Power adaptive feedback communication over an additive individual noise sequence channel

We consider a real-valued additive channel with an individual unknown noise sequence. We present a simple sequential communication scheme based on the celebrated Schalkwijk-Kailath scheme, which varies the transmit power according to the power of the sequence, so that asymptotically the relation between the SNR and the rate matches the Gaussian channel capacity R ¿ 1/2 log(1 + SNR) for almost every noise sequence.