Joint Design of QC-RA Codes and Performance Analysis of Coded Cooperation
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摘要: 重复累积(RA)码是一种特殊结构的低密度奇偶校验(LDPC)码，不仅具有LDPC码的优点，还能实现差分编码。针对LDPC编码协作系统编码复杂度高、时延长的问题，该文引入准循环RA(QC-RA)码，推导出信源节点和中继节点采用的QC-RA码对应的联合校验矩阵，基于公差构造方法设计该联合校验矩阵，并证明该方法设计的联合校验矩阵不存在围长为girth-4, girth-6的短环。理论分析和仿真结果表明，同等条件下该系统比相应点对点系统具有更优异的误码率性能。仿真结果同时表明，与采用一般构造QC-RA码或基于Z型构造QC-RA码相比，采用基于公差构造的联合设计QC-RA码的多信源多中继协作均可获得更高的编码增益。Abstract: Repeat Accumulate (RA) code is a special kind of Low Density Parity Check (LDPC) code, which not only has the advantages of LDPC code, but also realizes differential encoding. To solve the problems of high encoding complexity and long encoding delay of LDPC-coded cooperative system, Quasi-Cyclic RA (QC-RA) code is introduced. Firstly, a joint parity check matrix corresponding to the QC-RA codes adopted by the sources and relays is deduced; Secondly, the joint check matrix is designed based on the Common Difference Construction (CDC) method, and it is proved that the joint check matrix designed by the CDC method does not have short cycles with girth-4 or girth-6. Theoretical analysis and simulation results show that the system achieves better Bit Error Rate (BER) performance than the corresponding point-to-point system under the same conditions. The simulation results also demonstrate that the multi-source multi-relay coded cooperation with CDC constructed QC-RA code can obtain higher coding gain than that with generally constructed QC-RA code or Z-type constructed QC-RA code.
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表 1 双信源双中继编码协作及对应点对点系统采用的QC-RA码
信源节点采用的QC-RA码 中继节点采用的QC-RA码 双信源双中继
编码协作系统$\begin{array}{l} {{{H}}_{{S_1}}} = \left[ {\begin{array}{*{20}{c}} {{{A}}_{(1700 \times 850)}^{(1)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \\ {{{H}}_{{S_2}}} = \left[ {\begin{array}{*{20}{c}} {{{A}}_{(1700 \times 850)}^{(2)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \end{array} $
Rate=1/3$\begin{array}{l} {{{H}}_{{R_1}}} = \left[ {\begin{array}{*{20}{c}} {{{B}}_{1(1700 \times 850)}^{(1)}}&{{{B}}_{2(1700 \times 850)}^{(1)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \\ {{{H}}_{{R_2}}} = \left[ {\begin{array}{*{20}{c}} {{{B}}_{1(1700 \times 850)}^{(2)}}&{{{B}}_{2(1700 \times 850)}^{(2)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \end{array} $
Rate=3/4点对点系统 ${{{H}}_S} = \left[ {\begin{array}{*{20}{c}} {{{{H}}_{(6800 \times 1700)}}}&{{{{D}}_{(6800 \times 6800)}}} \end{array}} \right]$ Rate=1/5 \ 
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表 2 不同信源节点、中继节点数目情况下编码协作系统采用的RA码
信源节点采用的QC-RA码 中继节点采用的QC-RA码 双信源单中继系统 $\begin{array}{l} {{{H}}_{{S_1}}} = \left[ {\begin{array}{*{20}{c}} {{{A}}_{(1700 \times 1700)}^{(1)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \\ {{{H}}_{{S_2}}} = \left[ {\begin{array}{*{20}{c}} {{{A}}_{(1700 \times 1700)}^{(2)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \end{array} $
Rate=1/2${{{H}}_R} = \left[ {\begin{array}{*{20}{c}} {{{{B}}_{1(1700 \times 1700)}}}&{{{{B}}_{2(1700 \times 1700)}}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right]$
Rate=2/3单信源双中继系统 ${{{H}}_S} = \left[ {\begin{array}{*{20}{c}} {{{{A}}_{(1700 \times 1700)}}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right]$
Rate=1/2$\begin{array}{l} {{{H}}_{{R_1}}} = \left[ {\begin{array}{*{20}{c}} {{{B}}_{(1700 \times 1700)}^{(1)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \\ {{{H}}_{{R_2}}} = \left[ {\begin{array}{*{20}{c}} {{{B}}_{(1700 \times 1700)}^{(2)}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right] \end{array} $
Rate=1/2单信源单中继系统 ${{{H}}_S} = \left[ {\begin{array}{*{20}{c}} {{{{A}}_{(1700 \times 1700)}}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right]$
Rate=1/2${{{H}}_R} = \left[ {\begin{array}{*{20}{c}} {{{{B}}_{(1700 \times 1700)}}}&{{{{D}}_{(1700 \times 1700)}}} \end{array}} \right]$
Rate=1/2
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