Decoding system for LDPC code concatenated with 4QAM-NR code
A decoding system for LDPC code concatenated with 4QAM-NR code in a DTMB system is a two-stage decoding system. An NR decoder performs a 4QAM-NR decoding to obtain hard decision information. Then, the so obtained hard decision information together with corresponding soft symbol and channel state information are sent to a log-likelihood ratio (LLR) device for further computing a log-likelihood ratio after an adder adds a correction term associated with the hard decision information to a computed log-likelihood ratio without the hard decision information. An LDPC decoder receives the LLR for decoding.
1. A decoding system for Low-density Parity-check codes (LDPC codes) concatenated with 4 Quadrature Amplitude Modulation Nordstrom-Robinson codes (4QAM-NR codes) in digital terrestrial multimedia broadcast (DTMB) system, comprising:
a channel estimator and equalizer, for receiving input signals y n to accordingly produce a plurality of estimation input signals Y k and corresponding channel estimation signals Ĉ k ;
a data partition device, connected to the channel estimator and equalizer, for performing a data partition on the estimation input signals Y k and the corresponding channel estimation signals Ĉ k to produce a plurality of partition estimation input signals Z 8×1 and corresponding partition channel estimation signals {tilde over (H)} 8×1 ;
an NR decoder, connected to the data partition device, for performing a decoding operation on the partition estimation input signals Z 8×1 and the corresponding partition channel estimation signals {tilde over (H)} 8×1 to produce a plurality of symbols {circumflex over (X)} 4×1 Z 8×1 and corresponding partial partition estimation input signals Z 4x1 and corresponding partition channel estimation signals {tilde over (H)} 4×1 ;
a time de-interleaver, connected to the NR decoder, for producing a plurality of time de-interleaved symbols {circumflex over (X)} d,k and corresponding time de-interleaved partition estimation input signals Z d,k and corresponding partition channel estimation signals {tilde over (H)} d,k based on the plurality of symbols {circumflex over (X)} 4×1 and the corresponding partial partition estimation input signals Z 4×1 and the corresponding partition channel estimation signals {tilde over (H)} 4×1 ;
a noise power estimator, for estimating a noise power and producing a noise variance σ 2 ;
a log-likelihood ratio (LLR) computation device, connected to the noise power estimator and the time de-interleaver, for computing and producing an LLR based on the plurality of time de-interleaved symbols {circumflex over (X)} d,k , the corresponding time de-interleaved partition estimation input signals Z d,k , the corresponding partition channel estimation signals {tilde over (H)} d,k and the noise variance σ 2 ; and
an LDPC decoder, connected to the LLR computation device, for producing a codeword based on the LLR;
wherein the channel estimator and equalizer comprises:
a channel estimator, for receiving the plurality of input signals y n and producing a plurality of estimation channel frequency responses (CFRs) Ĥ k and a plurality of estimation channel impulse responses (CIRs) Ĥ k ;
an equalizer, connected to the channel estimator, for producing a single-carrier input signal Y k SC based on the plurality of input signals y n and the plurality of estimation CIRs Ĥ k ;
a Fast Fourier Transform (FFT) device, for receiving the plurality of input signals y n to produce a plurality of estimation frequency input signals Y k ;
a phase rotation device, connected to the channel estimator and the FFT device, for producing the corresponding channel estimation signals Ĉ k and a multi-carrier input signal Y k MC based on the plurality of estimation CFRs Ĥ k and the plurality of estimation frequency input signals Y k ; and
a first multiplexer, connected to the equalizer and the phase rotation device, for selecting the single-carrier input signal Y k SC or the multi-carrier input signal Y k MC as the plurality of estimation input signals Y k based on a single-carrier/multi-carrier signal.
2. The decoding system as claimed in claim 1 , wherein the corresponding channel estimation signals Ĉ k are expressed as:
Ĉ k =|Ĥ k |,
where Ĥ k denotes the plurality of estimation CFRs, and the multi-carrier input signal Y k MC is expressed as:
Y k MC =Y k *e −j∠Ĥ k ,
where Y k denotes the plurality of estimation frequency input signals, and Ĥ k denotes the estimation CFRs.
3. The decoding system as claimed in claim 1 , wherein the NR decoder performs the decoding operation on the partition estimation input signals Z 8×1 and the corresponding partition channel estimation signals {tilde over (H)} 8×1 according to a minimum distance estimation.
4. The decoding system as claimed in claim 3 , wherein the NR decoder comprises:
a second multiplexer, for selecting the partition channel estimation signals {tilde over (H)} 8×1 or a unit of vectors I 8×1 based on the single-carrier/multi-carrier signal to produce a temporary channel estimation signal C 8×1 ;
a data block generator, for producing comparative data;
an NR encoder, connected to the data block generator, for performing an NR coding on the comparative data to produce an NR symbol;
a 4QAM mapper, connected to the NR encoder for mapping the NR symbol into a comparative symbol {circumflex over (X)} 8× ; and
a minimum distance searcher, connected to the data partition device, the second multiplexer and the 4QAM mapper, for producing a plurality of symbols {circumflex over (X)} 8×1 based on the comparative symbol {circumflex over (X)} 8×1 , the temporary channel estimation signal C 8×1 and the plurality of partition estimation input signals Z 8×1 .
5. The decoding system as claimed in claim 4 , wherein the minimum distance searcher is based on an equation as follows to select and produce the plurality of symbols {circumflex over (X)} 8×1 :
X
⋒
8
×
1
=
arg
Min
X
⋒
8
×
1
∑
i
=
1
8
Z
8
×
1
i
-
X
⋒
8
×
1
i
•C
8
×
1
i
2
,
where i denotes a symbol index, Z 8×1 i denotes an i-th component of the plurality of partition estimation input signals Z 8×1 , {circumflex over (X)} 8×1 i denotes an i-th component of the comparative symbol {circumflex over (X)} 8×1 , and C 8×1 i denotes an i-th component of the temporary channel estimation signal C 8×1 .
6. The decoding system as claimed in claim 5 , further comprising a data extractor, connected to the minimum distance searcher, the second multiplexer and the data partition device, for extracting data from the plurality of partition estimation input signals Z 8×1 , the temporary channel estimation signal C 8×1 and the comparative symbol {circumflex over (X)} 8×1 to produce the plurality of symbols {circumflex over (X)} 8×1 and the corresponding partial partition estimation input signals Z 4×1 and the corresponding partition channel estimation signals {tilde over (H)} 4×1 .
7. The decoding system as claimed in claim 1 , wherein the LLR computation device comprises:
an inverse device, connected to the noise power estimator, for performing an inverse transformation on the noise variance σ 2 to produce the inverse
1
σ
2
of the noise variance σ 2 ;
a square device, connected to the time de-interleaver, for performing a square operation on the corresponding time de-interleaved partition channel estimation signals {tilde over (H)} d,k of the time de-interleaver to produce a square ({tilde over (H)} d,k ) 2 of the corresponding time de-interleaved partition channel estimation signals {tilde over (H)} d,k ;
a first multiplier, connected to the inverse device and the square device, for multiplying the inverse
1
σ
2
by the square ({tilde over (H)} d,k ) 2 to produce a product η k =({tilde over (H)} d,k ) 2 /σ 2 ;
a plurality of function generators, connected to the first multiplier, for producing a predetermined value based on the product η k ;
a range decider, connected to the first multiplier, for producing a select signal based on the product η k ;
a component selector, connected to the time de-interleaver, for selecting real or imaginary components of the plurality of time de-interleaved symbols {circumflex over (X)} d,k to produce a component output {circumflex over (X)} d,k μ ;)
a sign device, connected to the component selector, for determining a sign of the component output {circumflex over (X)} d,k μ based on a function of sgn(•);
a selector, connected to the plurality of function generators and the range decider, for selecting one as an output G(θ k ) from the outputs of the plurality of function generators based on the select signal;
a second multiplier, connected to the sign device and the selector in order to multiply the output G(θ k ) by the component output {circumflex over (X)} d,k μ to produce a correction item ξ({circumflex over (X)} d,k μ );
an LLR calculator, connected to the time de-interleaver and the inverse device for producing a non-hard-decision-assisted LLR R b,m μ on the inverse
1
σ
2
,
the plurality of time de-interleaved symbols {circumflex over (X)} d,k , the corresponding time de-interleaved partition estimation input signals Z d,k and the corresponding time de-interleaved partition channel estimation signals {tilde over (H)} d,k ; and
an adder, connected to the second multiplier and the LLR calculator for adding the correction item ξ({circumflex over (X)} d,k μ ) in the non-hard-decision-assisted LLR R b,m μ to produce the LLR.
8. The decoding system as claimed in claim 7 , wherein the LLR LLR(b m μ ) is expressed as:
LLR
(
b
m
μ
)
=
log
Pr
[
b
m
μ
=
1
|
Z
d
,
k
μ
,
H
~
d
,
k
,
X
^
d
,
k
]
Pr
[
b
m
μ
=
0
|
Z
d
,
k
μ
,
H
~
d
,
k
,
X
^
d
,
k
]
=
R
b
,
m
μ
+
ξ
(
X
^
d
,
k
μ
)
,
where ξ({circumflex over (X)} d,k μ ) denotes the correction item, and R b,m μ denotes the non-hard-decision-assisted LLR which is expressed as:
,
R
b
,
m
μ
=
1
2
σ
2
{
Min
α
∈
S
μ
,
m
(
1
)
(
Z
d
,
k
μ
-
α
μ
*
H
~
d
,
k
)
2
-
Min
α
∈
S
μ
,
m
(
0
)
(
Z
d
,
k
μ
-
α
μ
*
H
~
d
,
k
)
2
}
where S μ,m (1) , S μ,m (0) indicate a set of partition constellation points.
9. The decoding system as claimed in claim 8 , wherein the correction item ξ({circumflex over (X)} d,k μ ) is expressed as:
ξ({circumflex over (X)} d,k μ )=sgn({circumflex over (X)} d,k μ )* G(θ k ),
where sgn(•) denotes a sign function,
G
(
η
k
)
=
log
{
1
-
π
2
[
2
Q
(
η
k
)
-
1
]
1
+
π
2
[
2
Q
(
η
k
)
-
1
]
}
,
η
k
=
(
H
~
d
,
k
)
2
/
σ
2
,
and
Q
(
x
)
=
1
2
π
∫
x
∞
ⅇ
-
t
2
/
2
ⅆ
t
.
10. A decoding system for Low-density Parity-check codes (LDPC codes) concatenated with 4 Quadrature Amplitude Modulation Nordstrom-Robinson codes (4QAM-NR codes) in digital terrestrial multimedia broadcast (DTMB) system, comprising:
a channel estimator and equalizer, for receiving input signals y n to accordingly produce a plurality of estimation input signals Y k and corresponding channel estimation signals Ĉ k ;
a data partition device, connected to the channel estimator and equalizer, for performing a data partition on the estimation input signals Y k and the corresponding channel estimation signals Ĉ k to produce a plurality of partition estimation input signals Z 8×1 and corresponding partition channel estimation signals {tilde over (H)} 8×1 ;
an NR decoder, connected to the data partition device, for performing a decoding operation on the plurality of partition estimation input signals Z 8×1 and the corresponding partition channel estimation signals {tilde over (H)} 8×1 to produce a plurality of symbols {circumflex over (X)} 4×1 and corresponding partial partition estimation input signals Z 4×1 and corresponding partition channel estimation signals {tilde over (H)} 4×1 ;
a time de-interleaver, connected to the NR decoder, for producing a plurality of time de-interleaved symbols {circumflex over (X)} d,k and corresponding time de-interleaved partition estimation input signals Z d,k and corresponding partition channel estimation signals {tilde over (H)} d,k based on the plurality of symbols {circumflex over (X)} 4×1 and the corresponding partial partition estimation input signals Z 4×1 and the corresponding partition channel estimation signals {tilde over (H)} 4×1 ;
a noise power estimator, for estimating a noise power and producing a noise variance σ 2R b,m μ ;
a log-likelihood ratio (LLR) computation device, connected to the noise power estimator and the time de-interleaver, for computing and producing an LLR based on the plurality of time de-interleaved symbols {circumflex over (X)} d,k , the corresponding time de-interleaved partition estimation input signals Z d,k , the corresponding partition channel estimation signals {tilde over (H)} d,k and the noise variance σ 2 ; and
an LDPC decoder, connected to the LLR computation device, for producing a codeword based on the LLR;
wherein the NR decoder performs the decoding operation on the plurality of partition estimation input signals Z 8×1 and the corresponding partition channel estimation signals {tilde over (H)} 8×1 according to a minimum distance estimation, and the NR decoder comprises:
a second multiplexer, for selecting the partition channel estimation signals {tilde over (H)} 8×1 or a unit of vectors I 8×1 based on a single-carrier/multi-carrier signal to produce a temporary channel estimation signal C 8×1 ;
a data block generator, for producing comparative data;
an NR encoder, connected to the data block generator, for performing an NR coding on the comparative data to produce an NR symbol;
a 4QAM mapper, connected to the NR encoder for mapping the NR symbol into a comparative symbol {circumflex over (X)} 8×1 ; and
a minimum distance searcher, connected to the data partition device, the second multiplexer and the 4QAM mapper, for producing a plurality of symbols {circumflex over (X)} 8×1 based on the comparative symbol {circumflex over (X)} 8×1 the temporary channel estimation signal C 8×1 and the plurality of partition estimation input signals Z 8×1 .