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

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

Pairwise Check Decoding for LDPC Coded Two-Way Relay Block Fading Channels

Partial decoding has the potential to achieve a larger capacity region than full decoding in two-way relay (TWR) channels. Existing partial decoding realizations are however designed for Gaussian channels and with a static physical layer network coding (PLNC). In this paper, we propose a new solution for joint network coding and channel decoding at the relay, called pairwise check decoding (PCD), for low-density parity-check (LDPC) coded TWR system over block fading channels. The main idea is to form a check relationship table (check-relation-tab) for the superimposed LDPC coded packet pair in the multiple access (MA) phase in conjunction with an adaptive PLNC mapping in the broadcast (BC) phase. Using PCD, we then present a partial decoding method, two-stage closest-neighbor clustering with PCD (TS-CNC-PCD), with the aim of minimizing the worst pairwise error probability. Moreover, we propose the minimum correlation optimization (MCO) for selecting the better check-relation-tabs. Simulation results confirm that the proposed TS-CNC-PCD offers a sizable gain over the conventional XOR with belief propagation (BP) in fading channels.Comment: to appear in IEEE Trans. on Communications, 201

Broadcast Capacity Region of Two-Phase Bidirectional Relaying

In a three-node network a half-duplex relay node enables bidirectional communication between two nodes with a spectral efficient two phase protocol. In the first phase, two nodes transmit their message to the relay node, which decodes the messages and broadcast a re-encoded composition in the second phase. In this work we determine the capacity region of the broadcast phase. In this scenario each receiving node has perfect information about the message that is intended for the other node. The resulting set of achievable rates of the two-phase bidirectional relaying includes the region which can be achieved by applying XOR on the decoded messages at the relay node. We also prove the strong converse for the maximum error probability and show that this implies that the [\eps_1,\eps_2]-capacity region defined with respect to the average error probability is constant for small values of error parameters \eps_1, \eps_2.Comment: 25 pages, 2 figures, submitted to IEEE Transactions on Information Theor

Low-density Parity-check Codes for Wireless Relay Networks

In wireless networks, it has always been a challenge to satisfy high traffic throughput demands, due to limited spectrum resources. In past decades, various techniques, including cooperative communications, have been developed to achieve higher communication rates. This thesis addresses the challenges imposed by cooperative wireless networks, in particular focusing on practical code constructions and designs for wireless relay networks. The thesis is divided into the following four topics: 1) constructing and designing low-density parity-check (LDPC) codes for half-duplex three-phase two-way relay channels, 2) extending LDPC code constructions to half-duplex three-way relay channels, 3) proposing maximum-rate relay selection algorithms and LDPC code constructions for the broadcast problem in wireless relay networks, and 4) proposing an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels. Under the first topic, we construct codes for half-duplex three-phase two-way relay channels where two terminal nodes exchange information with the help of a relay node. Constructing codes for such channels is challenging, especially when messages are encoded into multiple streams and a destination node receives signals from multiple nodes. We first prove an achievable rate region by random coding. Next, a systematic LDPC code is constructed at the relay node where relay bits are generated from two source codewords. At the terminal nodes, messages are decoded from signals of the source node and the relay node. To analyze the performance of the codes, discretized density evolution is derived. Based on the discretized density evolution, degree distributions are optimized by iterative linear programming in three steps. The optimized codes obtained are 26% longer than the theoretic ones. For the second topic, we extend LDPC code constructions from half-duplex three-phase two-way relay channels to half-duplex three-way relay channels. An achievable rate region of half-duplex three-way relay channels is first proved. Next, LDPC codes for each sub-region of the achievable rate region are constructed, where relay bits can be generated only from a received codeword or from both the source codeword and received codewords. Under the third topic, we study relay selection and code constructions for the broadcast problem in wireless relay networks. We start with the system model, followed by a theorem stating that a node can decode a message by jointly decoding multiple blocks of received signals. Next, the maximum rate is given when a message is decoded hop-by-hop or decoded by a set of nodes in a transmission phase. Furthermore, optimal relay selection algorithms are proposed for the two relay schemes. Finally, LDPC codes are constructed for the broadcast problem in wireless relay networks. For the fourth topic, an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels is proposed. The decoder is based on log-likelihood ratios (LLRs). Interference is estimated, quantized and subtracted from channel outputs. To analyze the codes, density evolution is derived. We show that the required signal-to-noise ratio (SNR) for the proposed low-complexity decoder is 0.2 dB higher than that for an existing sub-optimal belief propagation decoder at code rate 1/3.4 month