无线复杂网络中Rateless LDPC系统码理论及关键技术的研究

In the wireless complex network, because of the delay and the varity of channel capacity between any two nodes in a network, the traditional error-correcting codes with designed rate and the auto-retransmittion protocol can not solve the error problem during the data transmition. Rateless LDPC codes，a new kind of digital fountain codes, can solve the above problem efficiently. However there are still some weak points in the research of this area: 1) There is no connection between the structure of the rateless LDPC codes and the delay and channel capacity; 2)The stopping set and Trapping set have been ignored;3)Since there must be some degree-one node in the Tanner graph, the decoding algorithm is not flexible. This project first build the mathematical model of the wireless complex network. Based on this, we will reveal the connection between the structure of the error-correcting code and the delay and channel capacity. Then, propose the encoding scheme of the rateless LDPC codes based on Graph Theory and the Chinese Remainder Theorem, and optimize the Stopping set and Trapping set; Finally, we design a flexible decoding algorithm which is not only for arbitrary degree distribution but also detect the Stopping set and the Trapping set. The result of this project will provide the theoritical and practical groundwork for the reliable transmittion in the wireless complex network systems.

在无线复杂网络背景下，由于通信时延约束以及端点间信道容量的多样性，传统的固定码率纠错编码以及自动重传机制不能有效保障数据的可靠传输。Rateless LDPC码作为新型的数字喷泉码能有效的应对以上可靠传输问题,然而该编码的研究尚存在以下不足：1）编码的构造并未与网络的延时和信道容量相联系；2）忽视了Stopping set和Trapping set方面的问题；3）译码中Tanner图必须存在degree-one的节点，缺乏灵活性。本项目首先基于图论建立无线复杂网络的数学模型。在此基础上，揭示延时和信道容量与纠错码构造的联系；然后提出基于图论和CRT的Rateless LDPC码的编码方案，并优化其Stopping set和Trapping set；最后设计能检测Stopping set和Trapping set并适合任意度分布的译码算法，为解决无线复杂网络的可靠传输问题奠定理论和应用基础。

在无线复杂网络背景下，由于通信时延约束以及端点间信道容量的多样性，传统的固定码率纠错编码以及自动重传机制不能有效保障数据的可靠传输。Rateless LDPC码作为新型的数字喷泉码能有效的应对以上可靠传输问题。本项目首先基于图论建立无线复杂网络的数学模型。在此基础上，揭示延时和信道容量与纠错码构造的联系；然后提出基于图论的任意大围长 LDPC 码的编码方案，并获得较优的译码性能；研究了应用于 GSM-MIMO 系统的双层低密度奇偶校验TL-LDPC码，在无误码率性能损失的前提下，TL-LDPC编码的GSM-MIMO系统中ML检测的复杂度远低于传统LDPC编码的GSM-MIMO系统中ML检测的复杂度；最后研究大规模无线复杂网络的控制器部署问题，从宏观上保障了网络的负载均衡性能，为解决无线复杂网络的可靠传输问题奠定理论和应用基础。