多信源多中繼編碼協(xié)作系統(tǒng)準循環(huán)LDPC碼的聯(lián)合設(shè)計與性能分析
doi: 10.11999/JEIT190069
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南京郵電大學(xué)通信與信息工程學(xué)院 ??南京 ??210003
基金項目: 國家自然科學(xué)基金(61501256)，江蘇省自然科學(xué)基金(BK20150857)，南京郵電大學(xué)國自基金孵化項目（NY219073)
Joint Design of Quasi-cyclic Low Density Parity Check Codes and Performance Analysis of Multi-source Multi-relay Coded Cooperative System
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College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
Funds: The National Natural Science Foundation of China (61501256), The Natural Science Foundation of Jiangsu Province (BK20150857), The NUPTSF(NY219073)
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摘要: 為解決多信源多中繼低密度奇偶校驗(LDPC)碼編碼協(xié)作系統(tǒng)編碼復(fù)雜度高、編碼時延長的問題，該文引入一種特殊結(jié)構(gòu)的LDPC碼—基于生成矩陣的準循環(huán)LDPC碼(QC-LDPC)碼。該類碼結(jié)合了QC-LDPC碼與基于生成矩陣LDPC (G-LDPC)碼的特點，可直接實現(xiàn)完全并行編碼，極大地降低了中繼節(jié)點的編碼時延及編碼復(fù)雜度。在此基礎(chǔ)上，推導(dǎo)出對應(yīng)于信源節(jié)點和中繼節(jié)點采用的QC-LDPC碼的聯(lián)合校驗矩陣，并基于最大公約數(shù)(GCD)定理聯(lián)合設(shè)計該矩陣以消除其所有圍長為4, 6(girth-4, girth-6)的短環(huán)。理論分析和仿真結(jié)果表明，在同等條件下該系統(tǒng)的誤碼率(BER)性能優(yōu)于相應(yīng)的點對點系統(tǒng)。仿真結(jié)果還表明，與采用顯式算法構(gòu)造QC-LDPC碼或一般構(gòu)造QC-LDPC碼的協(xié)作系統(tǒng)相比，采用聯(lián)合設(shè)計QC-LDPC碼的系統(tǒng)均可獲得更高的編碼增益。
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關(guān)鍵詞:
- 準循環(huán)低密度奇偶校驗碼 /
- 編碼協(xié)作 /
- 聯(lián)合校驗矩陣 /
- 最大公約數(shù)定理
Abstract: To solve the problems of high encoding complexity and long encoding delay in the multi-source multi-relay Low Density Parity Check (LDPC) coded cooperative system, a special kind of structured LDPC codes—Quasi-Cyclic LDPC (QC-LDPC) codes based on generator matrix is proposed, which combines the characteristics of QC-LDPC codes and Generator-matrix-based LDPC (G-LDPC) codes. It can perform completely parallel encoding, which greatly reduces the encoding complexity and delay at the relays. Based on this, a joint parity check matrix corresponding to the QC-LDPC codes adopted by the sources and relays is deduced, and the matrix is further jointly designed based on the Greatest Common Divisor (GCD) theorem to eliminate all cycles of girth-4 and girth-6. Theoretical analysis and simulation results show that under the same conditions, the Bit Error Rate (BER) performance of the proposed system is better than that of the corresponding point-to-point system. The simulation results also show that the cooperative system with jointly designed QC-LDPC codes can obtain a higher coding gain than the system with explicitly constructed QC-LDPC codes or generally constructed QC-LDPC codes. -
表 1 雙信源雙中繼編碼協(xié)作及對應(yīng)點對點系統(tǒng)所采用的QC-LDPC碼
信源節(jié)點所采用的QC-LDPC碼 中繼節(jié)點所采用的QC-LDPC碼 雙信源雙中繼系統(tǒng) $ {{\text{H}}_{{S_{1}}}} = {{\text{H}}_{1(1100 \times 2200)}} $ $ {{\text{H}}_{{R_{1}}}} = [ {{{\text{A}}_{1(1100 \times 2200)}}}\quad {{{\text{B}}_{1(1100 \times 2200)}}}\quad {\text{I}}_{(1100 \times 1100)}]$ ${{\text{H}}_{{S_{2}}}} = {{\text{H}}_{2(1100 \times 2200)}}$ $ {{\text{H}}_{{R_{2}}}} = [ {{{\text{A}}_{2(1100 \times 2200)}}}\quad {{{\text{B}}_{2(1100 \times 2200)}}}\quad {\text{I}}_{(1100 \times 1100)}] $ Rate=1/2 Rate=4/5 點對點系統(tǒng) ${{\text{H}}_S} = {{\text{H}}_{(2200 \times 6600)}}$
Rate=1/3\ 
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表 2 不同信源節(jié)點、中繼節(jié)點數(shù)目情況下編碼協(xié)作系統(tǒng)所采用的QC-LDPC碼
信源節(jié)點所采用的QC-LDPC碼 中繼節(jié)點所采用的QC-LDPC碼 雙信源雙中繼 $ {{\text{H}}_{{S_{1}}}} = {{\text{H}}_{1(1100 \times 2200)}} $ $ { {\text{H} }_{ {R_{1} } } } = [\begin{array}{*{20}{c} } { { {\text{A} }_{1(1100 \times 2200)} } } & { { {\text{B} }_{1(1100 \times 2200)} } } & {\text{I} }_{(1100 \times 1100)} \end{array}] $ $ {{\text{H}}_{{S_{2}}}} = {{\text{H}}_{2(1100 \times 2200)}} $ $ { {\text{H} }_{ {R_{2} } } } = [\begin{array}{*{20}{c} } { { {\text{A} }_{2(1100 \times 2200)} } } & { { {\text{B} }_{2(1100 \times 2200)} } } & {\text{I}_{(1100 \times 1100)} } \end{array} ]$ Rate=1/2 Rate=4/5 雙信源單中繼 $ {{\text{H}}_{{S_{1}}}} = {{\text{H}}_{1(1100 \times 2200)}} $ ${ {\text{H} }_R} = [\begin{array}{*{20}{c} } { { {\text{A} }_{(1100 \times 2200)} } } & { { {\text{B} }_{(1100 \times 2200)} } } & {{\text{I}}_{(1100 \times 1100)} } \end{array} ]$ $ {{\text{H}}_{{S_{2}}}} = {{\text{H}}_{2(1100 \times 2200)}} $ Rate=1/2 Rate=4/5 單信源雙中繼 ${{\text{H}}_S} = {{\text{H}}_{1(1100 \times 2200)}}$ $\begin{gathered} {{\text{H}}_{{R_{1}}}} = [\begin{array}{*{20}{c}} {{{\text{A}}_{1(1100 \times 2200)}}}&{{{\text{I}}_{(1100 \times 1100)}}} \end{array}] \\ {{\text{H}}_{{R_{2}}}} = [\begin{array}{*{20}{c}} {{{\text{A}}_{2(1100 \times 2200)}}}&{{{\text{I}}_{(1100 \times 1100)}}} \end{array}] \\ \end{gathered} $ Rate=1/2 Rate=2/3
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表 3 采用一般構(gòu)造QC-LDPC碼的協(xié)作系統(tǒng)各節(jié)點所采用的碼字
信源節(jié)點所采用的QC-LDPC碼 中繼節(jié)點所采用的QC-LDPC碼 雙信源雙中繼 ${d_{\rm v}} = 2$, ${d_{\rm c}} = 4$
B=550${d_{\rm v}} = 2$, ${d_{\rm c}} = 10$
B=550注：dv指每列“1”的個數(shù)，dc指每行“1”的個數(shù)
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表 4 采用顯式構(gòu)造QC-LDPC碼的協(xié)作系統(tǒng)所采用的碼字
信源節(jié)點所采用的QC-LDPC碼 中繼節(jié)點所采用的QC-LDPC碼 雙信源雙中繼 ${d_{\rm v}} = 2$, ${d_{\rm c}} = 3$
B=730${d_{\rm v}} = 2$, ${d_{\rm c}} = 8$
B=730
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