Cooperative multiple access channels with oblivious encoders

In this paper we study the cooperative multiple access channel (MAC) with oblivious encoders and characterize its capacity region. Cooperation means that one encoder sends a message to the other encoder via a rate-limited link prior to transmission, while partial cribbing means that one encoder obtains a deterministic function of the other encoder's output. Partial cribbing can be done strictly-causally, causally, and non-causally. Prior work in this field dealt with the case where the two encoders are aware of each other's chosen codebook. In this paper we consider the case of oblivious encoding, where each user in a network is unaware of the codebook chosen by other users. Since an oblivious encoder cannot decode the message sent from another encoder, it cannot implement the Decode-and-Forward coding scheme, as is usually done in cases of partial cribbing with codebook-aware encoders. To overcome this, we introduce the method of Bin-and-Forward, which does not require decoding. Since the possible cribbed signals are not known a priori, in our new coding scheme binning is done on all typical possible cribbed sequences. Instead of sending a decoded message, the oblivious encoder sends the bin in which the cribbed sequence lies. We compare the gain achieved using cooperation and partial cribbing with and without codebook knowledge. Evidently, in the cases of causal and non-causal perfect cribbing, the capacity region is the same for oblivious and codebook-aware encoding. As an example, we consider the Gaussian MAC with cooperation and quantized cribbing. For this model, we give an achievability scheme that shows how knowing the codebooks affects the capacity region for cooperation alone, for partial cribbing alone, and for combined cooperation and partial cribbing.