Minimum breakdown degradation in binary source encoding

A memoryless binary equiprobable source produces one letter per second. Two people each are provided separately with private information about the source data at a rate of
1/2
bit per second. Suppose that by pooling their information they can produce a long-mn reconstruction of the source output that has arbitrarily small error frequency. We prove that then the least common asymptotic error frequency d that each can achieve without the other's help is
(\sqrt{2}-1)/2=0.207
. Since it had been shown previously that
0.200 \leq d \leq 0.207
, our result closes the so-called "007 gap." New analytical techniques introduced to effect the proof are of broader significance in multiuser information theory.