Backward channels in multiterminal source coding

We consider the multiterminal source coding problem with general discrete memoryless sources. In previous work, we developed new inner and outer bounds to its rate region, and nave an expression for the gap between them, which explicitly depends on the code maps. In this work, we first construct a class of codes for our problem, based on the method of backward channels used by Csiszar and Korner in their proof of the two-terminal rate/distortion theorem. Next, we show that for each one of the codes in this class, the gap between the inner and the outer bounds above does vanish. Finally, we present a summary of results obtained to date with this purely combinatorial approach, as well as a statement of what it would take to completely solve the problem following this line of attack.