Nested linear codes achieve Marton's inner bound for general broadcast channels

In several multi-terminal communication systems, it has been noted that the average performance of linear code ensemble is better than that of the standard unstructured code ensemble. However, it is well-known that linear code ensembles cannot achieve the point-to-point capacity of an arbitrary discrete memoryless channel. In this paper, we study nested linear codes and prove they achieve capacity of arbitrary discrete memoryless point to point channel with and without channel state information at the transmitter. Furthermore, we prove nested linear codes achieve Marton's inner bound, the largest known inner bound for the general discrete broadcast channel.