Re: Calculating Shannon Limit for 8 bit code with a error chance of let's say 10%.

[Skybuck Flying]

(I shall re-post this question to these two newsgroups as well)

Hello,

Let's say there is a transmission channel which can send 8 bits per second.

There is a 10% chance of error ?

Some question about this:

What is the signal to noise ratio ?

How to plug these numbers into shannon's limit/equation/theory ?

I shall give it a try and you check if I did it correctly in your oppinion:

But first my gutt feeling:

10% of 8 bits is 0.8 bits... so roughly 1 bit is lost, so 7 bits should
remain per second or so..

Now calculating shannon limit.

Equation is giving as:

I < B * log2 (1 + (S / N) )

where

I is the information rate in bits per second excluding error-correcting
codes;
B is the bandwidth of the channel in hertz;
S is the total signal power (equivalent to the carrier power C); and
N is the total noise power in the bandwidth.


I < 8 * log2( 1 + (8 / 0.8) )
I < 8 * 3.4594316186372972561993630467258
I < 27.675452949098378049594904373806

So according to this formula I is roughly equal to 27 bits per second ?

Seems like I went wrong somewhere...

Perhaps the 8 must just be a 1 ?

Weird.

Also once shannon limit is calculated then max data rate would also be nice
to calculate... different formula's necessary for that.

Bye,
Skybuck.

[Skybuck Flying]

(Same posting, re-formulate for more clearity ;))

It is not clear to me how to calculate the shannon limit given the following
information:

Bits per second of a transmission channel.

Bit error rate.

If I try it out it doesn't seem right, example:

Information given:

Transmission channel 8 bits per second.

Error probability: 10 procent.

Trying to plug this into shannon's formula gives:

I < B * log2 (1 + (S / N) )

B = 8 ?
S = 8 ?
B = 0.8 ?
Result:

I < 8 * log2( 1 + (8 / 0.8) )
I < 8 * 3.4594316186372972561993630467258
I < 27.675452949098378049594904373806

What am I doing wrong ?

Bye, Skybuck.

[Skybuck Flying]

I suspect one of the problems is the bit error probablity and/or bit error
rate needs to be converted to some kind of signal to noise ratio... which
suits the "power" like approach to this formula better... db ? or something
like that ?

Hmmm...

Investigating...

Bye,
Skybuck.

[Skybuck Flying]

Shannon Limit looks like a simple formula... but I guess it's not, some
warnings about it:

http://www.vmsk.org/Shannon.pdf

Bye,
Skybuck.

[Skybuck Flying]

This document also seems nice.

I want to experiment a little bit with bit error rates and some coding
techniques.

So some Delphi and/or C code to simply calculate channel capacity given some
simple parameters, like bits / sec and error rate probability would be nice.

http://www.ece.ualberta.ca/~hcdc/Library/MIMOchClass/ChannelCapacity.pdf

Bye,
Skybuck.

[Skybuck Flying]

I think I am gonna follow some lectures about information theory... sounds
interesting:

https://www.youtube.com/watch?v=f8RvFlr5wRk

Bye,
Skybuck.