Principles of DVC - Distributed Multiple Description Coding - page 39

m P

D m; S k1 D m 0 ;R k1 ;R k ;R kC1 / Pr .d k D 1; S k

1

m 0

ƒ 1 .d k / D log m m 0

D m; S k1 D m 0 ;R k1
1

;R k ;R kC1 / Pr .d k D 0; S k

m m 0

Pr .R kC1 =S k D m/ Pr .S k1 D m 0 =R k1

1

/

D log m P

Pr .R kC1 =S k D m/ Pr .S k1 D m 0 =R k1

1

/

m 0

D m; R k =S k1 D m 0 / Pr .d k D 1; S k

Pr .d k D 0; S k D m; R k =S k1 D m 0 /

(3.8)

In order to calculate log-likelihood ratio of ( 3.8 ), we introduce the following
probability functions:

D m=R 1 /

˛ k .m/ D Pr .S k (3.9)

Pr .R k C 1 =S k D m/
Pr .R kC1 =R 1 /

ˇ k .m/ D (3.10)

i .R k ;m 0 ;m/ D D m;R k =S k1 D m 0 /

Pr .d k D i;S k (3.11)

Then

m m 0

1 .R k ;m 0 ;m/˛ k1 .m 0 /ˇ k .m/

ƒ 1 .d k / D m P (3.12)

log

0 .R k ;m 0 ;m/˛ k1 .m 0 /ˇ k .m/

m 0

Here, the probability functions ˛ k .m/ and ˇ k .m/ can be obtained by conducting
recursive computation for i .R k ;m 0 ;m/ .

3.3.3.2 The Conclusion of Turbo Decoding Steps

Step 1: Initialization, initialize ˛ and ˇ ; the prior information L e2;k of DEC1 should
be initialized to 0.

1SD 0
0S¤ 0

˛ 0 .S / D

(3.13)

1SD 0
0S¤ 0

ˇ k .S / D (3.14)

Step 2: For each observation R k

D .x k ;y 1;k ;L e2;k /