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Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Upon partioning a phase space into Alpha partitions, it is intended to find how good that partiton is. In this perspective, we need to find out the source entropy.

Now, I googled a lot but could not find out what source entropy is. Can anyone explain:. How to calculate Channel capacity? Below is the code for calculating Shannon's entropy for a data x.

**Matlab code to visualize Channel capacity variation with Bnadwidth and Signal Power**

I would be obliged if the following code is modified to calculate the channel capacity. Addressing your last question first, Kolmogorov entropy is the entropy of the possible trajectories a system can take, i.

Shannon entropy on the other hand is a measure of the randomness of the state of a system. From the fact that you are comparing x to yrather than multiple trajectories of x to multiple trajectories of yit looks like you should be computing the Shannon entropy.

Often we want to compute something called the mutual information, which is a measure of how much the entropy, or 'randomness' of our signal is reduced when we condition it on some other signal. In the case of your code above, you are trying to measure either how much entropy there is in xor how much entropy there is in x given y.

The difference between these two values is how much we have found out about x by knowing y. We call this different the mutual information or, if we first divide by the time-length of the series you're looking at, the channel capacity.

The source entropy would just be the entropy of yassuming y is your 'source'. To calculate the entropy of x given y you should be taking a 2D matrix of the joint probability distribution, computing the sum of the entropy in the x direction as you are now, but then also taking the mean along the remaining dimension.

Learn more. Implementation issues for Shannon's Channel capacity and entropy Ask Question. Asked 7 years, 9 months ago. Active 7 years, 9 months ago. Viewed 1k times. Can anyone explain: How is Shannon's entropy different from Source entropy and how to implement source entropy?

Michael Petrotta Chaitali Chaitali 2 2 silver badges 13 13 bronze badges. Active Oldest Votes.In this post let us discuss the bounds on communication given the signal power and bandwidth constraint. Further, the following writeup is based on Section Proakis, Masoud Salehi. The capacity is. Increasing the signal power will mean that we can split the signal level into more number of levels even while ensuring low probability of error. Hence increasing signal power will lead to more capacity.

However, as the increase in capacity is a logarithmic function of power, the returns are diminishing. Let us try to evaluate the capacity equation when bandwidth tends to infinity i.

From the Taylor series expansion, we know that. This means that increasing bandwidth alone will not lead to increase of the capacity.

### What is correct to calculate Rate or shannon capacity?

Can observe that the maximum achievable capacity by increasing bandwidth is 1. From our discussion till now, we have understood that a practical communication should have a rate which is lower than capacityi.

Dividing both sides of the equation by bandwidth. Further, from our discussion on Bit error rate for 16PSK modulation using Gray mappingwe know that symbol to noise ratio is times the bit to noise ratio, i. In the above equation, when tends to zero, the bit to noise ratio should be.

This means that for reliable communication, we need to have or equivalently expressing in decibels. Closer the performance of a communication system is to the curve, more optimal is the system. Thanks for visiting! Happy learning. D id you like this article? Make sure that you do not miss a new article by subscribing to RSS feed OR subscribing to e-mail newsletter. Have you written a post on that? Can you tell me how to calculate that?

When talking about throughput for eg.Another objective in the communication system design is the ability to reliably send information at the lowest practical power level. The system should be able to provide acceptable bit-error-rate BER performance at the lowest possible power level. Often, this performance is charted in terms of BER Vs. Last updated on January 20th, at pm As reiterated in the previous posts, a MIMO system is used to increase the capacity dramatically and also to improve the quality of a communication link.

Increased capacity is obtained by spatial multiplexing and increased quality is obtained by diversity techniques Space time coding. Last updated on December 5th, at pm In the previous post, derivation of SISO fading channel capacity was discussed. Last updated on December 5th, at pm As reiterated in the previous posts, a MIMO system is used to increase the capacity dramatically and also to improve the quality of a communication link.

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## Shannon Capacity

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### Bounds on Communication based on Shannonâ€™s capacity

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## Shannonâ€™s noisy channel coding theorem â€“ demystified

Abu-Haltam on 30 Sep Vote 1. Answered: Tercio Rodovalho on 31 Jul Answers 1. Tercio Rodovalho on 31 Jul Vote 2. Cancel Copy to Clipboard. See Also. Tags channel capacity channel modeling. Opportunities for recent engineering grads. Apply Today. An Error Occurred Unable to complete the action because of changes made to the page. Select a Web Site Choose a web site to get translated content where available and see local events and offers.

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Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Trial software. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Vote 0. Commented: ashwini yadao on 1 Apr Answers 1. Walter Roberson on 19 Jan

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