对于半双工中继信道，协作通信能够提高链路可靠性，提升资源效率和系统容量。如何设计编码方案在充分利用协作分集增益的基础上，获得额外的编码增益，提升系统性能一直是该领域的研究热点。空间耦合LDPC（Spatially Coupled LDPC, SC-LDPC）码因其在次最优的置信传播（Belief Propagation, BP）译码算法下能够达到最优的最大后验概率（Maximum a Posterior, MAP）译码性能而引起广泛关注。而空间耦合重复累加（Spatially Coupled Repeat Accumulate, SC-RA）码是一类特殊的SC-LDPC码，相较于传统SC-LDPC码，具有编码结构简单，阈值更优，译码复杂度低等优点。针对半双工译码转发中继信道，提出一种可逼近中继信道容量限的SC-RA码的设计方法，主要工作内容如下： （1）针对单源单中继的三节点中继信道，基于半双工译码转发中继策略，提出了一种可逼近三节点中继信道容量限的SC-RA码的设计方法。具体来说，针对二进制删除信道，源节点分别向中继节点和目的节点发送SC-RA码，中继节点先正确恢复出源节点发送的SC-RA然后再次编码产生额外的校验比特并转发给目的节点，目的节点结合中继节点发送的额外校验比特和源节点发送的SC-RA码进行译码，正确恢复出源节点的信息。为了评估所设计的SC-RA码在三节点中继信道下的渐近性能，推导了密度进化算法用于计算阈值。阈值分析结果表明所提出的SC-RA码能够同时逼近源到中继链路和源到目的链路的容量限。同时，基于半双工二进制删除中继信道，仿真了所设计的SC-RA码的误码性能。仿真结果表明，误码性能与所推导的密度进化算法计算的阈值结果一致，呈现出逼近于容量限的优异性能，且优于采用传统SC-LDPC码的性能。 （2）针对双源单中继的多址接入中继信道，根据半双工译码转发模式的可达速率和编码策略，研究基于SC-RA码的中继节点网络编码方案。具体来说，两个源节点分别向中继节点和目的节点发送SC-RA码，中继节点分别对两个源节点消息进行译码，恢复出源节点信息后再进行联合网络编码，将联合网络编码产生的校验比特发送给目的节点，目的节点将接收到两个源节点的信息和中继产生的校验比特合并后进行联合译码。接着，推导阈值分析算法来计算阈值结果与容量限的差值，阈值分析结果表明所提出的SC-RA码能够同时逼近源到中继链路和源到目的链路的容量限。最后，在二进制删除中继信道下仿真了所设计的编码方案在中继节点和目的节点的译码性能。仿真结果表明，误码性能与所推导的密度进化算法计算的阈值结果相吻合，相较于采用传统SC-LDPC码的性能有显著提升。

For half-duplex relay channel, cooperative communication technology can improve the reliability and the resource efficiency and increase the capacity of wireless communication system. How to design the coding scheme to obtain the coding gain combined with the spatial gain in order to further enhance the system performance is always a research focus. Spatially coupled LDPC (SC-LDPC) codes attract wide attention due to their ability to reach maximum a posterior (MAP) decoding performance under the belief propagation (BP) decoding algorithm. As a particular class of SC-LDPC codes, spatially coupled repeat accumulate (SC-RA) codes have the advantages of simple coding structure, better threshold value and low decoding complexity in comparison with SC-LDPC codes. For half-duplex decode-and-forward relay channel, one method to design the capacity-approaching SC-RA codes is proposed in this paper. The main works are as follows:

(1) For a three-node relay channel with one source and one relay, design of capacity-approaching SC-RA codes for half-duplex decode-and-forward relay channel is proposed in this paper. Specifically, for binary erasure channels, the source node sends one SC-RA code to the relay node and the destination node respectively. After receiving the information from the source node, the relay node first correctly recover this information and then encode them to generate additional check bits sent to the destination node. The destination node can correctly recover the information from the source node by combining the additional check bits sent by the relay node with the information sent by the source node. To evaluate the asymptotic performances of the proposed SC-RA codes in the three-node relay channel, a modified density evolution algorithm is derived to compute the decoding thresholds. The threshold analysis results show that the proposed SC-RA codes can approach the capacity of the source-to-relay link and the source-to-destination link simultaneously. Moreover, the decoding performances over the binary erasure half-duplex relay channels are also simulated to demonstrate the threshold analysis results. Simulation results show that the bit-error-rate performances are consistent with the decoding thresholds obtained by the derived density evolution algorithm, which can exhibit the excellent capacity-approaching performances and also are better than spatially coupled LDPC codes.

(2) For multiple access relay channel with two sources and one relay, according to the achievable rate and coding strategy of decode-and-forward mode, a network coding scheme based on SC-RA codes was studied. Specifically, two source nodes send the messages to the relay node and the destination node respectively. The relay node decodes the messages of the two source nodes respectively, and then jointly encode the recovered messages to generate the additional parity bits, which are then sent to the destination node. The destination node can jointly decode the information by combining the additional parity bits sent by the relay node with the information sent by the source node. A modified density evolution algorithm is derived to compute the gap between decoding threshold and Shannon limits. Moreover, the decoding performances over the binary erasure half-duplex relay channels are also simulated to demonstrate the threshold analysis results. Simulation results show that the bit-error-rate performances are consistent with the decoding thresholds obtained by the derived density evolution algorithm, which can exhibit the excellent capacity-approaching performances and also are better than SC-LDPC codes.

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