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Nth Extension Entropy Calculator

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Continuous Channels Source Coding

✖The nth source is the n sources of entropy present in the channel.ⓘ Nth Source [n]			+10% -10%
✖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.ⓘ Entropy [H[S]]			+10% -10%

✖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.ⓘ Nth Extension Entropy [H[Sⁿ]]

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Nth Extension Entropy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Extension Entropy = Nth Source*Entropy
H[Sⁿ] = n*H[S]
This formula uses 3 Variables

Variables Used

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.
Nth Source - The nth source is the n sources of entropy present in the channel.
Entropy - (Measured in Bit per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Nth Source: 7 --> No Conversion Required
Entropy: 1.8 Bit per Second --> 1.8 Bit per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H[Sⁿ] = n*H[S] --> 7*1.8

Evaluating ... ...

H[Sⁿ] = 12.6

STEP 3: Convert Result to Output's Unit

12.6 --> No Conversion Required

FINAL ANSWER

12.6 <-- Nth Extension Entropy

(Calculation completed in 00.004 seconds)

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< Continuous Channels Calculators

Channel Capacity

LaTeX Go Channel Capacity = Channel Bandwidth*log2(1+Signal to Noise Ratio)

Noise Power of Gaussian Channel

LaTeX Go Noise Power of Gaussian Channel = 2*Noise Power Spectral Density*Channel Bandwidth

Information Rate

LaTeX Go Information Rate = Symbol Rate*Entropy

Nyquist Rate

LaTeX Go Nyquist Rate = 2*Channel Bandwidth

Nth Extension Entropy Formula

LaTeX Go

Nth Extension Entropy = Nth Source*Entropy
H[Sⁿ] = n*H[S]

What is zero memory source?

The output symbols emitted from this kind of sources are independent on each
other (i.e. the current emitted symbol is independent on the previous one). Those
symbols are considered discrete random variables because at any time instant we
don't know exactly what will be the next output symbol. The existence of any
symbol is determined according to its probability which is predetermined before
the real operation of the source in the stage source testing.

What are the examples of extension entropy?

The 2nd extension of binary source will have 4 symbols. for example, the first
three extensions have alphabets {0, 1}, {00, 01, 10,11} and {000, 001, 010, 011, 100, 101, 110, 111}.

How to Calculate Nth Extension Entropy?

Nth Extension Entropy calculator uses Nth Extension Entropy = Nth Source*Entropy to calculate 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 calculate Nth Extension Entropy using this online calculator? To use this online calculator for Nth Extension Entropy, enter Nth Source (n) & Entropy (H[S]) and hit the calculate button. Here is how the Nth Extension Entropy calculation can be explained with given input values -> 12.6 = 7*1.8.

FAQ

What is 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 and is represented as H[Sⁿ] = n*H[S] or Nth Extension Entropy = Nth Source*Entropy. The nth source is the n sources of entropy present in the channel & 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.

How to calculate 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 is calculated using Nth Extension Entropy = Nth Source*Entropy. To calculate Nth Extension Entropy, you need Nth Source (n) & Entropy (H[S]). With our tool, you need to enter the respective value for Nth Source & Entropy and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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