Forward error correction codes are commonly adopted in dual-hop relay communications, among which Luby transform (LT) codes are favorable because of their low-complexity decoder and rate adaptability to erasure channels. To alleviate the high computational cost in the primitive LT-based cooperative communications, hybrid decomposed LT (h-DLT) codes are proposed recently. By dispersing the computational cost of LT codes into the source and the relay, the computational cost of both nodes can be reduced considerably. However, there are some practical limitations. First, the nonnegative decomposition algorithm developed for h-DLT codes construction has no control of decomposition accuracy. Second, the cooperative relay communication protocol based on the original h-DLT codes can induce high communication cost. In this paper, we propose a stochastic nonnegative polynomial decomposition algorithm, which achieves robust decomposition and higher decomposition accuracy for h-DLT codes construction. Based on the new algorithm, a new type of h-DLT codes is proposed for cooperative relay communications with higher energy efficiency. Simulations are conducted to manifest the performance of the new h-DLT codes and benefits of the corresponding cooperative relay communication system. In addition, multiple design factors are investigated.

Underwater acoustic communications (UAC) features limited bandwidth, distance-dependent attenuation, long and variable propagation delay, and doubly-selective fading. Therefore, the design of reliable and efficient UAC protocols is very challenging. Cooperative relay communications is promising for future UAC as it can improve its reliability and extend the data transmission ranges. In this work, we consider the adaptive relay-aided OFDM UAC (RA-UAC) using the amplifyand- forward (AF) protocol. We first present the results of the optimal power allocation between the source and the relay as well as the power distribution over all subcarriers based on instantaneous channel state information (CSI). However, the adaptive power allocation is very challenging. The fast timevarying UAC channels and the long propagation delay can make the CSI feedback outdated and therefore degrade the performance of the RA-UAC system using the optimal power allocation. To overcome this problem, we implement channel prediction to compensate the channel variation during the CSI signal propagation. The recursive least square (RLS) adaptive filter is utilized to predict the future channel impulse response (CIR) due to its low computational cost and small storage size. The approximate mean square error (MSE) of the RLS filter is derived. Simulation results confirm the necessity of channel prediction through MSE and overall system performance comparison.