Error Detection and Correction-Basic Data Communication Systems-Lecture Slides, Slides of Digital Systems Design

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Error Detection

and

Correction

Data can be corruptedduring transmission.

Some applications require that

errors be detected and corrected.

Note

Figure 10.

Single-bit error

A burst error means that 2 or more bits

in the data unit have changed.

Note

Note To detect or correct errors, we need tosend extra (redundant) bits with data.

Figure 10.

The structure of encoder and decoder

BLOCK CODING

In block coding, we divide our message into blocks,each of k bits, called datawords. We add r redundantbits to each block to make the length n = k + r. Theresulting n-bit blocks are called codewords.

Figure 10.

Datawords and codewords in block coding

Let us assume that k = 2 and n = 3. Table 10.1 shows the

list of datawords and codewords. Later, we will seehow to derive a codeword from a dataword. Assume the sender encodes the dataword 01 as 011 andsends it to the receiver. Consider the following cases:1. The receiver receives 011. It is a valid codeword. The

receiver extracts the dataword 01 from it.

Example 10.

2. The codeword is corrupted during transmission, and

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

3. The codeword is corrupted during transmission, and

000 is received. This is a valid codeword. The receiverincorrectly extracts the dataword 00. Two corruptedbits have made the error undetectable.

Example 10.2 (continued)

An error-detecting code can detect

only the types of errors for which it isdesigned; other types of errors may

remain undetected.

Note

Figure 10.

Structure of encoder and decoder in error correction

Comparing

the

received

codeword

with

the

first

codeword

in

the

table

versus

the

receiver decides that the first codeword is not the onethat was sent because there are two different bits.

2. By the same reasoning, the original codeword cannot

be the third or fourth one in the table.

3. The original codeword must be the second one in the

table because this is the only one that differs from thereceived

codeword

by

bit.

The

receiver

replaces

01001 with 01011 and consults the table to find thedataword 01.

Example 10.3 (continued)

Table 10.

A code for error correction (Example 10.3)