卷积码的定义,编码和应用
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= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + … C = (11, 01, 11, 11, 00, 00, 00, …)
+ (00, 11, 01, 11, 11, 00, 00, …) + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
D2
ck1 ck
ck2
ck1 mk mk 2 mk 3
ck 2 mk mk 1 mk 2 mk 3
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck 编码约束度
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
卷积码框图：
1
M
1 → k0 k0
S/P
（ 串 / 并)
(n0 , k0 , m) n0
有记忆
n0 → 1
P/S
编编码码
（并 / 串)
1
C
Definition and application of convolutional codes
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
Definition and application of convolutional codes
1. 生成矩阵描述
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)
Definition and application of convolutional codes
Definition and application of convolutional codes
一、The basic concept of convolution code
Definition and application of convolutional codes
二、A description of the convolution code
mk
D0
D1
D2
ck ck2
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
D2
ck1 ck
ck2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck 编码约束度
mk+1 mk mk-1 mk+2 mk+1 mk
ck+1 编码约束长度
ck+2
n0(m+1)
Definition and application of convolutional codes
+
+
ck1
mk
D0
D1
ck
ck2 +
n0=2 k0=1 m=2 （ 2 ， 1 ， 2 ）卷积码 编码存储
Definition and application of convolutional codes
+
+
ck1
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + … CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …)
+ (00, 11, 01, 11, 11, 00, 00, …) + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
P/S
C
（串 / 并)
编码
（并 / 串)
Definition and application of convolutional codes
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
P/S
C
（串 / 并)
编码
（并 / 串)
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …)
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …)
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 +
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + … CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …)
+ (00, 11, 01, 11, 11, 00, 00, …) 生成矩阵
+ (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + …
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)
M = (1 1 1 0 0 …)
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
P/S
C
（串 / 并)
编码
（并 / 串)
卷积码框图：
1→ k
(n , k , m)
n →1
M 1每个编S/码P0 分组k0 不仅有0取记0决忆 于当n0 前单位P0 /S时间对1 应C的 k0
比特信息组（，串）而/ 并且与前 m编个码信息组有关（并。）/ 串
Definition and application of convolutional codes
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
Definition and application of convolutional codes
பைடு நூலகம்
基本生成矩阵
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + …
CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …) + (00, 11, 01, 11, 11, 00, 00, …) 生成矩阵 + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
+
+
ck1
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
+
+
mk
D0
D1
+ n0=2 k0=1
ck1 ck
ck2
Definition and application of convolutional codes
+
+
mk
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
+ n0=2 k0=1 m=2
ck1 ck
ck2
Definition and application of convolutional codes
+
+
mk
D0
D1
+
n0=2 k0=1 m=2 编码存储
ck1 ck
ck2
Definition and application of convolutional codes
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)
+ (00, 11, 01, 11, 11, 00, 00, …) + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
D2
ck1 ck
ck2
ck1 mk mk 2 mk 3
ck 2 mk mk 1 mk 2 mk 3
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck 编码约束度
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
卷积码框图：
1
M
1 → k0 k0
S/P
（ 串 / 并)
(n0 , k0 , m) n0
有记忆
n0 → 1
P/S
编编码码
（并 / 串)
1
C
Definition and application of convolutional codes
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
Definition and application of convolutional codes
1. 生成矩阵描述
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)
Definition and application of convolutional codes
Definition and application of convolutional codes
一、The basic concept of convolution code
Definition and application of convolutional codes
二、A description of the convolution code
mk
D0
D1
D2
ck ck2
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
mk
D0
D1
D2
ck1 ck
ck2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck 编码约束度
mk+1 mk mk-1 mk+2 mk+1 mk
ck+1 编码约束长度
ck+2
n0(m+1)
Definition and application of convolutional codes
+
+
ck1
mk
D0
D1
ck
ck2 +
n0=2 k0=1 m=2 （ 2 ， 1 ， 2 ）卷积码 编码存储
Definition and application of convolutional codes
+
+
ck1
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + … CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …)
+ (00, 11, 01, 11, 11, 00, 00, …) + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
P/S
C
（串 / 并)
编码
（并 / 串)
Definition and application of convolutional codes
分组码框图：
1
1→k k
(n, k ) n
n →1
1
M
S/P
无记忆
P/S
C
（串 / 并)
编码
（并 / 串)
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …)
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …)
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 +
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + … CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …)
+ (00, 11, 01, 11, 11, 00, 00, …) 生成矩阵
+ (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + …
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)
M = (1 1 1 0 0 …)
Definition and application of convolutional codes
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …) M = (1 1 1 0 0 …)
P/S
C
（串 / 并)
编码
（并 / 串)
卷积码框图：
1→ k
(n , k , m)
n →1
M 1每个编S/码P0 分组k0 不仅有0取记0决忆 于当n0 前单位P0 /S时间对1 应C的 k0
比特信息组（，串）而/ 并且与前 m编个码信息组有关（并。）/ 串
Definition and application of convolutional codes
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
ck ck 2 mk mk 2
ck2 ck (ck1, ck 2 )
+
Definition and application of convolutional codes
பைடு நூலகம்
基本生成矩阵
= (1 0 0 …) + (0 1 0 0 … ) + (0 0 1 0…) + …
CC=M(1G1, 01[,11111,0101..,.]00, 00, 00, …) + (00, 11, 01, 11, 11, 00, 00, …) 生成矩阵 + (00, 00, 11, 01, 11, 11, 00, …) + … = (11, 10, 01, 01, 00, 11, 00, … )
+
+
ck1
mk
D0
D1
ck
ck2 +
Definition and application of convolutional codes
+
+
mk
D0
D1
+ n0=2 k0=1
ck1 ck
ck2
Definition and application of convolutional codes
+
+
mk
ck2 ck (ck1, ck 2 )
+
mk mk-1 mk-2
ck
mk+1 mk mk-1
ck+1
mk+2 mk+1 mk
ck+2
Definition and application of convolutional codes
+
+
ck1 ck1 mk mk 1 mk 2
mk
D0
D1
+ n0=2 k0=1 m=2
ck1 ck
ck2
Definition and application of convolutional codes
+
+
mk
D0
D1
+
n0=2 k0=1 m=2 编码存储
ck1 ck
ck2
Definition and application of convolutional codes
Definition and application of convolutional codes
（ 2 ， 1 ， 3 ）卷积码
ck1
mk
D0
D1
D2
ck ck2
M = (m0, m1, m2, …) = (1 0 0 …) C = (c0, c1, c2, …) = (11, 01, 11, 11, 00, 00, 00 …)