Disclosed herein is a system for binaural noise reduction for hearing assistance devices using information generated at a first hearing assistance device and information received from a second hearing assistance device. In various embodiments, the present subject matter provides a gain measurement for noise reduction using information from a second hearing assistance device that is transferred at a lower bit rate or bandwidth by the use of coding for further quantization of the information to reduce the amount of information needed to make a gain calculation at the first hearing assistance device. The present subject matter can be used for hearing aids with wireless or wired connections.