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96

ETSI ES 201 980 V4.1.2 (2017-04)

The overall code rate for each protection part for the HMsym is approximately:

RVSPP = R0

RSPP,all = (R1 + R2 ) / 2

7.3.1.3Partitioning of bitstream in HMmix

The bitstream of the SPP (ui) shall be partitioned into five streams (xRep,i , xImp,i ) . The bits of the higher protected part

shall be fed to the encoders on p = 0 to 2, then the bits of the lower protected part shall be fed to the encoders on p = 0 to 2. This results in:

(xIm

, xIm ,..., xIm

Im

, xRe , xRe ,K, xRe

Re

, xIm , xIm ,..., xIm

Im

 

, xRe , xRe

,K, xRe

Re

, xIm

, xIm

0,0

 

0,1

 

0,M

0,1

1

1,0

1,1

 

1,M1,1

1

1,0

1,1

1,M

1,1

 

1

2,0

2,1

 

 

2,M

2,1 1

2,0

2,1

xIm

Im , xIm

Im

,..., xIm

Im

Im

 

, xRe Re , xRe

Re

+1

,K, xRe

Re

+ M

 

Re

1

, xIm

Im , xIm Im

,..., xIm

Im

Im

0,M 0,1

0,M

0,1 +1

 

0,M 0,1 + M 0, 2 1

1,M1,1

 

1,M

1,1

 

1,M

1,1

1,2

1,M1,1

 

1,M1,1

+1

 

1,M

1,1

+ M1,1

xRe

Re

, xRe

Re

,K, xRe

Re

Re

 

, xIm

Im

, xIm

Im

+1

,..., xIm

Im

 

 

Im

) =

(u

0

,u ,Ku

L1 + L2 1

)

 

2,M 2,1

2,M 2,1

+1

 

2,M

2,1

+ M 2, 2

1 2,M

2,1

2,M

2,1

2,M

2,1 + M

2,1

1

 

1

 

 

 

The bits of the VSPP (u'i) shall be fed to the encoder for the real part on level p = 0:

,..., xIm Im ,

2,M 2,1 1

1,

(x0,0Re , x0,1Re ,, , xRe Re

) = (u

0'

,u1' ,

uL'

1 )

0,M 0, 2

1

 

 

VSPP

 

When using only one protection level (EEP) the elements with negative indexes shall not be taken into account.

The number of bits on each level p is calculated for the higher protected and lower protected parts for the real and imaginary component by:

M 0Re,1 = 0 , M 0Im,1 = N1R0Im

 

 

N

1

+ N

2

12

 

 

 

M Im

 

 

RX Im

N

2

12

M Re

= RX Re

 

 

 

 

 

 

= L

 

,

=

 

 

 

 

 

 

 

RY Re

 

RY Im

0,2

0

 

 

 

 

VSSP

 

0,2

 

 

 

0

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

M Re

= N RRe

 

and

M Im

= N RIm

 

for

p {1,2}

 

 

 

 

p,1

 

 

 

1

 

p

 

 

 

p,1

 

1

p

 

 

 

 

 

 

 

 

 

 

 

 

 

N

2

12

 

 

 

 

 

 

 

N

2

12

 

 

 

p {1,2}

M Rep,2 = RX Rep

 

 

 

 

 

 

 

and

M Imp,2

= RX Imp

 

 

 

 

 

 

for

 

 

 

 

Re

 

 

 

 

 

Im

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RYp

 

 

 

 

 

 

 

 

 

 

 

RYp

 

 

 

 

 

 

 

The total number of bits on each level p in the real and imaginary component results in:

M Rep = M Rep,1 + M Rep,2

and M Imp

= M Imp,1 + M Imp,2 for p {0,1,2}

 

From these formulas it can be derived that the input bitstreams (xRep,i )

and (xImp,i ) to the encoders C Rep

and C Imp

respectively have different lengths according to their code rate so that all the encoder output bitstreams

p {0,1,2} have

the same length.

 

 

 

 

 

 

 

The overall code rate for the HMmix schemes of each protection part is approximately:

 

 

 

 

R

= R Re

 

 

 

 

 

 

VSPP

0

 

 

 

R

SPP,all

= (R Im + R Re + R Im

+ R Re

+ R Im ) / 5

 

 

0

1

1

2

2

 

ETSI

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