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Q2(b)(i) · Block coding capacity

2022-11-16 · AI-only Sem V

Exact historical variant. Current-syllabus questions solved; excluded topics and source limitations stated.

Q2(b)(i). In a block coding scheme k=4 and n=5. Find the number of datawords and codewords. How many datawords are successfully received? [4 marks]

Answer

Source note: The phrase “successfully received” does not specify a channel/error event. The answer distinguishes the 16 valid encoded words from the 32 possible received 5-bit patterns.

Given

k=4 data bits; n=5 coded bits.

To find

Dataword count, possible received words, valid codewords.

Formula and why

N_{data}=2^k,\quad N_{possible}=2^n,\quad N_{valid}=2^kLaTeX: N_{data}=2^k,\quad N_{possible}=2^n,\quad N_{valid}=2^k

A one-to-one encoder maps every dataword to exactly one valid codeword. The remaining n-bit patterns are not valid codewords.

Solution

Step 1. Count datawords

2⁴=16.

Step 2. Count all 5-bit patterns

2⁵=32 possible received patterns; only16 are selected valid codewords.

Step 3. Interpret successful reception carefully

All16 distinct datawords can be represented and recovered when received correctly. The question gives no channel outcomes, so an actual count of successful transmissions cannot be calculated. Invalid patterns indicate an error; an error that changes one valid word to another can go undetected.