卷积码可以用多种不同的方法来描述引言中介绍三种方法.ppt

10. Convolutional codes For this figure, we have A(x) = x 5 / (1 – 2x) = x 5 +2x 6 + 4 x 7 + … + 2 ix 5 + i + … AB A B AB A B A+B B C A D D BC A B C AB/(1 – C) Figure A more elaborately labeled version Complete path enumerator For CC1, the complete path enumerator turns out as Figure Some trellis path Figure A depth 0 error event Figure Some depth j error events * 第十章 卷积码 10.1 Introduction 引言 Convolutional codes can be studied from many different points of view. Here we present three approaches, which we have called the polynomial matrix approach, the scalar matrix approach, and the shift-register approach. 卷积码可以用多种不同的方法来描述。引言中介绍三种方法：多项式矩阵表示法、标量矩阵表示法和移位寄存器表示法。 The polynomial matrix approach is the generator matrix for a (2, 1) CC, which we label CC 1. is the generator matrix for a (3, 2) CC, which we label CC 2. The memory : The constraint length : The rate : Example 10.1 In CC 1, the polynomial information I = (x 3 + x + 1) would be encoded into the polynomial codeword C = (x 5 + x 2 + x + 1, x 5 + x?4 + 1). Example 10.2 In CC 2, the polynomial information I = (x 2 + x，x 3 + 1) would be encoded into the polynomial codeword C = (x 2 + x, x 3 + 1, x 4 + x?3 ). The scalar matrix approach C = (C00, C10, …, Cn – 1,0, C01, Cn – 1,1, …) The scalar generator matrix of a CC with polynomial generator matrix given by Eq. above. (shaded area = all 0’s) Example 10.3 The polynomial generator matrix for CC1, expanded as in Eq. above, is: Hence, the scalar generator matrix for CC 1 is: The scalar information corresponding to the polynomial information I=(x3+x+1) is (1101)[not (1011)] and the scalar codeword corresponding to the polynomial codeword C=(x5+x2+x+1, x5+x4+1) is (111010000111). Example 10.4 The polynomial generator matrix for CC2, expanded as in Eq. above, is: The scalar information corresponding to the polynomial information I =(x2+x, x3+1) is and the scalar codeword corresponding to the polynomial codeword C =(x 2+x, x3+1,