Communication Scheme
Computer Science
Level
2
A pulse-amplitude-modulation communication scheme can transmit 16 distinct amplitudes. If the pulse rate is 1 kHz, what is the equivalent bit rate?
16,000 bits/second
8000 bits/second
1000 bits/second
4000 bits/second
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1 solution
The number of bits per symbol is the base-2 logarithm of the number of states the symbol can take. Here, the pulses (symbols) can take 16 distinct values, and each pulse therefore represents 4 bits. Since there are 1000 pulses per second, with each pulse representing 4 bits, the equivalent bit rate is 4000 bits/second.
To put this more simply, how many permutations are there for 4 bits? The answer is obviously 16. In our comm scheme, we have 16 possible pulse amplitudes, for a 1-to-1 mapping between pulse amplitudes and 4-bit binary states.