Directions:

In the following question there are two statements, one labelled as 'Statement (I)' and the other as 'Statement (II)'. You are to examine these two statements carefully and select the answers to these items using the code given below.

Statement (I):

Shannon has shown that it is possible to achieve error-free communication by adding sufficient redundancy.

Statement(II):

The addition of an extra check digit increases redundancy.

Question

Question

This question was previously asked in

UPSC ESE Electronics & Communication 2022 Official Paper

Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
Statement (I) is true but Statement (II) is false
Statement (I) is false but Statement (II) is true

Answer 1

Key Points

An error-correcting code (ECC) or forward error correction (FEC) code is a system of adding additional information(Redundancy), or parity data, to a message, such that it can be recovered by a receiver even when a number of errors (up to the capability of the code being used) were introduced, either during the process of transmission or on storage.
Shannon's theorem is an important theorem in forward error correction;
- describes the maximum information rate at which reliable communication is possible over a channel that has a certain error probability or signal-to-noise ratio (SNR).
- This strict upper limit is expressed in terms of the channel capacity.
- The theorem says that there exist codes such that with increasing encoding length the probability of error on a discrete memory less channel can be made arbitrarily small, provided that the code rate is smaller than the channel capacity.
- The code rate is defined as the fraction k/n of k source symbols and n encoded symbols.