Signaling over the Gaussian channel with intermittent feedback

Optimal signaling is studied over a power-limited Gaussian channel with intermittent feedback, where a random mechanism-whose outcome is unknown to the receiver-determines whether or not the output symbol is fed back to the encoder. If the output symbols are fed back with probability smaller than one half, then even the two-messages error probability cannot decay faster than exponentially in the blocklength. But if this probability is greater than one half, then, even for some positive rates, a doubly exponential decay is achievable.