Digital Communications 1

3Source Coding for Non-disturbance Channels

3.1. Introduction

The purpose of source coding for non-disturbance channels is:

• – to transcribe the symbols of the source in the form of a sequence of letters taken from a predefined alphabet, making it possible to easily elaborate the signal that will carry the information, or to easily handle this information automatically. For this, different codes for information representation are used;
• – to minimize redundancy of the source;
• – to generate maximum mutual information: a statistical adaptation of the source to the channel.

We will now study the performance of some important codes.

3.2. Interest of binary codes

To show the interest of binary codes, we will take the example of coding a message in French. We can consider the following solutions:

• – number every word in the dictionary, i.e. in number N and then assign one amplitude out of N of a signal to each word;
• – assign one amplitude out of 27 of a signal to each letter of the alphabet (26 + 1);
• – use five binary digits to encode numbers from 0 to 31, each of which represents a letter of the alphabet. In this case, it is sufficient to use a two-level signal, which is easily achievable, but at the cost of a longer decoding time in reception.

3.3. Single decoding codes

Let us take a discrete memoryless source which provides symbols taken on a set [S] of symbols s called the source alphabet:

[S] = [s₁₍ s₂, ..., s_N]

Whose probabilities of use by the source are:

[P] = [p(