New results on a fundamental problem in network information theory

his paper is concerned with two new results on coding strategies for the binary multiplying channel. The binary multiplying channel is a two-way channel that models, for example, a wired-AND connection. The coding strategies are described as a progressive subdivision of the unit square into so-called resolution products. The first part of the paper concerns a new class of constructive coding strategies for the binary multiplying channel that achieve surprisingly high transmission rates. The second part of the paper establishes a new region of achievable rate pairs (R1,R2) for the binary multiplying channel that includes the equal rate point R=R2~0.63072 bit per transmission. A further substantial improvement of the achievable rate region by unit square division is prohibitively difficult