On an extension of an achievable rate region for the binary multiplying channel (Corresp.)

Shannon showed that for the binary multiplying channel (BMC) his inner and outer hounds to the capacity region differ. Schalkwijk gave a simple coding strategy that yields rate pairs
(R_{1}, R_{2})
outside the Shannon inner bound region. For the case of equal rates in both directions this strategy achieves
R_{1} = R_{2} = 0.6 1914
beyond Shannon's inner bound rate
R_{1} = R_{2} = 0.61695
. In this correspondence it is shown that using a result by Slepian and Wolf one can bootstrap the Schalkwijk strategy to find an even larger achievable rate region. In fact, symmetric
R_{1} = R_{2}
operation of the BMC now yields a common rate
R_{1} = R_{2} = 0.63056
.