On the duality between multiple-access codes and computation codes

Abstract

For a two-user Gaussian multiple access channel, computation codes are designed for the scenarios where the decoder is not interested in decoding the two codewords, but only the sum of them. It has been observed that good computation codes should possess some algebraic structure. In this note, we expose the fact that such algebraic structure could undermine the capability of the codes for recovering the messages, i.e., for the purpose of multiple-access. Particularly, we establish duality results between the codes which are good for computation and the codes which are good for multiple access.