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Nth Extension Entropy Formula

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The nth Extension Entropy is a measure of the amount of uncertainty or randomness in a system. It is a generalization of the Shannon entropy to higher-order probability distributions. Check FAQs

H[S n] = n \cdot H[S]

H[Sⁿ] - Nth Extension Entropy?n - Nth Source?H[S] - Entropy?

Nth Extension Entropy Example

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Here is how the Nth Extension Entropy equation looks like with Values.

Here is how the Nth Extension Entropy equation looks like with Units.

Here is how the Nth Extension Entropy equation looks like.

12.6 = 7 \cdot 1.8

12.6 = 7 \cdot 1.8b/s

12.6 = 7 \cdot 1.8

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Nth Extension Entropy Solution

Follow our step by step solution on how to calculate Nth Extension Entropy?

FIRST Step Consider the formula

H[S n] = n \cdot H[S]

Next Step Substitute values of Variables

∴

H[S n] = 7 \cdot 1.8b/s

Next Step Prepare to Evaluate

∴

H[S n] = 7 \cdot 1.8

LAST Step Evaluate

∴

H[S n] = 12.6

Nth Extension Entropy Formula Elements

Variables

Nth Extension Entropy

The nth Extension Entropy is a measure of the amount of uncertainty or randomness in a system. It is a generalization of the Shannon entropy to higher-order probability distributions.

Symbol: H[Sⁿ]

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Nth Extension Entropy

Nth Source

The nth source is the n sources of entropy present in the channel.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Nth Source

Entropy

Entropy is a measure of the uncertainty of a random variable. Specifically, it measures the average amount of information contained in each possible outcome of the random variable.

Symbol: H[S]

Measurement: Data TransferUnit: b/s

Note: Value should be greater than 0.

Formulas to find Entropy

Other formulas in Continuous Channels category

Go Channel Capacity

C = B \cdot \log 2 (1 + SNR)

Go Noise Power of Gaussian Channel

N o = 2 \cdot P SD \cdot B

Go Nyquist Rate

N r = 2 \cdot B

Go Information Rate

R = r s \cdot H[S]

How to Evaluate Nth Extension Entropy?

Nth Extension Entropy evaluator uses Nth Extension Entropy = Nth Source*Entropy to evaluate the Nth Extension Entropy, The Nth Extension Entropy formula is defined as an extension of a source is that new source which results when the emitted symbols are considered in groups. In other words the entropy of the n_th extension of a source is n times the entropy of the source itself. Nth Extension Entropy is denoted by H[Sⁿ] symbol.

How to evaluate Nth Extension Entropy using this online evaluator? To use this online evaluator for Nth Extension Entropy, enter Nth Source (n) & Entropy (H[S]) and hit the calculate button.

FAQs on Nth Extension Entropy

What is the formula to find Nth Extension Entropy?

The formula of Nth Extension Entropy is expressed as Nth Extension Entropy = Nth Source*Entropy. Here is an example- 12.6 = 7*1.8.

How to calculate Nth Extension Entropy?

With Nth Source (n) & Entropy (H[S]) we can find Nth Extension Entropy using the formula - Nth Extension Entropy = Nth Source*Entropy.

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