard resources and dynamic task requirements from Internet of Things (IoT) devices, online energy management becomes a critical challenge that hinders the scalability and deployment of satellite edge computing systems. In this paper, we propose an online energy management framework based on satellite-edge collaboration. A queue-based collaboration scheme is designed to coordinate satellites in handling tasks with random arrival patterns. Building upon this scheme, we formulate a joint optimization problem that integrates transmission resource allocation, computational resource assignment, power control, routing strategies, and collaboration policies, aiming to minimize the energy consumption of the satellite network. Given the dynamic, complex, and distributed nature of the problem, we present a Lyapunov-based multi-agent deep reinforcement learning (MADRL) algorithm. Specifically, we first transform the long-term stochastic optimization problem into a sequence of deterministic subproblems using the Lyapunov theory. Sub-sequently, each subproblem is decomposed into a resource allocation subproblem and an edge collaboration subproblem. Correspondingly, we devise a MADRL-based algorithm for edge collaboration and a Lagrangian multiplier iteration (LMI)-based algorithm for resource allocation. Finally, the overall problem is iteratively optimized using the block coordinate descent (BCD) framework. Simulation results demonstrate that the proposed approach achieves significant performance improvements over both baseline methods and several state-of-the-art pure deep reinforcement learning (DRL) approaches.

This article presents a new optical integrated sensing and communication (O-ISAC) framework tailored for cost-effective light-emitting diode (LED) for enhanced Internet of Things (IoT) applications. Unlike prior research on ISAC, which predominantly focused on radio frequency (RF) band, O-ISAC capitalizes on the inherent advantages of the optical spectrum, including the ultrawide license-free bandwidth, immunity to RF interference, and energy efficiency—attributes crucial for IoT communications. The communication and sensing in our O-ISAC system unfold in two phases: 1) directionless O-ISAC and 2) directional O-ISAC. In the first phase, distributed optical access points emit nondirectional light for communication and leverage small-aperture imaging principles for sensing. In the second phase, we put forth the concept of optical beamforming, using collimating lenses to concentrate light, resulting in substantial performance enhancements in both communication and sensing. Numerical and simulation results demonstrate the feasibility and impressive performance of O-ISAC benchmarked against optical separate communication and sensing systems.

This paper puts forth a new metric, dubbed channel cycle time (CCT), to measure the short-term fairness of communication networks. CCT characterizes the average duration between two consecutive successful transmissions of a user, during which all other users successfully accessed the channel at least once. In contrast to existing short-term fairness measures, CCT provides more comprehensive insight into the transient dynamics of communication networks, with a particular focus on users’ delays and jitter. To validate the efficacy of our approach, we analytically characterize the CCTs for two classical communication protocols: slotted Aloha and CSMA/CA. The analysis demonstrates that CSMA/CA exhibits superior short-term fairness over slotted Aloha. Beyond its role as a measurement metric, CCT has broader implications as a guiding principle for the design of future communication networks by emphasizing factors like fairness, delay, and jitter in short-term behaviors.

This paper puts forth a new metric, dubbed channel cycle time (CCT), to measure the short-term fairness of Communication networks. CCT characterizes the average duration between two consecutive successful transmissions of a user, during which all other users successfully accessed the channel at least once. In contrast to existing short-term fairness measures, CCT provides more comprehensive insight into the transient dynamics of communication networks, with a particular focus on users' delays and jitter. To validate the efficacy of our approach, we analytically characterize the CCTs for two classical commu-nication protocols: slotted Aloha and CSMA/CA. The analysis demonstrates that CSMA/CA exhibits superior short-term fairness over slotted Aloha. Beyond its role as a measurement metric, CCT has broader implications as a guiding principle for the design of future communication networks by emphasizing factors like fairness, delay, and jitter in short-term behaviors.

Discovering sequences with desired properties has long been an interesting intellectual pursuit. In pulse compression radar (PCR), discovering phase codes with low aperiodic autocorrelations is essential for a good estimation performance. The design of phase code, however, is mathematically non-trivial as the aperiodic autocorrelation properties of a sequence are intractable to characterize. In this paper, we put forth a genetic algorithm (GA) approach to discover new phase codes for PCR with the mismatched filter (MMF) receiver. The developed GA, dubbed GASeq, discovers better phase codes than the state of the art. At a code length of 59, the sequence discovered by GASeq achieves a signal-to-clutter ratio (SCR) of 50.84, while the best-known sequence has an SCR of 45.16. In addition, the efficiency and scalability of GASeq enable us to search phase codes with a longer code length, which thwarts existing deep learning-based approaches. At a code length of 100, the best phase code discovered by GASeq exhibit an SCR of 63.23.

This paper investigates noncoherent detection in a two-way relay channel operated with physical- layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. We design a noncoherent detector that jointly estimates relative phase and detects data using a belief propagation algorithm. Numerical results show that our detector performs as well as a “fictitious” optimal detector that has perfect knowledge of the relative phase. Although this paper focuses on PNC with FSK modulation, we believe the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve detection performance.

This paper presents the first network-coded multiple access (NCMA) downlink system on unmanned aerial vehicle (UAV). The use of UAV as a mobile aerial base station has received much attention in the 5G community in the context of highly mobile and flexible-configurable communication systems. As UAVs are limited by their flight time in the air, achieving high spectral and power efficiency while they are inflight is of great importance. Non-orthogonal multiple access (NOMA) is a promising technique to increase the spectral and power efficiency. Conventional NOMA downlink that makes use of superposition coding in combination with successive interference cancellation (SIC) decoding does not work well in scenarios where the channel conditions of different downlink users are not readily available at the transmitter side. This is the case, for example, in the UAV scenario in which the UAV transmitter moves quickly, causing the channel conditions to vary in a very dynamic manner. This paper investigates a new NOMA downlink architecture, referred to as network-coded multiple access. In the absence of channel information, an NCMA transmitter allocates equal power to the superposed signals of different downlink users. A key challenge is how to achieve high NOMA throughput under such equal power allocation. Toward this end, NCMA makes joint use of physical-layer network coding (PNC) and multiuser decoding (MUD) together with a new superposition coding scheme, referred to as NCMA-based superposition coding. In NCMA-based superposition coding, equal powers are allocated to the signals of different users, but a relative phase offset between the signals is introduced to optimize PNC and MUD decodings. To demonstrate the feasibility and advantage of the NCMA downlink, we implemented our designs on a software-defined radio and UAV. Our experimental results show that NCMA is robust against varying channel conditions. Moreover, the throughput of NCMA can outperform the state-of-the-art SIC-based superposition coding system and the time-division multiple access system by 50% and 80%, respectively, demonstrating that NCMA is a practical solution to boost throughput in UAV NOMA.

This paper investigates the noncoherent detection in a two-way relay channel operated with physical-layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, and hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. Our overall detector design consists of two components: 1) a channel gains estimator that estimates channel gains without preambles; and 2) a detector that builds on top of the estimated channel gains to jointly estimate relative phase and detect data using a belief propagation algorithm. Numerical results show that our detector performs nearly as well as a “fictitious” optimal detector that has perfect knowledge of the channel gains and relative phase. Although this paper focuses on PNC with FSK modulation, we believe that the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve the detection performance.

In practical asynchronous physical-layer network coding (PNC) systems, the symbols from multiple transmitters to a common receiver may be misaligned. The good performance of an asynchronous PNC decoder hinges on accurate estimation of the symbol misalignment. This paper puts forth an optimal symbol misalignment estimator that considerably improves the estimation accuracy over prior schemes. Our scheme makes use of double baud-rate sampling of the received preambles consisting of Zadoff-Chu (ZC) sequences used by different transmitters. The sampling process is information-lossless because the double baud-rate samples capture all the information embedded in the continuous-time signal shaped by the assumed root-raised-cosine (RRC) pulse. The estimation consists of three steps: (i) cross-correlation of the double baud-rate samples with “interpolated double baud-rate ZC sequences” (ii) noise whitening; (iii) maximum likelihood (ML) estimation of the symbol misalignment. Extensive simulations show that the mean-square-error (MSE) performance of our estimator is superior to that of the baudrate estimator - e.g., for the RRC pulse with roll-off factor 1, our double baud-rate estimator yields improvement 8 dB over the baud-rate estimator. Furthermore, our double baudrate estimator yields square errors of less than 0.001 with 90% probability when the SNR is 10 dB in both AWGN and Rayleigh fading channels.

This paper presents the first Network-Coded Multiple Access (NCMA) system with multiple users adopting different signal modulations, referred to as rate-diverse NCMA. A distinguishing feature of NCMA is the joint use of physical-layer network coding (PNC) and multiuser decoding (MUD) to boost throughput of multipacket reception systems. In previous NCMA systems, users adopt the same modulation regardless of their individual channel conditions. This leads to suboptimal throughput for many practical scenarios, especially when different users have widely varying channel conditions. A rate-diverse NCMA system allows different users to use modulations that are commensurate with their channel conditions. A key challenge is the design of PNC mapping and decoding mechanisms in NCMA when different users adopt different modulations. While there have been past work on non-channel-coded rate-diverse PNC, this paper is the first attempt to design channel-coded rate-diverse PNC to ensure the reliability of the overall NCMA system. Specifically, we put forth a symbol-splitting channel coding and modulation design so that PNC/NCMA can work over different modulations. We implemented our rate-diverse NCMA system on software-defined radios. Experimental results show that the throughput of rate-diverse NCMA can outperform the state-of-the-art rate-homogeneous NCMA by 80%. Overall, the introduction of rate diversity significantly boosts the NCMA system throughput in practical scenarios.

This paper is a theoretical-plus-experimental investigation of practical 5G strategies for power-balanced non-orthogonal multiple access (NOMA). By allowing multiple users to share the same time and frequency, NOMA can scale up the number of served users and increase spectral efficiency compared with existing OMA. Conventional NOMA schemes with successive interference cancellation (SIC) do not work well when users with comparable received powers transmit together. To allow power-balanced NOMA (more exactly, near power-balanced NOMA), this paper investigates a new NOMA architecture, named network-coded multiple access (NCMA). A distinguishing feature of NCMA is the joint use of physical-layer network coding (PNC) and multiuser decoding to boost NOMA throughputs. We first show that a simple NCMA architecture in which all users use the same modulation, referred to as rate-homogeneous NCMA, can achieve substantial throughput improvement over SIC-based NOMA under near power-balanced scenarios. Then, we put forth a new NCMA architecture, referred to as rate-diverse NCMA, in which different users may adopt different modulations commensurate with their relative SNRs. A challenge for rate-diverse NCMA is the design of a channel-coded PNC system. This paper is the first attempt to design channel-coded rate-diverse PNC. Experimental results on our software-defined radio prototype show that the throughput of rate-diverse NCMA can outperform the state-of-the-art rate-homogeneous NCMA by 80%. Overall, rate-diverse NCMA is a practical solution for near power-balanced NOMA.

This paper presents the first reliable physical-layer network coding (PNC) system that supports real TCP/IP applications for the two-way relay network (TWRN). Theoretically, PNC could boost the throughput of TWRN by a factor of 2 compared with traditional scheduling (TS) in the high signal-to-noise (SNR) regime. Although there have been many theoretical studies on PNC performance, there have been relatively few experimental and implementation efforts. Our earlier PNC prototype, built in 2012, was an offline system that processed signals offline. For a system that supports real applications, signals must be processed online in real-time. Our real-time reliable PNC prototype, referred to as RPNC, solves a number of key challenges to enable the support of real TCP/IP applications. The enabling components include: 1) a time-slotted system that achieves μs-level synchronization for the PNC system; 2) reduction of PNC signal processing complexity to meet real-time constraints; 3) an ARQ design tailored for PNC to ensure reliable packet delivery; and 4) an interface to the application layer. We took on the challenge to implement all of the above with general-purpose processors in PC through an SDR platform rather than ASIC or FPGA. With all of these components, we have successfully demonstrated image exchange with TCP and two-party video conferencing with UDP over RPNC. Experimental results show that the achieved throughput approaches the PHY-layer data rate at high SNR, demonstrating the high efficiency of the RPNC system.

In asynchronous physical-layer network coding (APNC) systems, the symbols from multiple transmitters to a common receiver may be misaligned. Knowledge of the amount of symbol misalignment, hence its estimation, is important to PNC decoding. This paper addresses the problems of symbol-misalignment estimation and optimal PNC decoding given the misalignment estimate, assuming the APNC system uses the root-raised-cosine pulse to carry signals (RRC-APNC). Our contributions are as follows. First, we put forth an optimal symbol-misalignment estimator that makes use of double baud-rate samples. Second, we devise optimal RRC-APNC decoders in the presence of non-exact symbol-misalignment estimates. In particular, we show how to whiten the colored noise in the double baud-rate samples to simplify the design of optimal decoders. Third, we investigate the decoding performance of various estimation-and-decoding schemes for RRC-APNC. Extensive simulations show that: 1) our double baud-rate estimator yields substantially more accurate symbol-misalignment estimates than the baud-rate estimator does; the mean square error gains are up to 8 dB and 2) an overall estimation-and-decoding scheme in which both estimation and decoding are based on double baud-rate samples yields much better performance than other schemes. Compared with a scheme in which both estimation and decoding are based on baud-rate samples, the double baud-rate sampling scheme yields 4.5 dB gains on symbol error rate performance in an additive white Gaussian noise channel, and 2 dB gains on packet error rate performance in a Rayleigh fading channel.

Physical-layer network coding (PNC) channel decoding at the relay is of key importance for good performance in PNC systems. However, PNC channel decoders can have prohibitive computation complexity. Low complexity non-iterative PNC channel decoders are desired in practice. For such PNC decoders, decoding performance may degrade significantly when there is a relative phase offset between the simultaneous signals of multiple nodes received at the relay, particularly when bit-likelihood-based decoding is adopted. In this paper, we thoroughly investigate and numerically quantify the impact of relative phase offset on decoding performance. To maintain good decoding performance under relative phase offset, we introduce and experimentally evaluate symbol-likelihood-based decoding (in contrast to bit-likelihood-based decoding) for PNC systems. Our experimental results show that symbol-likelihood-based decoding improves the packet throughput over bit-likelihood-based decoding by 100% to 400% at SNR of 15 dBs. Moreover, we study the computational complexity under both these decoding methods. We find that a reduced-complexity decoder with symbol-likelihood-based decoding provides the best performance-complexity tradeoff for practical PNC systems.

Physical-layer network coding (PNC) can potentially boost the throughput of a two-way relay network by 100% compared with conventional packet forwarding schemes. However, the complexity of PNC channel decoders can be considerably higher than the complexity of channel decoders for point-to-point communication systems. Although many PNC channel decoders proposed to date have good decoding performance, they may not be feasibly implemented in practical systems due to their high computation complexities. This paper presents a reduced-complexity decoder (RCD), a PNC decoder with adjustable decoding complexity that is amenable to real-time implementation. We experimentally evaluate the performance-complexity trade-off of RCD. Our experimental results show that RCD can achieve substantial throughput gain over state-of-the-art decoders proposed for real-time PNC systems.

This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with q-level pulse amplitude modulation (q-PAM) in two-way relay channels. A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of q-PAM PNC. Our contributions are as follows. First, we give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all q. In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. Second, we show that the performance of q-PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as q increases, calling into question the robustness of highorder modulated PNC. Third, we propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built.

This paper presents the first network-coded multiple access (NCMA) system operated on higher- order modulations beyond BPSK. NCMA allows multiple nodes to transmit simultaneously to an access point (AP) to boost throughput of wireless local area networks (WLAN): the key idea is to jointly exploit multiuser decoding (MUD) and physical-layer network coding (PNC). High- order modulations are commonly adopted in WLAN systems when the signal-to-noise ratio (SNR) is medium or high. However, direct generalization of the existing NCMA decoding algorithm, originally designed for BPSK, to higher-order modulations will lead to huge performance degradation. We find that the throughput degradation is caused by the relative phase offset between received signals from different nodes. To circumvent the throughput degradation, this paper investigates an NCMA system with multiple receive antennas at the AP, referred to as MIMO-NCMA. We have implemented MIMO-NCMA on software-defined radios. Our experimental results show that, at SNR of 10dB, the throughput of MIMO-NCMA outperforms single-antenna NCMA and conventional distributed MIMO-MUD, respectively. We believe that MIMO-NCMA throughput can be further improved with modulations beyond QPSK (e.g., 64-QAM).

This paper considers physical-layer network coding (PNC) in vehicular ad-hoc network (VANET) to solve the problem of short contact time between fast-moving vehicles. PNC enables data exchange between nodes in a relay network within a short airtime, e.g., twice faster than relay networks based on traditional communication, and can be a powerful performance booster in VANET. One of the most important challenges in applying PNC to VANET, however, is the Doppler shift caused by vehicular motions. Doppler shift leads to carrier frequency offset (CFO) that induces inter-carrier interference (ICI) in OFDM systems. The ICI destroys the orthogonality of modulated symbols, causing degradation in PNC signal detection. This paper puts forth a detection method to mitigate the CFO/ICI effect on PNC. The method, referred to as BP-VPNC, makes use of a belief propagation (BP) algorithm to process the outputs of the OFDM correlators. BP extracts useful hidden information embedded in ICI to improve signal detection in VANET PNC. Our study shows that the BER performance of PNC VANET operated with BP-VPNC can be achieved close to that of traditional VANET at various CFO levels. These results suggest that with BP-VPNC, a potential shortcoming of PNC, vulnerability to CFO, can be circumvented, and that PNC can be used to overcome the short vehicular contact time in VANET.

This paper presents a first real-time network-coded multiple access (NCMA) system that jointly exploits physical (PHY)-layer network coding (PNC) and multiuser decoding (MUD) to boost the throughput of a wireless local area network (WLAN). NCMA is a new design paradigm for multipacket reception wireless networks, in which the access point can receive and decode several packets simultaneously transmitted by multiple users. Conventionally, multipacket reception is realized using MUD only, whereas the key idea of NCMA is to use PNC together with MUD to realize multipacket reception. Although the feasibility of NCMA has previously been studied by the authors, our previous NCMA prototype was a version with offline signal processing. In addition, our previous investigation left open a number of theoretical and implementation issues, the resolution of which is critical to the adoption of NCMA in real practice. The current investigation makes the following state-of-the-art contributions toward NCMA: 1) we demonstrate a first NCMA system with integrated real-time PHY and MAC-layer decoding; 2) we construct a new unified framework for MAC-layer decoding that yields higher throughput with faster decoding-the faster decoding is one of the key enablers of our real-time implementation; and 3) we design new PHY-layer decoding techniques that overcome the poor performance of the first-generation NCMA prototype at low SNR. Experimental results show that, compared with the previous NCMA prototype, our new NCMA prototype improves real-time throughput by more than 100% at medium-high SNR (≥ 8 dB).

Vehicular Ad-hoc Network (VANET) is expected to play a major role in improving road safety and traffic efficiency in people's daily life. However, the main issue in VANETs remains to be intermittent node connectivity and relatively short contact duration due to the high mobility of vehicles. Physical-layer Network Coding (PNC) that enables data exchange within a much shorter airtime (e.g., twice faster than traditional scheduling) favors the highly-dynamic link condition in vehicular environments and hence appears to be a powerful tool in VANETs. One of the most important challenges in applying PNC to VANETs comes from the Doppler shift due to high-speed vehicle motion, which leads to carrier frequency offset (CFO) and hence introduces inter-carrier interference (ICI) that degrades the bit error rate performance. In this paper, we investigate the impact of motion-induced CFO/ICI on the overall signal detection. In particular, we study whether PNC in VANETs can be made feasible with conventional equalization techniques that suppress the effect of CFO. We found that PNC suffers only a 3 dB SINR penalty in the worst case compared with generic point-to-point (P2P) communications, and generally PNC is feasible in vehicular environments even if the transmission powers of source nodes cannot be finely controlled.

This paper proposes and experimentally demonstrates a first wireless local area network (WLAN) system that jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost system throughput. We refer to this multiple access mode as network-coded multiple access (NCMA). Prior studies on PNC mostly focused on relay networks. NCMA is the first realized multiple access scheme that establishes the usefulness of PNC in a non-relay setting. NCMA allows multiple nodes to transmit simultaneously to the access point (AP) to boost throughput. In the non-relay setting, when two nodes A and B transmit to the AP simultaneously, the AP aims to obtain both packet A and packet B rather than their network-coded packet. An interesting question is whether network coding, specifically PNC which extracts packet A ⊕ B, can still be useful in such a setting. We provide an affirmative answer to this question with a novel two-layer decoding approach amenable to real-time implementation. Our USRP prototype indicates that NCMA can boost throughput by 100 percent in the medium-high SNR regime (≥10 dB). We believe further throughput enhancement is possible by allowing more than two users to transmit together.

This paper investigates interference-cancellation schemes at the receiver, in which the original data of the interference is known a priori. Such a priori knowledge is common in wireless relay networks. Directly removing the known interference requires accurate estimate of the interference channel, which may be difficult in many situations. In [1], we proposed a novel scheme, Blind Known Interference Cancellation (BKIC), for blind cancellation of known interference without interference channel information. BKIC consists of two steps. The first step combines adjacent symbols to cancel the interference, exploiting the fact that the channel coefficients are almost the same between successive symbols. After such interference cancellation, however, the signal of interest is also distorted. The second step recovers the signal of interest amidst the distortion. Two schemes for the second step, BKIC-S and successive BKIC-RBP, were proposed in [1]. BKIC-S removes distortion by smoothing while BKIC-RBP does so using a real-value belief propagation algorithm. Although successive BKIC-RBP performs well and is superior to BKIC-S, it requires a long processing time proportional to the packet length. To overcome this problem, this paper proposes a parallel BKIC-RBP algorithm. Parallel BKIC-RBP has similar performance as successive BKIC-RBP. It has the advantage of being amenable to parallel implementation with a much shorter processing time.

This paper presents the first implementation of a two-way relay network based on the principle of physical-layer network coding. To date, only a simplified version of physical-layer network coding (PNC), called analog network coding (ANC), has been successfully implemented. The advantage of ANC is that it is simple to implement; the disadvantage, on the other hand, is that the relay amplifies the noise along with the signal before forwarding the signal. PNC systems in which the relay performs XOR or other denoising PNC mappings of the received signal have the potential for significantly better performance. However, their implementation also poses many challenges. For example, the relay must be able to deal with symbol and carrier-phase asynchronies of the simultaneous signals received from the two end nodes, and the relay must perform channel estimation before decoding. We investigate a PNC implementation in the frequency domain, referred to as FPNC, to tackle these challenges. FPNC is based on OFDM. In FPNC, XOR mapping is performed on the OFDM samples in each subcarrier rather than on the samples in the time domain. We implement FPNC on the universal soft radio peripheral (USRP) platform. Our implementation requires only moderate modifications of the packet preamble design of 802.11a/g OFDM PHY. With the help of the cyclic prefix (CP) in OFDM, symbol asynchrony and the multi-path fading effects can be dealt with simultaneously in a similar fashion. Our experimental results show that symbol-synchronous and symbol-asynchronous FPNC have essentially the same BER performance, for both channel-coded and unchannel-coded FPNC.

A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For QPSK unchannel-coded PNC, with a half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.

A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. In this paper, 1) we propose and investigate a general framework based on belief propagation (BP) that can effectively deal with symbol and phase asynchronies; 2) we show that for BPSK and QPSK modulations, our BP method can significantly reduce the SNR penalty due to asynchrony compared with prior methods; 3) we find that symbol misalignment makes the system performance less sensitive and more robust against carrier-phase offset. Observation 3) has the following practical implication. It is relatively easier to control symbol timing than carrier-phase offset. Our results indicate that if we could control the symbol offset in PNC, it would actually be advantageous to deliberately introduce symbol misalignment to desensitize the system to phase offset.

Physical-layer Network Coding (PNC) can significantly improve the throughput of two-way relay channels. An interesting variant of PNC is Analog Network Coding (ANC). Almost all ANC schemes proposed to date, however, operate in a symbol by symbol manner (memoryless) and cannot exploit the redundant information in channel-coded packets to enhance performance. This paper proposes a non-memoryless ANC scheme. In particular, we design a soft-input soft-output decoder for the relay node to process the superimposed packets from the two end nodes to yield an estimated MMSE packet for forwarding back to the end nodes. Our decoder takes into account the correlation among different symbols in the packets due to channel coding, and provides significantly improved MSE performance. Our analysis shows that the SNR improvement at the relay node is lower bounded by IIR (R is the code rate) with the simplest LDPC code (repeat code). The SNR improvement is also verified by numerical simulation with LDPC code. Our results indicate that LDPC codes of different degrees are preferred in different SNR regions. Generally speaking, smaller degrees are preferred for lower SNRs.

In random-access networks, such as the IEEE 802.11 network, different users may transmit their packets simultaneously, resulting in packet collisions. Traditionally, the collided packets are simply discarded. To improve performance, advanced signal processing techniques can be applied to extract the individual packets from the collided signals. Prior work of ours has shown that the symbol misalignment among the collided packets can be exploited to improve the likelihood of successfully extracting the individual packets. However, the failure rate is still unacceptably high. This paper investigates how channel coding can be used to reduce the failure rate. We propose and investigate a decoding scheme that incorporates the exploitation of the aforementioned symbol misalignment into the channel decoding process. This is a fine-grained integration at the symbol level. In particular, collision resolution and channel decoding are applied in an integrated manner. Simulation results indicate that our method outperforms other schemes, including the straightforward method in which collision resolution and channel coding are applied separately.

Direct application of network coding at the physical layer - physical layer network coding (PNC) - is a promising technique for two-way relay wireless networks. In a two-way relay network, relay nodes are used to relay two-way information flows between pairs of end nodes. This paper proposes a precise definition for PNC. Specifically, in PNC, a relay node does not decode the source information from the two ends separately, but rather directly maps the combined signals received simultaneously to a signal to be relayed. Based on this definition, PNC can be further sub-classed into two categories - PNCF (PNC over finite field) and PNCI (PNC over infinite field) - according to whether the network-code field (or groups, rings) adopted is finite or infinite. For each of PNCF and PNCI, we consider two specific estimation techniques for dealing with noise in the mapping process. The performance of the four schemes is investigated by means of analysis and simulation, assuming symbol-level time synchronization only.

Valuation of image coding relies on not only the efficiency of the coding, but also the quality of the coded image. We present a new objective quality assessment metric for image coding based on matching pursuit. First of all, we get the characteristics of the most important structure by projecting the reference image onto the base functions from a dictionary using matching pursuit. Secondly, we process the reference image and gain the structure information of the images in the order of importance, projecting the images onto the structural characteristics. Finally the objective quality score is given by comparing the differences of structure information between the reference and coded images. Experimental results show that the proposed approach is well consistent with the subjective quality score.