Error Control Coding - Digital Communication: Principles and System Modelling - page 187

9.3 Linear Block Code

In FEC (Forward Error Correction) method the channel encoder automatically adds
digits to the message that can be checked in the receiver side to find out errors and
correct it. The message with the additional digits is now called code. There are two
categories of this code:

1. Block Code
2. Convolutional Code

The continuous message from the source is divided into segments of n number
of bits. These segments are called blocks. The channel encoder then adds another k
bits to the blocks to form the codes. These k check bits are derived from the message
bits and are added to them. The ( n

k ) bits of the encoder output are called code
word. In the coding techniques where the message bits appear at the beginning of
the code word are called Systematic Codes (Fig. 9.2 )

+

Message blocks Code blocks

Fig. 9.2 Block code format

Channel
encoder

Check bits

Message

Message
n bits

( n +1) Bits

If sum of any two code words gives another code word of a block code then the
block code is said to be linear, i.e. Linear Block Code.

c i + c j = c k

where c i, c j, c k are code words of a block code.

9.3.1 Coding Technique Using Generator Matrix

In systematic linear block code, the code word is the information bits followed by
the check bits. These check bits are generated from the message bits according to
some predefined rule. Let us consider a systematic linear block code with k no. of
message bits and n

− k no. of check bits. So the code word is c j where j = 1, 2, 3 ... ., n.

Now for j d j where d j is the message bit. The check bits are calculated

using the following rule:

= 1tok,c j =