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