The Degraded Gaussian Many-Access Wiretap Channel

The Gaussian multiple-access wiretap channel when the number of transmitters grows unbounded and at most linearly with the blocklength is studied. Its capacity region is characterized when the eavesdropper channel is degraded and when the transmitters' activities are random. Unlike the conventional Gaussian multiple-access wiretap channel, the capacity region is independent of the power of the transmitters and depends only on the sum of the message lengths of the transmitters.