Physical Network Coding Research Articles

Precoding Designs Based on Minimum Distance for Two-Way Relaying MIMO Systems with Physical Network Coding

In this paper, we propose new precoding methods for two-way multiple input multiple output physical network coding (PNC) systems which employ the modulo operation. In our work, the transmit and receive filters are determined to maximize the minimum distance of the received constellations assuming global channel state information. The precoding operations are separately optimized for the multiple access (MA) and the broadcast stages, and the optimal precoding is obtained by applying a semidefinite relaxation method. Especially, we prove that for the system with linear detection the modulo operation for the PNC achieves optimality with the derived precoding for the MA stage in terms of the minimum distance. Also, we present a closed-form solution for the optimal filter designs for two special cases. For computing solutions, we transform our max min problem into a simple maximization problem by imposing additional constraints. Also, we propose a suboptimal non-iterative precoding scheme whose performance is within 1 dB at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> compared to the optimum iterative method with much reduced complexity. Finally, the simulation results show that the proposed systems achieve 2-3 dB gains at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> compared to the optimal amplify-and-forward systems.

Joint physical network coding and LDPC decoding for two way wireless relaying

In this paper, we investigate the joint design of channel and network coding in bi-directional relaying systems and propose a combined low complexity physical network coding and LDPC decoding scheme. For the same LDPC codes employed at both source nodes, we show that the relay can decode the network coded codewords from the superimposed signal received from the BPSK-modulated multiple-access channel. Simulation results show that this novel joint physical network coding and LDPC decoding method outperforms the existing MMSE network coding and LDPC decoding method over the AWGN and complex MAC channel.

Decoding Generalized Joint Channel Coding and Physical Network Coding in the LLR Domain

This letter develops a log-likelihood-ratio-based decoder for a generalized joint channel-coding-and-physical-network coding used in a two-way relay system. Assuming that the same low-density parity-check codes are used at the source nodes, the proposed decoder shows identical error performance as the probability-domain-based decoder but with a much lower computational complexity.

A Serial Joint Channel and Physical Layer Network Decoding in Two-Way Relay Networks

This paper presents a novel joint channel and physical layer network decoding scheme for a two-way relay communication system. The proposed decoding scheme can be viewed as a serial concatenated decoding scheme with the source codes, different or identical, as the outer codes and the physical network coding (PNC) as the inner code. To achieve good error performance, iteratively decodable codes are used as the source codes. Decoding of the scheme consists of two loops, the inner-loop for which the source codes are decoded with a message-passing decoding algorithm and the outer-loop for which the reliability messages are passed between the source decoders and the PNC decoder for updating message reliabilities. Using two different protograph repeat-accumulate codes as the source codes for low decoder complexity, the proposed scheme achieves a superior performance. In the case that the source codes are identical, the proposed scheme outperforms the previously proposed decoding schemes for two-way relay communication systems with two source nodes.

Opportunistic Scheduling for Multi-User Two-Way Relay Systems with Physical Network Coding

This letter considers a multi-user wireless communication system employing physical network coding (PNC), where a pair of users communicates with each other via a relay. To attain reliable communication over time varying channels, we apply an opportunistic scheduling scheme for the PNC to both the broadcast channel phase and the multiple access channel phase. We propose two criteria for selecting users based on the channel norm and the minimum distance. Also, an efficient method to compute the minimum distance for superposed QPSK signals is introduced. Simulation results show that the proposed scheduling for PNC provides a significant improvement over conventional schemes.

Optimal Power Control for OFDM Signals over Two-Way Relay with Physical Network Coding

This paper describes an optimal power allocation scheme for orthogonal frequency division multiple access two-way relay networks with physical network coding. The aim is to enhance the achievable sum rate of the terminals for a constrained total transmit power. Convex optimization is used to derive a closed-form solution for the power allocation between the relay node and the two terminals. This reduces the variable dimensionality of the objective function for the power assignment problem among multiple carriers when the total transmit power is constrained. This solution is then used to derive the optimal power control scheme. This method reduces the implementation complexity compared with the traditional resource allocation scheme. Numerical and simulation results show that the approach achieves almost the optimal sum rate and outperforms the fixed power assignment method with less computational load in various scenarios.

Cooperative Spectrum Sensing Algorithm Based on the Relay

Cooperative spectrum sensing is investigated in cognitive radio (CR) networks over Rayleigh fading channels. By utilizing the relay to enhance the reliability of the sensing information reporting, cooperative spectrum sensing algorithm based on the relay is proposed. Physical network coding is used for the relay and the method for relay selection is discussed. The simulation results show that cooperative spectrum sensing algorithm based on the relay can achieve better performance.

Optimized constellations for two-way wireless relaying with physical network coding

We investigate modulation schemes optimized for two-way wireless relaying systems, for which network coding is employed at the physical layer. We consider network coding based on denoise-and-forward (DNF) protocol, which consists of two stages: multiple access (MA) stage, where two terminals transmit simultaneously towards a relay, and broadcast (BC) stage, where the relay transmits towards the both terminals. We introduce a design principle of modulation and network coding, considering the superposed constellations during the MA stage. For the case of QPSK modulations at the MA stage, we show that QPSK constellations with an exclusive-or (XOR) network coding do not always offer the best transmission for the BC stage, and that there are several channel conditions in which unconventional 5-ary constellations lead to a better throughput performance. Through the use of sphere packing, we optimize the constellation for such an irregular network coding. We further discuss the design issue of the modulation in the case when the relay exploits diversity receptions such as multiple-antenna diversity and path diversity in frequency-selective fading. In addition, we apply our design strategy to a relaying system using higher-level modulations of 16QAM in the MA stage. Performance evaluations confirm that the proposed scheme can significantly improve end-to-end throughput for two-way relaying systems.