Errors in Communication-Basic Data Communication Systems-Lecture Slides, Slides of Digital Systems Design

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Data can be corruptedduring transmission.

Some applications require that

errors be detected and corrected.

Note

INTRODUCTION

Let us first discuss some issues related, directly orindirectly, to error detection and correction. Topics discussed in this section: Types of ErrorsRedundancyDetection Versus CorrectionForward Error Correction Versus RetransmissionCodingModular Arithmetic

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

In modulo-N arithmetic, we use only theintegers in the range 0 to N

1, inclusive.

Note

Figure 10.

XORing of two single bits or two words

Figure 10.

Datawords and codewords in block coding

The 4B/5B block coding discussed in Chapter 4 is a goodexample of this type of coding. In this coding scheme,k = 4 and n = 5. As we saw, we have 2

k^

= 16 datawords

and

n^

=^

codewords.

We

saw

that

out

of

codewords are used for message transfer and the rest areeither used for other purposes or unused.

Example 10.

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