A joint typicality approach to compute-forward

A general framework for analyzing linear codes with joint typicality encoders and decoders is presented. Using this approach, we provide a new perspective on the compute-forward framework. In particular, an achievable rate region for computing the weighted sum of nested linear codewords over a discrete memoryless multiple access channel (MAC) is established. When specialized to the Gaussian MAC, we recover the lattice-based compute-forward rate region by Nazer and Gastpar, providing a unified treatment over both discrete memoryless and Gaussian networks. By further utilizing simultaneous joint typicality decoders, we provide a joint decoding rate region for computing two linear combinations of nested linear codewords from K-senders. Our result provides some insight on one of the main open problems in the compute-forward framework, the joint decoding rate region of compute-forward.