Linear block code, Lecture notes of Digital Communication Systems

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Linear Block Codes[1]

Manjunatha. P

[email protected]

Professor

Dept. of ECE

J.N.N. College of Engineering, Shimoga

January 20, 2014

Overview

1 Generator and Parity check Matrices

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

4 Minimum Distance Considerations

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

4 Minimum Distance Considerations

5 Error detecting and Error correcting capabilities

6 Standard array and Syndrome decoding

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

4 Minimum Distance Considerations

5 Error detecting and Error correcting capabilities

6 Standard array and Syndrome decoding

7 Decoding circuits

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

4 Minimum Distance Considerations

5 Error detecting and Error correcting capabilities

6 Standard array and Syndrome decoding

7 Decoding circuits

8 Hamming Codes

9 Reed Muller codes

Overview

1 Generator and Parity check Matrices

2 Encoding circuits

3 Syndrome and Error Detection

4 Minimum Distance Considerations

5 Error detecting and Error correcting capabilities

6 Standard array and Syndrome decoding

7 Decoding circuits

8 Hamming Codes

9 Reed Muller codes

10 The (24, 12) Golay code

Introduction to Linear Block Codes Linear Block Codes

Introduction to Linear Block Codes

Introduction to Linear Block Codes Linear Block Codes

Transmission through noisy channel.

Introduction to Linear Block Codes Linear Block Codes

Transmission through noisy channel.

Transmission errors can occur, 1’s become 0’s and 0’s become 1’s.

To correct the errors, some redundancy bits are added to the

information sequence, at the receiver the correlation is exploited to

locate transmission errors.

Introduction to Linear Block Codes Linear Block Codes

Transmission through noisy channel.

Transmission errors can occur, 1’s become 0’s and 0’s become 1’s.

To correct the errors, some redundancy bits are added to the

information sequence, at the receiver the correlation is exploited to

locate transmission errors.

Here, only binary transmission is considered.

Introduction to Linear Block Codes Linear Block Codes

Type of Errors

Introduction to Linear Block Codes Linear Block Codes

Type of Errors

Single-bit error