Consider the following statements related to the source coding :

1. A conversion of the output of a discrete memoryless source (DMS) into a sequence of binary symbols is called source coding.

2. The source code efficiency (η) is defined as \(\rm η = \frac{L_{min}}{L}\), where L_min is the minimum possible value of L, and L is the average codeword length.

3. The code redundancy (γ) is defined as γ = 1 + η.

Which of the above statements are correct ?

Source coding:

The Code produced by a discrete memoryless source has to be efficiently represented, which is an important problem in communications. For this to happen, there are code words, which represent these source codes.

Hence, the conversion of the output of a discrete memoryless source (DMS) into a sequence of binary symbols is called source coding.

Source code efficiency:

The source code efficiency (η) is defined as \(\rm η = \frac{L_{min}}{L}\)

where Lmin is the minimum possible value of L, and L is the average codeword length.

The source encoder is considered efficient when  η=1

This source coding theorem is called a noiseless coding theorem as it establishes an error-free encoding. It is also called Shannon’s first theorem.

Code redundancy:

Code redundancy occurs when a character or group of characters in a code word can be partially or completely deduced from the remaining characters of the code word.

The relationship between code redundancy (γ) and source code efficiency (η) is:

γ = 1 - η

Statements 1 and 2 are true.

Hence, option 1 is correct.