Compute-and-Forward: Multiple bi-directional sessions on the line network

Signal superposition and broadcast are important features of the wireless medium. Compute-and-Forward, also known as Physical Layer Network Coding, is a technique exploiting these features in order to improve performance of wireless networks. In this paper, the possible benefits for the line network with multiple bi-directional sessions and local interference are investigated. Four different modes, indicating whether or not broadcast and/or superposition are exploited, are considered. In particular, expressions for the maximum achievable common rate are derived for each of the four different modes. Scheduling and coding schemes achieving these rates are presented. From the results it follows that, in most cases, the common rate is improved by a factor close to two by using Compute-and-Forward. However, it is also found that the benefit may be smaller for particular session configurations.