Which of the following statements are true?

(A) A parity check code can detect and correct single bit error

(B) The efficiency of Huffman code is linearly proportional to average entropy

(C) Coding increases the channel bandwidth

(D) Coding increases the information rate

(E) A code dictionary with minimum distance 2 is not capable of error correction.

Choose the correct answer from the options given below:

(1) (A), (B), (D) only

(2) (B), (D), (E) only

(3) (A), (C), (D) only

(4) (B), (C), (D) only

This question was previously asked in

UGC NET Paper 2: Electronic Science Nov 2020 Official Paper

Option 4 : 4

Official Paper 1: Held on 24 Sep 2020 Shift 1

12883

50 Questions
100 Marks
60 Mins

__Concept:__

**Error correction and detection**

Any code which is capable of correcting the ‘t’ errors should satisfy the following condition:

**d _{min} ≥ 2t + 1**

Any code which is capable of detecting the ‘t’ errors should satisfy the following condition:

**d _{min} ≥ t + 1**

**statement E is true.**

Error detection is the process of detecting the errors that are present in the data transmitted from transmitter to receiver, in a communication system. We use some redundancy codes to detect these errors, by adding to the data while it is transmitted from source (transmitter). These codes are called “Error detecting codes”.

**Types of error detection**

- Parity check
- Cyclic Redundancy Check (CRC)
- Long Redundancy Check (LRC)
- Check sum

**Types of error correction**

The codes which are used for both error detecting and error correction are called as “Error Correction Codes”. The error correction techniques are of two types. They are,

- Single error
- Burst error

Hamming code or Hamming Distance Code is the best error correcting code we use in most of the communication network and digital systems.

**Statement A is false.**

**Coding efficiency**

The coding efficiency (η) of an encoding scheme is expressed as the ratio of the source entropy H(z) to the average code word length L(z) and is given by

\(\eta = \frac{{H\left( z \right)}}{{L\left( z \right)}}\)

Since L(z) ≥ H(z) according to Shannon’s Coding theorem and both L(z) and H(z) are positive, **0≤ η ≤ 1**

If m(z) is the minimum of the average code word length obtained out of different uniquely decipherable coding schemes, then as per Shannon’s theorem, we can state that **m(z) ≥ H(z)**

**Statement B is true.**

**Channel coding**

When it comes to channel coding, we always have to compromise between energy efficiency and bandwidth efficiency.

Low-rate codes are not very efficient due to the reason that:

- They have large overheads
- Requires more bandwidth to transmit the data.
- The decoders are more complex.

While codes with greater redundancy are more efficient in correcting errors, as the efficiency of the code increases:

- It contributes greatly by operating at a lower transmit power and transmitting over long distances.
- It is also more tolerant towards interference and hence can be used with small antennas.
- Transmits at a higher data rate.

**Statement C is false.**

**Statement D is true**

__Conclusion:__

Option 2 is correct.