3.2.4.13.2. TPC Decoder parameters¶
The TPC decoder first decodes columns once with the ChasePyndiah algorithm, then rows, and columns again then rows again and so on.
Let’s say \(C\) is the \(N \times N\) a priori matrix from the demodulator.
Let’s say \(R_{i+1}^c\) is the \(N \times N\) a posteriori matrix computed by this decoder after the \(i^{th}\) iteration on the columns. Initially, \(R_0^c = C\).
Let’s say \(R_{i+1}^r\) is the \(N \times N\) a posteriori matrix computed by this decoder after the \(i^{th}\) iteration on the rows, with \(R_i^r = R_{i+1}^c\).
The process of the columns for the \(i^{th}\) iteration gives:
\(R_{i+1}^c = alpha_{2i+0}.W_i^c + C\)
with \(W_i^c\) the extrinsic from the ChasePyndiah decoder computed on \(R_{i}^c\).
The process of the rows for the \(i^{th}\) iteration gives:
\(R_{i+1}^r = alpha_{2i+1}.W_i^r + C\)
with \(W_i^r\) the extrinsic from the ChasePyndiah decoder computed on \(R_{i}^r\).
Parameter \(alpha\) is set with the argument decalpha.
3.2.4.13.2.1. decsubcwsize, N
¶
 Type
integer
 Examples
decsubcwsize 1
Set the codeword size \(N\).
3.2.4.13.2.2. decsubinfobits, K
¶
 Type
integer
 Examples
decsubinfobits 1
Set the number of information bits \(K\).
3.2.4.13.2.3. dectype, D
¶
 Type
text
 Allowed values
CHASE
CP
ML
 Default
CP
 Examples
dectype CP
Select the decoder algorithm.
This algorithm will decode each column and row of the TPC.
Description of the allowed values:
Value 
Description 


Decode with the ChasePyndiah algorithm of the TPC 

See the common dectype, D parameter. 

See the common dectype, D parameter. 
The CP
algorithm is the implementation of
[TrbpPyn98] but in a more generic way in order to let the user
chose its configuration:
 Chase step: find the more reliable codeword \(D\):
Take hard decision \(H\) on input \(R\).
Select the \(p\) (set with decp) least reliable positions from \(R\) to get a metric set \(P\) of \(p\) elements.
Create \(t\) (set with dect) test vectors from test patterns.
Hard decode with the subdecoder to get the competitors with good syndrome set \(C\).
Remove competitors from \(C\) to keep \(c\) of them (set with decc).
Compute the metrics \(C_m\) (euclidean distance) of each competitor compared to \(H\).
Select the competitors with the smallest metric to get the decided word \(D\) with a metric \(D_m\) and where \(D_j = \begin{cases} +1 & \text{when } H_j = 0 \\ 1 & \text{when } H_j = 1 \end{cases}\)
 Pyndiah step: compute reliabilities of each bit of \(D\)
\(a, b, c, d\) and \(e\) are simulation constants changeable by the user with deccpcoef
Compute the reliability \(F\) of \(D\) for each bit \(D_j\) of the word:
Find \(C^s\) the competitor with the smallest metric \(C_m\) that have \(C_j^s \neq D_j\).
when \(C^s\) exists:
\(F_j = b . D_j . [C_m  D_m]\)
when \(C^s\) does not exist and if decbeta is given:
\(F_j = D_j . beta\)
else:
\(F_j = D_j . \left[ \displaystyle\sum_{i=0}^{e} P_i  c . D_m + d . R_j \right]\) where \(P\) is considered sorted, \(0 < e < p\), and when \(e == 0 \implies e = p  1\).
Compute extrinsic \(W = F  a . R\)
3.2.4.13.2.4. decimplem
¶
 Type
text
 Allowed values
STD
 Default
STD
 Examples
decimplem STD
Select the implementation of the decoder algorithm.
Description of the allowed values:
Value 
Description 


A standard implementation 
3.2.4.13.2.5. decite, i
¶
 Type
integer
 Default
4
 Examples
decite 8
Set the number of iterations in the turbo decoding process.
3.2.4.13.2.6. decalpha
¶
 Type
list of real numbers
 Default
all at 0.5
 Examples
decalpha "0.1,0.1,0.2,0.25,0.3,0.35,.5,.5,1.2"
Give the weighting factor alpha, one by half iteration (so twice more than the number of iterations).
The first one is for the first columns process, the second for the first rows process, the third for the second columns process, the fourth for the second rows process, and so on.
If there are not enough values, then the last one given is automatically extended to the rest of the halfiterations. Conversely, if there are too many, the surplus is truncated.
3.2.4.13.2.7. decbeta
¶
 Type
list of real numbers
 Examples
decbeta "0.1,0.1,0.2,0.25,0.3,0.35,.5,.5,1.2"
Give the reliability factor beta, one by half iteration (so twice more than the number of iterations).
The first one is for the first columns process, the second for the first rows process, the third for the second columns process, the fourth for the second rows process, and so on.
If there are not enough values, then the last one given is automatically extended to the rest of the halfiterations. Conversely, if there are too many, the surplus is truncated.
If not given, then beta is dynamically computed as described in dectype, D.
3.2.4.13.2.8. decc
¶
 Type
integer
 Default
0
 Examples
decc 3
Set the number of competitors. A value of 0 means that the latter is set to the number of test vectors, 1 means only the decided word.
3.2.4.13.2.9. decp
¶
 Type
integer
 Default
2
 Examples
decp 1
Set the number of least reliable positions.
3.2.4.13.2.10. dect
¶
 Type
integer
 Default
0
 Examples
dect 1
Set the number of test vectors. A value of 0 means equal to \(2^p\) where \(p\) is the number of least reliable positions.
3.2.4.13.2.11. deccpcoef
¶
 Type
list of real numbers
 Default
"1,1,1,1,0"
 Examples
deccpcoef "0,0.25,0,0,3"
Give the 5 CP
constant coefficients \(a, b, c, d, e\).
See the dectype, D parameter.
3.2.4.13.2.12. decsubtype, D
¶
Please refer to the BCH dectype, D parameter.
3.2.4.13.2.13. decsubcorrpow, T
¶
Please refer to the BCH deccorrpow, T parameter.
3.2.4.13.2.14. decsubimplem
¶
Please refer to the BCH decimplem parameter.
3.2.4.13.2.15. References¶
 TrbpPyn98
R.M. Pyndiah. Nearoptimum decoding of product codes: block turbo codes. IEEE Transactions on Communications (TCOM), 46(8):1003–1010, August 1998. doi:10.1109/26.705396.