IEICE TRANS. FUNDAMENTALS, VOL.Exx{A, NO.xx XXXX 200x 1 PAPER Special Section on Information Theory and Its Applications Simple Nonbinary Coding Strategy for Very Noisy Relay

SUMMARY From an information-theoretic point of view, it is well known that the capacity of relay channels comprised of three terminals is much greater than that of two terminal direct channels especially for low SNR region. Previously invented relay coding strategies have not designed to achieve this relaying gain occurred in the low SNR region. In this paper, we propose a new simple coding strategy for relay channels of low SNR or equiv-alently very noisy relay channels. The multiplicative repetition is utilized to design this simple coding strategy. We claim that the proposed strategy is simple since the destination and the re-lay can decode with almost the same computational complexity by sharing the same structure of decoder. An appropriate static power allocation which yields the maximum throughput close to the optimal one in low SNRs is also suggested. Under practical constraints such as equal time-sharing etc., the asymptotic per-formance of this simple strategy is within 0.5 dB from the achiev-able rate for the relay channels. Furthermore, the performance at few thousand bits enjoy a relaying gain by approximately 1 dB. key words: nonbinary LDPC code, multiplicative repetition, decode-and-forward, half duplex relaying, relay channel, very noisy relay channel 1