The Additive Noise Channel with a Helper

Abstract

The additive noise channel is studied in the presence of a helper who observes the noise and can describe it to the receiver over a rate-limited noise-free bit-pipe. It is shown that the capacity of this network is typically the sum of the capacity of the channel in the absence of the helper and the capacity of the bit-pipe from the helper to the receiver. This holds for finite-variance stationary and ergodic noises under fairly general power-like constraints on the transmitted signal. A helper that is only cognizant of the noise is thus as helpful as an omniscient helper that is cognizant of both the noise and the transmitted message. The achievability proof is based on “flash helping” and requires no binning. Extensions to additive-noise multi-access channels are also discussed.