# 3.2.4.13.2. 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.

## 3.2.4.13.2.1. --dec-sub-cw-size, -N¶

Type

integer

Examples

--dec-sub-cw-size 1

Set the codeword size $$N$$.

## 3.2.4.13.2.2. --dec-sub-info-bits, -K¶

Type

integer

Examples

--dec-sub-info-bits 1

Set the number of information bits $$K$$.

## 3.2.4.13.2.3. --dec-type, -D¶

Type

text

Allowed values

CHASE CP ML

Default

CP

Examples

--dec-type CP

Select the decoder algorithm.

This algorithm will 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 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 $$W = F - a . R$$

## 3.2.4.13.2.4. --dec-implem¶

Type

text

Allowed values

STD

Default

STD

Examples

--dec-implem STD

Select the implementation of the decoder algorithm.

Description of the allowed values:

Value

Description

STD

A standard implementation

## 3.2.4.13.2.5. --dec-ite, -i¶

Type

integer

Default

4

Examples

--dec-ite 8

Set the number of iterations in the turbo decoding process.

## 3.2.4.13.2.6. --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.

## 3.2.4.13.2.7. --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.

## 3.2.4.13.2.8. --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.

## 3.2.4.13.2.9. --dec-p¶

Type

integer

Default

2

Examples

--dec-p 1

Set the number of least reliable positions.

## 3.2.4.13.2.10. --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.

## 3.2.4.13.2.11. --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 $$a, b, c, d, e$$.

See the --dec-type, -D parameter.

## 3.2.4.13.2.12. --dec-sub-type, -D¶

Please refer to the BCH --dec-type, -D parameter.

## 3.2.4.13.2.13. --dec-sub-corr-pow, -T¶

Please refer to the BCH --dec-corr-pow, -T parameter.

## 3.2.4.13.2.14. --dec-sub-implem¶

Please refer to the BCH --dec-implem parameter.

## 3.2.4.13.2.15. References¶

Trbp-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.