ISRO CS 2023 Q.16: solution and answer

ISRO 2023 · CSQ.16 · 1 mark · MCQ

Which of the following is true?

(A)
Both Parity and Cyclic Redundancy Check are error correcting codes
(B)
Both Parity and Low Density Parity Check Code are error correcting codes
(C)
Both Reed-Solomon code and Low Density Parity Check Code are error correcting codes
(D)
Both Cyclic Redundancy Check and Low Density Parity Check Code are error correcting codes

See the question in the paper

Answer and solution

ANSWER

Option (c): both Reed-Solomon code and Low Density Parity Check code are error-correcting codes.

Error-detecting codes only reveal that some bits are wrong. Error-correcting codes carry enough redundancy to locate the wrong bits and repair them without asking for a retransmission.
A single parity bit detects any odd number of bit errors. It cannot say which bit is wrong, so it is an error-detecting code only. This rules out options (a) and (b).
A Cyclic Redundancy Check divides the message polynomial by a generator polynomial and compares the remainder. It detects burst and random errors, and in the data link layer a bad frame is discarded or retransmitted rather than repaired. So CRC is an error-detecting code only, which rules out options (a) and (d).
Reed-Solomon is a block code over symbols, not single bits. It adds $2 t$ check symbols and can correct up to $t$ erroneous symbols. It is used in CDs, DVDs and QR codes, so it is an error-correcting code.
A Low Density Parity Check code has a sparse parity-check matrix and is decoded by iterative message passing. It performs close to the Shannon limit and corrects errors, so it is an error-correcting code.
Only option (c) names two error-correcting codes, so (c) is the true statement.

KEY IDEA

Parity and CRC only detect errors. Reed-Solomon and LDPC carry enough structured redundancy to correct them.

WATCH OUT FOR

Treating CRC as an error-correcting code because it is a powerful check. It only detects errors, and the receiver asks for the frame again.