On Dependence Balance Bounds for Two Way Channels

The idea that no more dependence can be consumed than produced was used to obtain an outer bound to the capacity region of the single output two-way channel in A. P. Hekstra and F. M. J. Willems (1989). A parallel channel extension of this bound was used to obtain an outer bound of 0.64628 bits/transmission for the sum-rate point of the binary multiplying channel (BMC) which improved over Zhang- Berger-Schalkwijk bound of 0.64891 bits/transmission. It is not obvious that this selection of parallel channel would yield the best sum-rate outer bound for the BMC using the idea of dependence balance. We show that for all binary adaptive parallel channels, the best sum-rate outer bound for the BMC is 0.64628 bits/transmission and corresponds to the parallel channel selection of A. P. Hekstra and F. M. J. Willems (1989).