Simple Nonbinary Coding Strategy for Very Noisy Relay Channels

From an information-theoretic point of view, it is well known that the capacity of relay channels comprising 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 been designed to achieve this relaying gain occurring in the low SNR region. In this paper, we propose a new simple coding strategy for a relay channel with low SNR or, equivalently, for a very noisy relay channel. The multiplicative repetition is utilized to design this simple coding strategy. We claim that the proposed strategy is simple since the destination and the relay 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 performance of this simple strategy is within 0.5dB from the achievable rate of a relay channel. Furthermore, the performance at few thousand bits enjoys a relaying gain by approximately 1dB.