Coding schemes for discrete memoryless multicast networks with and without feedback

This paper studies the multiple-access channel (MAC) with rate-limited feedback. The channel output is encoded into one stream of bits, which is provided causally to the two users at the channel input. An achievable rate region for this setup is derived, based on superposition of information, block Markov coding, and coding with various degrees of side information for the feedback link. The suggested region coincides with the Cover-Leung inner bound for large feedback rates. The result is then extended for cases where there is only a feedback link to one of the transmitters, and for a more general case where there are two separate feedback links to both transmitters. We compute achievable regions for the Gaussian MAC and for the binary erasure MAC. The Gaussian region is computed for the case of common rate-limited feedback, whereas the region for the binary erasure MAC is computed for one-sided feedback. It is known that for the latter, the Cover-Leung region is tight, and we obtain results that coincide with the feedback capacity region for high feedback rates.

Short message noisy network coding (SNNC) transmits independent short messages in blocks rather than using long message repetitive encoding. SNNC is shown to achieve the same rates as noisy network coding (NNC) for discrete memoryless networks where each node transmits a multicast message. One advantage of SNNC is that backward decoding may be used which simplifies the analysis and understanding of the achievability proof. The analysis reveals that each decoder may ignore certain other nodes rather than including their message in the decoding procedure. Additionally, SNNC enables early decoding at nodes if the channel quality happens to be good.

With the emergence of vehicular Internet-of-Things (IoT) applications, it is a significant challenge for vehicular IoT systems to obtain higher throughput in vehicle-to-cloud multipath transmission. Network Coding (NC) has been recognized as a promising paradigm for improving vehicular wireless network throughput by reducing packet loss in transmission. However, existing researches on NC do not consider the influence of the rapid quality change of wireless links on NC schemes, which poses a great challenge to dynamically adjust the coding rate according to the variation of link quality in vehicle-to-cloud multipath transmission in order to avoid consuming unnecessary bandwidth resources and to increase network throughput. Therefore, we propose an Adaptive Network Coding (ANC) scheme brought by the novel integration of the Hidden Markov Model (HMM) into the NC scheme to efficiently adjust the coding rate according to the estimated packet loss rate (PLR). The ANC scheme conquers the rapid change of wireless link quality to obtain the utmost throughput and reduce the packet loss in transmission. In terms of the throughput performance, the simulations and real experiment results show that the ANC scheme outperforms state-of-the-art NC schemes for vehicular wireless multipath transmission in vehicular IoT systems.

Network coding has been shown to be useful for throughput and reliability in various network topologies, under a fixed-rate, point-to-multipoint wireless network model. We study the effect of introducing a wireless network model where link capacity depends on the network geometry and the signal to interference and noise ratio. In particular, we compare strategies with and without network coding on a multicast network with and without fading, and on single-user multiple path networks with fading. For the multicast network without fading, we find that the network geometry affects which scheme attains higher throughput. For the case with fading, we compare the throughput-outage probability curves achieved by network coding and repetition schemes. For the multiple path networks, we further consider the case where multiple simultaneous transmissions of identical information signals can be combined at a receiver. We find that the relative performance of the schemes we consider depends on the network geometry, the ratio of signal to noise power, whether multiple simultaneous transmissions can be combined, and the operating point on the throughput-outage probability curve

Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning. However, the nature of the emergent representations is still unclear. To understand the effect of learning on representations, we investigate fully-connected, wide neural networks learning classification tasks using the Bayesian framework where learning shapes the posterior distribution of the network weights. Consistent with previous findings, our analysis of the feature learning regime (also known as ‘non-lazy’ regime) shows that the networks acquire strong, data-dependent features, denoted as coding schemes, where neuronal responses to each input are dominated by its class membership. Surprisingly, the nature of the coding schemes depends crucially on the neuronal nonlinearity. In linear networks, an analog coding scheme of the task emerges; in nonlinear networks, strong spontaneous symmetry breaking leads to either redundant or sparse coding schemes. Our findings highlight how network properties such as scaling of weights and neuronal nonlinearity can profoundly influence the emergent representations.

With the development of the underwater acoustic (UWA) adaptive communication system, energy-efficient transmission has become a critical topic in underwater acoustic (UWA) communications. Due to the unique characteristics of the underwater environment, the transmitter node will almost always have outdated channel state information (CSI), which results in low energy efficiency. In this paper, we take full advantage of bidirectional links and propose an adaptive modulation and coding (AMC) scheme that aims to maximize the long-term energy efficiency of a single link by jointly scheduling the coding rate, modulation order, and transmission power. Considering the complexity characteristics of UWA channels, we proposed a bit error ratio (BER) estimation method based on deep neural networks (DNN). The proposed network could realize channel estimation, feature extraction, and BER estimation by using a fixed pilot of the feedback link. Then, we design a channel classification method based on the estimated BERs of the modulation and coding scheme (MCS) and further model the UWA channels as a finite-state Markov chain (FSMC) with an unknown transition probability. Thus, we formulate the AMC problem as a Markov Decision Process (MDP) and solve it through a reinforcement learning framework. Considering the large state-action pairs, a double deep Q-network (DDQN) based scheme is proposed. Simulation results demonstrate that the proposed AMC scheme outperforms the fixed MCS with a perfect channel information state, and achieves near-optimal energy efficiency.

Wireless Sensor Networks generally operate under severe energy constraints. In many cases, the networks are star connected with battery-powered nodes sensing data and sending it to a centrally-powered base station, whose energy constraints are more fore-bearing than that of the nodes. In this paper, an approach for energy efficient communication by using different channel codes on the base-station to node link (downlink) and node to base-station link (uplink) is proposed and analysed for such a network topology. This is in effect shifting complexity from the node to the base station while continuing to have the same BER performance. Also the use of more energy efficient modulation schemes are explored.

In this paper, a vertical physical-layer network coding (VPNC) scheme based pulse amplitude modulation (PAM) for two-way relay channel (TWRC) is proposed. Different from the conventional physical layer network coding (PNC) scheme in which the relay superimposes two users' signals of the same constellation, in the proposed VPNC scheme two users transmit PAM signals with vertical constellation and the relay superimposes two signals of vertical constellation in the multiple access (MA) phase. In addition, when the VPNC is exploited in conjunction with channel coding, joint channel VPNC is proposed to further improve the BER performance. Simulation results show that the proposed VPNC scheme outperforms the conventional PNC scheme on BER performance.

Distributed source coding (DSC) can be used to compress multiple correlated sensor measurements. These sensors send their compressed data to a central station for joint decoding. However, the issue on designing an optimal transmission scheduling scheme of DSC packets for WSNs have not been well addressed in the literature. In this work, we proposed a novel DSC coding scheme--hierarchical coding scheme, which exploits inter-node coding dependency in sensing-driven and correlated manner. In addition, the interaction between hierarchical coding topology and transmission is considered. We optimize the transmission schedule of DSC nodes to achieve better decoding quality. Our approach can be practically applied to any WSN topologies with correlated source coding nodes. Simulation shows that our work can achieve higher decoding accuracy and compression rate than previous approaches, and the decoding accuracy would not have much degradation under the error-prone wireless environment.

A channel estimation based opportunistic scheduling scheme in wireless bidirectional networks

Cooperative communication is shown to be an efficient method of combating fading in wireless networks. By ”sharing” their antennas cooperating single-antenna nodes create a virtual multi-antenna system and therefore, benefit from spatial diversity. Network coding being a particular cooperative communication technique provides substantial gains in data rate, especially in networks with many sink nodes. By allowing intermediate nodes of a network to mix the incoming data streams, one can achieve the multicast capacity. Recently, Xiao and Skoglund showed that binary network coding (BNC) is not optimal for multi-user multi-relay networks in terms of diversity and proposed diversity network coding (DNC) scheme that outperforms BNC approach. Following this approach we examine potential diversity gains of using the DNC scheme for multi-source line networks. We show that the DNC technique outperforms both conventional time-orthogonal transmission and the BNC scheme. Further, the problem of optimal scheduling of the transmission is explored. We formulate the optimization problem and propose efficient solutions. Numerical results are presented to support theoretical findings.

For noisy network with multiple relays, short message noisy network coding with rate splitting (SNNC-RS) scheme is presented. It has recently been shown by Hou and Kramer that mixed cooperative strategies in which relays in favorable positions decode-and-forward (DF) and the rest quantize via short message noisy network coding (SNNC) can outperform existing cooperative strategies (e.g., noisy network coding (NNC) and decode-and-forward). A drawback of such schemes is that forwarding of quantized signals at SNNC relays introduces interference to the rest of the relays. Our proposed relaying scheme has a capability to reduce such interference and thereby improve the rate performance. In the proposed scheme, superposition coding is incorporated into SNNC encoding to enable partial interference cancellation at DF relays. The achievable rate with proposed scheme is derived for the discrete two-relay network and evaluated in the Gaussian case where gains over the rate achievable without rate splitting are demonstrated.

In this paper, a distributed network coding (DNC) scheme based on improved online fountain codes is proposed for wireless sensor networks (WSNs). Specifically we propose an improved online fountain codes with the objection of optimizing the build-up phase of the conventional online fountain codes. Then based upon this method, we develop a distributed network coding scheme for sensed data gathering over wireless sensor networks. We analyze the properties of the proposed DNC scheme and derive the upper coding overhead bound for it over binary erasure channels under belief propagation (BP) decoding. Simulation results show that the proposed DNC scheme can achieve a better performance with respect to both coding overhead and complexities.

We propose a novel linear physical-layer network coding (NC) scheme for a fading Y-channel without channel state information at transmitters. In this three-user scheme, each user intends to realize a full data exchange with the other two users via a relay. Instead of directly decoding the users' messages from the received signal, the relay determines NC generator matrices and reconstructs linear NC codewords from its received signals to facilitate the information exchange. We present an explicit solution for NC generator matrices that minimize the NC error probability at high SNRs. We also present and prove an approximation of the NC error probability of the proposed scheme at high SNRs. Numerical results show that the proposed scheme outperforms existing ones, and its performance can be well characterized by the approximation.

This paper presents an efficient data gathering framework of network coding (NC) coupled compressed sensing (CS) in wireless sensor networks (WSNs), called network compressed coding (NCC). We employ network coding to adapt to the dynamic nature of WSNs, such as moving obstacles and link failure. Measurements from sensor networks are often correlated because sensors nodes nearby observe the contiguous phenomenon, and the operation of the random linear network coding (RLNC) scheme is similar to that of the random projection in compressed sensing. Therefore, we introduce compressed sensing into the network coding (NC), to prevent all-or-nothing impact on NC. NCC simultaneously transmits and encodes specific packets of sensor measurements to form random projections for CS recovery. CS technology guarantees that the data gathered at all nodes are accurately recovered with a high probability from a small number of projections, which is less than the total number of source nodes in the network. Our simulation results show that, only less than half number of packets are required to reconstruct measurements with reasonable quality compared with the traditional network coding schemes. Also, NCC increases the data gathering efficiency by over 20% compared to the conventional NC scheme.