Cooperation in the low power regime for the MAC using multiplexed rateless codes

In this paper, we consider cooperation in the low power (low SNR) regime for the multiple access channel with the assumption that the transmitters have no channel state information. A relevant performance measure to consider is therefore the outage capacity. We develop cooperation methods based on multiplexed coding in conjunction with rateless codes and find the achievable rates and in particular the minimum energy per bit required to achieve a certain outage probability. We consider two modes of operation: full duplex [code-division multiple access (CDMA)], where nodes can transmit and receive simultaneously on the same frequency band, and half duplex [frequency-division multiple access (FDMA)], where the nodes transmit and listen on different frequency bands. We show that, perhaps surprisingly, there is little loss in performance when using FDMA. Furthermore, our results show that multiplexed rateless codes come within 0.1 dB of the outer bound on capacity. We also develop practical rateless coding methods for FDMA using multiplexed Raptor codes which operate within 0.52 and 1.1 dB of the theoretical limit for the two- and four-user case, respectively.