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Chapter 10

Error Detection

and

Correction

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Data can be corrupted

during transmission.

Some applications require that

errors be detected and corrected.

Note

In a single-bit error, only 1 bit in the data

unit has changed.

Note

Figure 10.1 Single-bit error

• Figure 10.2 Burst error of length

To detect or correct errors, we need to

send extra (redundant) bits with data.

Note

In this book, we concentrate on block

codes; we leave convolution codes

to advanced texts.

Note

In modulo-N arithmetic, we use only the

integers in the range 0 to N −1,

inclusive.

Note

10-2 BLOCK CODING

10-2 BLOCK CODING

In block coding, we divide our message into blocks,

In block coding, we divide our message into blocks,

each of k bits, called

each of k bits, called datawords

datawords

. We add r redundant . We add r redundant

bits to each block to make the length n = k + r. The

bits to each block to make the length n = k + r. The

resulting n-bit blocks are called

resulting n-bit blocks are called codewords

codewords .

Error Detection

Error Correction

Hamming Distance

Minimum Hamming Distance

Topics discussed in this section:

Topics discussed in this section:

Figure 10.5 Datawords and codewords in block coding

Error Detection



Enough redundancy is added to

detect an error.



The receiver knows an error

occurred but does not know which

bit(s) is(are) in error.



Has less overhead than error

correction.

Figure 10.6 Process of error detection in block coding

2. The codeword is corrupted during transmission, and

111 is received. This is not a valid codeword and is

discarded.

3. The codeword is corrupted during transmission, and

000 is received. This is a valid codeword. The receiver

incorrectly extracts the dataword 00. Two corrupted

bits have made the error undetectable.

Example 10.2 (continued)

Table 10.1 A code for error detection (Example 10.2)