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A source emits three symbols with probability p1=0.2,p2=0.7 and p3=0.1. Calculate:

(a) Source entropy
(b) Maximum entropy
(c) Source efficiency
(d) Redundancy.

User Omalave
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Final answer:

The source entropy, maximum entropy, source efficiency, and redundancy can be calculated for the given source emitting three symbols with probabilities p1=0.2, p2=0.7, and p3=0.1.

Step-by-step explanation:

For the given source that emits three symbols with probabilities p1=0.2, p2=0.7, and p3=0.1, we can calculate the source entropy, maximum entropy, source efficiency, and redundancy as follows:

(a) Source entropy: The source entropy is calculated using the formula H(S) = -∑(pi * log2(pi)), where pi represents the probability of each symbol. So, H(S) = -0.2 * log2(0.2) - 0.7 * log2(0.7) - 0.1 * log2(0.1).

(b) Maximum entropy: The maximum entropy is the case when all symbols have equal probabilities. Since there are three symbols, each has a probability of 1/3. So, the maximum entropy, Hmax = -3 * (1/3) * log2(1/3).

(c) Source efficiency: The source efficiency is calculated as (Hmax - H(S)) / Hmax * 100%.

(d) Redundancy: The redundancy is calculated as Hmax - H(S).

User Mayur Chavan
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