No abstract

Compute-and-forward is a framework for reliable physical layer network coding introduced by Nazer and Gastpar. Instead of decoding single messages, it decodes linear combinations of messages with the help of nested lattice codes. Nazer and Gastpar derived an achievable rate for each node depending on the channel coefficients and the desired equation coefficients. However, it is open how to choose the coefficient vector with the equation coefficients. We provide a branch-and-bound algorithm that calculates the coefficient vector, which results in the highest computation rate at a single node. We implemented the algorithm in Matlab and compared the number of iterations to the number of needed iterations if we use a complete search over all possible vectors.Index Terms-compute-and-forward, network coding, branch-and-bound algorithm

No abstract

We investigate the problem of secure communications in a Gaussian multi-way relay channel applying the compute-and-forward scheme under usage of nested lattice codes. All nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme.We start with the general case of the single-input multipleoutput (SIMO) L-user multi-way relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the single-input single-output (SISO) and the multiple-input single-input (MISO) L-user multi-way relay channel as well as the two-way relay channel. We discuss these results and show the dependency between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the compute-andforward rate without secrecy.

No abstract