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 code-words are protected against noise and to preserve the modulo operation of the finite field. The authors develop a block Markov coding scheme where the relay recovers the real sum of the code-words and retransmits it coherently with the two transmitters.