The Case for Structured Random Codes: Beyond Linear Models
Recent work has shown that for some multi-user networks, carefully controlling the algebraic structure of the coding scheme may be just as useful as selecting the correct input distribution. In particular, for linear channel models, including finite field and Gaussian networks, linearly structured codes have been successfully used to prove new capacity results. In this note, we show that the benefits of structured random codes is not limited to linear channel models and networks. We show that for general discrete memoryless networks, there are benefits to allowing intermediate nodes to decode only a function of their inputs. These benefits are illustrated through the aid of an example based on the binary multiplying channel.