JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year ERROR CORRECTING CODES Previous Question Paper (March - 2021 - R18)

A typical data transmission or storage system consists of an information source, a transmitter, a channel, a receiver, and a destination. The system aims to transfer information reliably despite the presence of noise or interference.

• Information Source: Generates the raw data or message signal to be transmitted.
• Source Encoder: Compresses the data by removing redundancy to improve efficiency.
• Channel Encoder: Adds controlled redundancy to the data to detect and correct errors caused by the channel.
• Modulator: Converts the digital data into a signal suitable for transmission over the physical medium.
• Channel: The physical medium (e.g., copper wire, fiber optics, or free space) where noise and distortion are introduced.
• Demodulator: Reconstructs the signal from the channel output.
• Channel Decoder: Uses the added redundancy to identify and correct errors introduced by the channel.
• Source Decoder: Decompresses the data to recover the original message for the destination.

For a fair coin, the probability of heads (H) is p = 0.5 and the probability of tails (T) is q = 0.5. The entropy H(X) is calculated using the Shannon entropy formula:

Substituting the values:

The entropy of a fair coin is 1 bit per toss.