Physical Layer Network Coding for the Multiple Access Relay Channel

We consider the two user wireless Multiple Access Relay Channel (MARC), in which nodes $A$ and $B$ want to transmit messages to a destination node $D$ with the help of a relay node $R$. For the MARC, Wang and Giannakis proposed a Complex Field Network Coding (CFNC) scheme. As an alternative, we propose a scheme based on Physical layer Network Coding (PNC), which has so far been studied widely only in the context of two-way relaying. For the proposed PNC scheme, transmission takes place in two phases: (i) Phase 1 during which $A$ and $B$ simultaneously transmit and, $R$ and $D$ receive, (ii) Phase 2 during which $A$, $B$ and $R$ simultaneously transmit to $D$. At the end of Phase 1, $R$ decodes the messages $x_A$ of $A$ and $x_B$ of $B,$ and during Phase 2 transmits $f(x_A,x_B),$ where $f$ is many-to-one. Communication protocols in which the relay node decodes are prone to loss of diversity order, due to error propagation from the relay node. To counter this, we propose a novel decoder which takes into account the possibility of an error event at $R$, without having any knowledge about the links from $A$ to $R$ and $B$ to $R$. It is shown that if certain parameters are chosen properly and if the map $f$ satisfies a condition called exclusive law, the proposed decoder offers the maximum diversity order of two. Also, it is shown that for a proper choice of the parameters, the proposed decoder admits fast decoding, with the same decoding complexity order as that of the CFNC scheme. Simulation results indicate that the proposed PNC scheme performs better than the CFNC scheme.Comment: 10 pages, 5 figure

Physical Layer Network Coding for the K-user Multiple Access Relay Channel

A Physical layer Network Coding (PNC) scheme is proposed for the $K$-user wireless Multiple Access Relay Channel (MARC), in which $K$ source nodes transmit their messages to the destination node $D$ with the help of a relay node $R.$ The proposed PNC scheme involves two transmission phases: (i) Phase 1 during which the source nodes transmit, the relay node and the destination node receive and (ii) Phase 2 during which the source nodes and the relay node transmit, and the destination node receives. At the end of Phase 1, the relay node decodes the messages of the source nodes and during Phase 2 transmits a many-to-one function of the decoded messages. Wireless networks in which the relay node decodes, suffer from loss of diversity order if the decoder at the destination is not chosen properly. A novel decoder is proposed for the PNC scheme, which offers the maximum possible diversity order of $2,$ for a proper choice of certain parameters and the network coding map. Specifically, the network coding map used at the relay is chosen to be a $K$-dimensional Latin Hypercube, in order to ensure the maximum diversity order of $2.$ Also, it is shown that the proposed decoder can be implemented by a fast decoding algorithm. Simulation results presented for the 3-user MARC show that the proposed scheme offers a large gain over the existing scheme for the $K$-user MARC.Comment: More Simulation results added, 12 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1210.049

Network Coding Tree Algorithm for Multiple Access System

Network coding is famous for significantly improving the throughput of networks. The successful decoding of the network coded data relies on some side information of the original data. In that framework, independent data flows are usually first decoded and then network coded by relay nodes. If appropriate signal design is adopted, physical layer network coding is a natural way in wireless networks. In this work, a network coding tree algorithm which enhances the efficiency of the multiple access system (MAS) is presented. For MAS, existing works tried to avoid the collisions while collisions happen frequently under heavy load. By introducing network coding to MAS, our proposed algorithm achieves a better performance of throughput and delay. When multiple users transmit signal in a time slot, the mexed signals are saved and used to jointly decode the collided frames after some component frames of the network coded frame are received. Splitting tree structure is extended to the new algorithm for collision solving. The throughput of the system and average delay of frames are presented in a recursive way. Besides, extensive simulations show that network coding tree algorithm enhances the system throughput and decreases the average frame delay compared with other algorithms. Hence, it improves the system performance

Enabling decentralized wireless index coding in practice

Index coding is a problem in theoretical computer science and network information theory that studies the optimal coding scheme for transmitting multiple messages across a network to receivers with different side information. The ultimate goal of index coding is to reduce transmission time in a communication network by minimizing the number of messages based on shared information. Index coding theory extends to several key engineering problems in network communication including peer to peer communication, distributed broadcast networks, and interference alignment. Although the theoretical connection between index coding and wireless networks is valuable, we focus on finding index coding strategies for a realistic wireless network. More specifically, we investigate how index coding can be applied to an OFDMA downlink network during the retransmission phase. An orthogonal frequency-division multiple access (OFDMA) downlink network is a network where data is sent downward from a designated higher-level transmitter to a group of receiving nodes. In addition, receivers can often decode the other receivers' physical layer signals on the other sub-channels that can be exploited as side information. If this side information is sent back to the transmitter, it can then be coded to cancel the interference in subsequent retransmission phases resulting in fewer retransmission messages. In this report, we explain the coding model and characterize the benefits of index coding for retransmissions within an OFDMA downlink network. In addition, we demonstrate the results of applying this index coding scheme in such network in both simulation and in an active wireless mesh network.Electrical and Computer Engineerin

Performance Analysis of Adaptive Physical Layer Network Coding for Wireless Two-way Relaying

The analysis of modulation schemes for the physical layer network-coded two way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. It was shown by Koike-Akino et. al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. Depending on the signal set used at the end nodes, deep fades occur for a finite number of channel fade states referred as the singular fade states. The singular fade states fall into the following two classes: The ones which are caused due to channel outage and whose harmful effect cannot be mitigated by adaptive network coding are referred as the \textit{non-removable singular fade states}. The ones which occur due to the choice of the signal set and whose harmful effects can be removed by a proper choice of the adaptive network coding map are referred as the \textit{removable} singular fade states. In this paper, we derive an upper bound on the average end-to-end Symbol Error Rate (SER), with and without adaptive network coding at the relay, for a Rician fading scenario. It is shown that without adaptive network coding, at high Signal to Noise Ratio (SNR), the contribution to the end-to-end SER comes from the following error events which fall as $\text{SNR}^{-1}$: the error events associated with the removable singular fade states, the error events associated with the non-removable singular fade states and the error event during the BC phase. In contrast, for the adaptive network coding scheme, the error events associated with the removable singular fade states contributing to the average end-to-end SER fall as $\text{SNR}^{-2}$ and as a result the adaptive network coding scheme provides a coding gain over the case when adaptive network coding is not used.Comment: 10 pages, 5 figure

Achievable Rate and Optimal Physical Layer Rate Allocation in Interference-Free Wireless Networks

We analyze the achievable rate in interference-free wireless networks with physical layer fading channels and orthogonal multiple access. As a starting point, the point-to-point channel is considered. We find the optimal physical and network layer rate trade-off which maximizes the achievable overall rate for both a fixed rate transmission scheme and an improved scheme based on multiple virtual users and superposition coding. These initial results are extended to the network setting, where, based on a cut-set formulation, the achievable rate at each node and its upper bound are derived. We propose a distributed optimization algorithm which allows to jointly determine the maximum achievable rate, the optimal physical layer rates on each network link, and an opportunistic back-pressure-type routing strategy on the network layer. This inherently justifies the layered architecture in existing wireless networks. Finally, we show that the proposed layered optimization approach can achieve almost all of the ergodic network capacity in high SNR.Comment: 5 pages, to appear in Proc. IEEE ISIT, July 200

Wireless Network-Coded Four-Way Relaying Using Latin Hyper-Cubes

This paper deals with physical layer network-coding for the four-way wireless relaying scenario where four nodes A, B, C and D wish to communicate their messages to all the other nodes with the help of the relay node R. The scheme given in the paper is based on the denoise-and-forward scheme proposed first by Popovski et al. Intending to minimize the number of channel uses, the protocol employs two phases: Multiple Access (MA) phase and Broadcast (BC) phase with each phase utilizing one channel use. This paper does the equivalent for the four-way relaying scenario as was done for the two-way relaying scenario by Koike-Akino et al., and for three-way relaying scenario in [3]. It is observed that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. These network coding maps are so chosen so that they satisfy a requirement called exclusive law. We show that when the four users transmit points from the same M-PSK constellation, every such network coding map that satisfies the exclusive law can be represented by a 4-fold Latin Hyper-Cube of side M. The network code map used by the relay for the BC phase is explicitly obtained and is aimed at reducing the effect of interference at the MA stage.Comment: 14 pages, 6 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1112.158

Wireless Bidirectional Relaying using Physical Layer Network Coding with Heterogeneous PSK Modulation

In bidirectional relaying using Physical Layer Network Coding (PLNC), it is generally assumed that users employ same modulation schemes in the Multiple Access phase. However, as observed by Zhang et al., it may not be desirable for the users to always use the same modulation schemes, particularly when user-relay channels are not equally strong. Such a scheme is called Heterogeneous PLNC. However, the approach in [1] uses the computationally intensive Closest Neighbour Clustering (CNC) algorithm to find the network coding maps to be applied at the relay. Also, the treatment is specific to certain cases of heterogeneous modulations. In this paper, we show that, when users employ heterogeneous but symmetric PSK modulations, the network coding maps and the mapping regions in the fade state plane can be obtained analytically. Performance results are provided in terms of Relay Error Rate (RER) and Bit Error Rate (BER).Comment: 10 pages, 10 figures and 3 table