3.2.4.12.2. TPC Decoder parameters

The TPC decoder first decodes columns once with the Chase-Pyndiah 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 Chase-Pyndiah 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 Chase-Pyndiah decoder computed on \(R_{i}^r\).

Parameter \(alpha\) is set with the argument --dec-alpha.

3.2.4.12.2.1. --dec-type, -D

Type:text
Allowed values:CHASE CP ML
Default:CP
Examples:--dec-type CP

Select the algorithm to decode each column and row of the TPC.

Description of the allowed values:

Value Description
CP Decode with the Chase-Pyndiah algorithm of the TPC
CHASE See the common --dec-type, -D parameter.
ML See the common --dec-type, -D parameter.

The CP algorithm is the implementation of [Pyn98] 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 --dec-p) least reliable positions from \(R\) to get a metric set \(P\) of \(p\) elements.
    • Create \(t\) (set with --dec-t) test vectors from test patterns.
    • Hard decode with the sub-decoder to get the competitors with good syndrome set \(C\).
    • Remove competitors from \(C\) to keep \(c\) of them (set with --dec-c).
    • 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 --dec-cp-coef

    • 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 --dec-beta 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 \(W = F - a . R\)

3.2.4.12.2.2. --dec-implem

Type:text
Allowed values:STD
Default:STD
Examples:--dec-implem STD

Select the implementation of the algorithm to decode.

Description of the allowed values:

Value Description
STD A standard implementation

3.2.4.12.2.3. --dec-ite, -i

Type:integer
Default:4
Examples:--dec-ite 8

Set the number of iterations in the turbo.

3.2.4.12.2.4. --dec-alpha

Type:list of real numbers
Default:all at 0.5
Examples:--dec-alpha "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 half-iterations. Conversely, if there are too many, the surplus is truncated.

3.2.4.12.2.5. --dec-beta

Type:list of real numbers
Examples:--dec-beta "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 half-iterations. Conversely, if there are too many, the surplus is truncated.

If not given, then beta is dynamically computed as described in --dec-type, -D.

3.2.4.12.2.6. --dec-c

Type:integer
Default:0
Examples:--dec-c 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.

3.2.4.12.2.7. --dec-p

Type:integer
Default:2
Examples:--dec-p 1

Set the number of least reliable positions.

3.2.4.12.2.8. --dec-t

Type:integer
Default:0
Examples:--dec-t 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.

3.2.4.12.2.9. --dec-cp-coef

Type:list of real numbers
Default:"1,1,1,1,0"
Examples:--dec-cp-coef "0,0.25,0,0,3"

Give the 5 CP constant coefficients \(a, b, c, d, e\) as described in --dec-type, -D.

3.2.4.12.2.10. --dec-sub-type, -D

Type:text
Allowed values:ALGEBRAIC CHASE ML
Examples:--dec-sub-type ALGEBRAIC

Select the algorithm of the sub-decoder to decode each row and column.

Description of the allowed values:

Value Description
ALGEBRAIC See the BCH code --dec-type, -D.
CHASE See the common --dec-type, -D parameter.
ML See the common --dec-type, -D parameter.

3.2.4.12.2.11. --dec-sub-corr-pow, -T

Type:integer
Default:1
Examples:-T 2

Give the correction power of the BCH ALGEBRAIC sub-decoder.

3.2.4.12.2.12. --dec-sub-implem

Type:text
Allowed values:FAST GENIUS NAIVE STD
Examples:--dec-sub-implem FAST

Select the implementation of the algorithm of the sub-decoder.

Description of the allowed values:

Value Description
NAIVE See the common --dec-implem parameter.
STD See the common --dec-implem parameter, and the BCH code --dec-implem parameter.
FAST See the BCH code --dec-implem parameter.
GENIUS See the BCH code --dec-implem parameter.

3.2.4.12.2.13. --dec-sub-flips

Type:integer
Examples:--dec-sub-flips 1

Set the maximum number of flips in the CHASE sub-decoder.

3.2.4.12.2.14. --dec-sub-hamming

Enable the computation of the Hamming distance instead of the Euclidean distance in the ML/CHASE sub-decoders.

3.2.4.12.2.15. --dec-sub-cw-size, -N Required

Type:integer
Examples:--dec-sub-cw-size 1

The codeword size.

3.2.4.12.2.16. --dec-sub-info-bits, -K Required

Type:integer
Examples:--dec-sub-info-bits 1

Useful number of bit transmitted (information bits).

3.2.4.12.2.17. References

[Pyn98]R.M. Pyndiah. Near-optimum decoding of product codes: block turbo codes. IEEE Transactions on Communications (TCOM), 46(8):1003–1010, August 1998. doi:10.1109/26.705396.