The Listsize Capacity of the Gaussian Channel with Decoder Assistance

The listsize capacity is computed for the Gaussian channel with a helper that—cognizant of the channel-noise sequence but not of the transmitted message—provides the decoder with a rate-limited description of said sequence. This capacity is shown to equal the sum of the cutoff rate of the Gaussian channel without help and the rate of help. In particular, zero-rate help raises the listsize capacity from zero to the cutoff rate. This is achieved by having the helper provide the decoder with a sufficiently fine quantization of the normalized squared Euclidean norm of the noise sequence.