Semi-feedback for the binary multiplying channel

In his paper on two-way channels (TWC) Shannon (1961) derived the so-called inner and outer bound region. For a TWC without feedback the outer bound coincides with the inner bound. As a consequence, the capacity region of a TWC without feedback is equal to its inner bound. Furthermore, Shannon showed that for the binary multiplying channel (BMC) the inner and outer bound are different. Dueck (1980) also proved the existence of a TWC with feedback at one terminal (semi-feedback) for which the capacity region is in excess of its inner bound region. However, the BMC with semi-feedback was believed to have a capacity region that coincides with the inner bound region. Nevertheless, a semi-strategy has been constructed for the BMC that operates beyond the inner bound region. The semi-strategy is based on both the new message percolation technique of Schalkwijk (see Proceedings Joint Swedish-Russian International Workshop on Information Theory, vol.6, p. 87-91, Sweden, 1993) and the old bootstrapping technique