Interval+communications=Walsh: for signal multiplexing under interval uncertainty, Walsh functions are optimal

In communications, often, statistical characteristics of the noise vary so much that, in essence, we can only have an interval estimates for this noise. We show that under this interval uncertainty, the optimal multiplexing technique consists of using Walsh functions. This result provides a new theoretical explanation for the success of Walsh-based multiplexing techniques which are actively used in cellular phones and in other types of wireless communication.