Capacity Region of the Gaussian Arbitrarily-Varying Broadcast Channel

This paper considers the two-user Gaussian arbitrarily-varying broadcast channel, wherein a power-limited transmitter wishes to send a message to each of two receivers. Each receiver sees a superposition of the transmitter's sequence, Gaussian noise, and a signal from a power-limited malicious jammer. The jammer is assumed to know the code, but is oblivious to real-time transmissions. The exact capacity region of this setting is determined to be the capacity region of the standard Gaussian broadcast channel, but with the noise variance increased by the power of the jammer, as long as the received power of the jammer at each receiver is less than that of the legitimate transmitter. A key aspect of the achievable scheme involves sharing randomness from the transmitter to the receivers by breaking the transmitted sequence into segments, and either transmitting at full power in a segment, or sending zero. By coding over the on/off signal, a small shared randomness can be established without corruption by the jammer, and without interfering with the standard superposition coding strategy for the Gaussian broadcast channel.