Compute-and-forward using nested linear codes for the Gaussian MAC

The classical modulo-lattice construction of Erez et al. has been successfully applied to several coding problems under Gaussian noise, including coding for computation over multiple-access channels (MAC). For the latter problem, an alternative construction can be developed by extending a recently proposed nested linear code to Gaussian case. In this note, it is shown that using the nested linear code with judiciously chosen input distributions, the original compute-and-forward result is recovered and larger computation rates are achievable. In particular we show that the Gaussian input distribution is not optimal in general for the computation problem over Gaussian MAC. Among other results, new achievable rates for the Gaussian two-way relay channel (TWRC) are given. © 2015 IEEE

Compute-and-forward for discrete memoryless networks

Consider a receiver that observes multiple interfering codewords. The compute-and-forward technique makes it possible for the receiver to directly decode linear combinations of the codewords. Previous work has focused on compute-and-forward for linear Gaussian networks. This paper explores the corresponding technique for discrete memoryless networks. As a by-product, this leads to a novel way of attaining non-trivial points on the dominant face of the capacity region of discrete memoryless multiple-access channels