已知 [tex=6.357x1.214]4VWP+cE0BWrE7vbyeKcy1A==[/tex]的卷积码,其基本生成矩阵为[tex=5.857x1.357]QGBs/dZvxxWlpvFgRdmpiQ==[/tex]。试求该卷积码的生成矩阵[tex=0.929x1.0]rGq0+wwusEFO0LgjMJZJMvpknGyDqi+aORVwkF+3ikY=[/tex]和监督矩阵[tex=1.0x1.0]5cCYlc8KT4YbU5w753RaBuepE+1r6xIU/VfSPN0Fj+0=[/tex] 。

2022-06-05

已知 [tex=6.357x1.214]4VWP+cE0BWrE7vbyeKcy1A==[/tex]的卷积码,其基本生成矩阵为[tex=5.857x1.357]QGBs/dZvxxWlpvFgRdmpiQ==[/tex]。试求该卷积码的生成矩阵[tex=0.929x1.0]rGq0+wwusEFO0LgjMJZJMvpknGyDqi+aORVwkF+3ikY=[/tex]和监督矩阵[tex=1.0x1.0]5cCYlc8KT4YbU5w753RaBuepE+1r6xIU/VfSPN0Fj+0=[/tex] 。

答案：

解 其截短生成矩阵为[tex=19.357x5.786]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[/tex]式中[tex=0.786x1.214]2sF8NlOj2LhbkgC8CXSnTaWNT1PopUCllcMuaNpydWM=[/tex] 为一阶单位方阵, [tex=0.857x1.214]CvzOKCj+yanDEIDAQCVx3A==[/tex] 为[tex=7.429x1.357]nGnKUAeF1B1tm0G0jCo42vucsvt6+tJyg9u9kSiYALA=[/tex] 阶矩阵,即[tex=10.571x1.214]Gxx8wKxcBsK8QD975y+9Q/dtyv8m4Uq1Ozjpc7IkP1Usdd/zRQrDxhzYKWk4B6UD[/tex] 因为[tex=3.0x1.5]PnmZYskxzGW8F1XgGw/uKLCyMN2ZGV0+bkdzH3U1mKw=[/tex],对于一阶矩阵来说,转置即其自身不变,所以由《通信原理(第 7 版)》教材中式[tex=3.857x1.357]wI9+1T3wWD49KYZltgHV+g==[/tex]可得[tex=42.643x6.929]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[/tex]由上面求出的 [tex=1.286x1.214]BZQ81Voqzw8rg9kH0zwBfTO8WYUz5IvaUPFWZ3zgfmU=[/tex]和 [tex=1.357x1.214]AL900Jm8Gi4f0NHl3km9fjbMbwQpD7exR6XxNar8nfU=[/tex], 很容易写出 [tex=0.929x1.0]rGq0+wwusEFO0LgjMJZJMvpknGyDqi+aORVwkF+3ikY=[/tex]和[tex=1.0x1.0]5cCYlc8KT4YbU5w753RaBuepE+1r6xIU/VfSPN0Fj+0=[/tex] (略)。

举一反三

内容

0
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1
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2
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3
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4
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