New rate pairs in the zero-error capacity region of the binary multiplying channel without feedback

We construct uniquely decodable (UD) code pairs for the binary multiplying channel without feedback, using pairs of binary codes. By taking appropriate cosets of linear codes with many information sets for these binary codes, we obtain new rate pairs in the zero-error capacity region Z of this channel. In particular, the rate pair (log(3/2), log(3/2)) is in Z and yields the largest known sum of the rates of pairs in Z. As this rate pair can be achieved with UD pairs with equal members, we have obtained an asymptotically optimal construction for the combinatorial concept of cancellative families of sets