Cyclic code codecs construction principles research

LABORATORY WORKS

Laboratory work 1

Cyclic code codecs construction principles research

Objective: To calculate the optimal parameters of the cyclic code using the formula of the relative information transfer rate in a discrete channel. To build a structural diagram of a cyclic code codecs.

Laboratory emulator:

After opening the file “ÖÊ English.exe” you can see interface like fig. 3.1.

Figure 3.1 – Interface of laboratory work

For the calculation of a cyclic code parameters enter the input data from the table 3.1 in the group “Code calculation parameters”:

- modulation rate B, baud;

- error probability in the discrete channel p_{er};

- the distance between the transmitter and receiver L, km;

- the minimal code distance for the cyclic code d_{0};

- bursts factor of errors in the discrete channel α;

- undetected errors probability Đ_{un.er};

- the signal propagation velocity V = 280000 km/s.

Table 3.1 – Initial data for calculating parameters of cyclic code

Initial data

Number of brigade

Modulation rate Â, baud

9 600

64 000

14 400

28 800

33 600

31 000

12 200

9 600

For each person:
Error probability P_{er}

5·10^{-3}
3·10^{-3}
4·10^{-4}
2·10^{-4}

5·10^{-3}
3·10^{-3}
6·10^{-4}
2·10^{-4}

2·10^{-3}
3·10^{-3}
4·10^{-4}
5·10^{-4}

7·10^{-3}
3·10^{-3}
8·10^{-4}
2·10^{-4}

5·10^{-3}
3·10^{-3}
4·10^{-4}
6·10^{-4}

2·10^{-3}
3·10^{-3}
7·10^{-4}
4·10^{-4}

5·10^{-3}
3·10^{-3}
4·10^{-4}
2·10^{-4}

5·10^{-3}
8·10^{-3}
4·10^{-4}
6·10^{-4}

Undetected errors probability, Đ_{und.er}

10^{-6}

2·10^{-6}

3·10^{-6}

2·10^{-6}

3·10^{-6}

4·10^{-6}

5·10^{-6}

6·10^{-6}

For each person:
The distance between the transmitter and receiver L, km

1 200
2 500

1 200
5 600

2 500
5 600

1 200
2 500
5 600

1 200
2 500
5 600

1 200
2 500

1 200
5 600

2 500
5 600

For each person:
Minimal code distance d_{0}

For each person:
bursts factor of errors α

0,35
0,44
0,52
0,64

0,35
0,44
0,52
0,72

0,35
0,44
0,64
0,72

0,35
0,52
0,64
0,72

0,44
0,52
0,64
0,72

0,35
0,44
0,52
0,64

0,35
0,44
0,52
0,72

0,35
0,44
0,64
0,72

The data for p_{er}, P_{un.er} and α enters into the text cells of emulator as a decimal comma. After entering the initial data press the button "Calculate". In the group "Calculated parameters" as a result of the calculation the optimum parameters of a cyclic code: n, k, r and the generator polynomial P(x) will appear, as it shown in fig. 3.2. Selection of optimum parameters means: choose a length of the codeword when relative information transfer rate is maximum, that is obvious from the diagram.

In the group "Powers of selected polynomials" a list of polynomials for calculated code is formed. You can select any polynomial or enter degrees of the polynomial to the text cell. Press the button "Coder" to build the structural diagram of the cyclic code coder. Coder built by rules, which were described in item 1.2.3. You can see this in fig. 3.2.

Figure 3.2 – Structural diagram of the cyclic code coder

After pressing the button "Decoder" the structural diagram of the cyclic code decoder will appear.

Laboratory task:

1. To run the program “ÖÊ English.exe”.

2. To enter initial data according to personal variant from the table 3.1 in the group “Code calculation parameters”.

3. To calculate optimum parameters of the cyclic code:

- build the graph R(n) and table with the values R(n);

- write down the optimum parameters of a cyclic code;

- select and write the generator polynomial for the calculated cyclic code.

4. To build a structural diagram of a cyclic code coder.

5. To build a structural diagram of a cyclic code decoder.

Home task:

1. To learn items 1.1 – 1.2 of this teaching manual.

2. To write down the answers to the general questions.

General questions:

1. Which classes do cyclic codes belong to?

2. Describe the main properties of the generator polynomial Đ(ơ) of the cyclic codes.

3. What is minimum code distance? How is it with the amount of detecting and correcting errors associated?

4. What is the redundancy of the code?

5. How is the length of the check part of the code combination with another parameters of cyclic code associated?

6. Describe the main parameters of cyclic codes.

7. How is the relative information transfer rate in the discrete channel with the bursts of errors calculated?

8. How is the amount of memory cells of the cyclic code codec determined?

9. How is the amount of adders modulo 2 of the cyclic code codec determined? Where are adders in the chart set?

10. Describe the work of the cyclic code coder.

11. Describe the work of the cyclic code syndrome decoder.

12. In what modes can the cyclic code decoders be used?

Protocol content:

1. Subject and objective.

2. Executed home task.

3. Initial data according to personal variant.

4. Calculated optimum parameters of the cyclic code.

5. Graph and diagrams according to laboratory task.

6. Conclusion about optimum criterion to choose the cyclic code.