Distance enumerator analysis for multi-user codes

A distance enumerator analysis is given for multiuser codes over a Gaussian multiple-access channel (MAC). A multi-user code distance is defined as the Euclidean distance between two multi-user codewords after their inter-user super-position caused by MAC. By employing a user-interleaving and a user-scrambling, a multi-user code ensemble is defined, and its distance enumerator is calculated as a concatenated multiple single-user codes and a superposition code.