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This paper presents some decoding methods based on Tanner graph for the analysis of the repeat accumulate code which has been proved to be linear time encoding and linear time decoding. We study the structure of the repeat accumulate code and make a detail derivation of the procedure of these iterative algorithms. The extensive simulation results show that these efficient decoding methods based on the message passing algorithm are suitable for the repeat accumulate code both in performance and complexity.

In this study, a mix inexact-quadratic fuzzy water resources management model of floodplain (IQT-WMMF) has developed, through incorporating techniques of credibility-constrained programming (CP), two-stage programming (TP), interval-parameter programming (IPP) and quadratic programming (QP) within a general framework for limited data availability. The IQT-WMMF can provide an effective linkage between system benefit and the associated economic penalty attributed to the violation of the pre-regulated water target under limited data availabilities expressed probabilistic distributions and interval values, meanwhile, imprecise and no-linear economic data would be resolved. The developed method is applied to a real case of planning water resources in the Dahuangbaowa floodplain, China, with the aim to develop a sustainable water resources management in the study region. A number of scenarios with wet land expansion strategies under various credibility levels are analyzed, implying that different policies can lead to varied water-allocation patterns, system benefits, and system-failure risks. The results discover that water deficits and flood damages have brought negative effects on economic development synchronously, which need to effective plans to reduce losses of shortages and floods for achieving higher system benefits. Tradeoffs between economic benefit and system-failure risk can support generating an increased robustness in risk control for water resources allocation under uncertainties, which is beneficial to adjust the current water-allocation sustainably.

In this study, a two-stage inexact credibility-constrained programming (TICP) method is developed for identifying the efficiency of water trading under multiple uncertainties. TICP can tackle uncertainties expressed as probabilistic distributions, discrete intervals and fuzzy sets. It can also provide an effective linkage between the benefits to the system and the associated economic penalties attributed to the violation of the predefined policies for water resource allocation. The developed TICP method is applied to a real case of water resource allocation management and planning in the Kaidu-kongque River Basin, which is a typical arid region in Northwest China. Different water resource allocation policies based on changes to the water permit and trading ratio levels are examined. The results indicate that the efficiencies of water trading are sensitive to the degrees of satisfaction (i.e., interval credibility levels), which correspond to different water resource management policies. Furthermore, the comparison of benefits and shortages between trading and non-trading schemes implies that trading is more optimal and effective than non-trading. The results are helpful for making decisions about water allocation in an efficient way and for gaining insight into the tradeoffs between water trading and economic objectives.