Sawtooth Relaying

We consider the three-node AWGN relay channel with a memoryless relay, in contrast to the conventional decode-and-forward or compress-and-forward schemes, which require complex encoding and decoding processing at the relay. We model the operation of the relay as a single-variable deterministic mapping. We then in particular propose to use a "modulo function" or a "triangular function" to implement the mapping at the relay. Since both these have a sawtooth-like shape we coin the term "sawtooth relaying." We demonstrate significantly improved achievable rates of our proposed schemes over the conventional memoryless amplify-and-forward relaying.