Relays that cooperate to compute

This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multiple-access relay channel where two transmitters attempt to send the modulo sum of their finite field messages to the receiver with the help of the relay. The transmitters use nested lattice codes to ensure that sums of codewords are protected against noise and to preserve the modulo operation of the finite field. We develop a block Markov coding scheme where the relay recovers the real sum of the codewords and retransmits it coherently with the two transmitters.