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transmitting information when signal is lower than the noise

Started by omg January 7, 2006
base on the shannon capacity limit,dicuss the possibility of transmitting
information when siganl is lower than the noise?

some ways of trasmitting would be be spreading the specturm,using reed
coding method.

what are some other ways to transmit information when signal is lower than
the noise
"omg" <jimmybai123@yahoo.com> wrote in message 
news:_JCdncegjus_ESLeRVn-pQ@giganews.com...
> base on the shannon capacity limit,dicuss the possibility of transmitting > information when siganl is lower than the noise? > > some ways of trasmitting would be be spreading the specturm,using reed > coding method. > > what are some other ways to transmit information when signal is lower than > the noise
One very obvious way is just to repeat the information until it finally gets through. Best of Luck - Mike
Hi

The shannon capacity limit is known as:

C =1/2 * log2(1 + Pxx/Pnn) bits/channel use

where C is the capacity, Pxx is the average signal power and Pnn is the
average noise power per channel use.

If the channel bandwidth is W, then during T seconds we have 2WT
parallel channels.
So the total capacity is multiplied by 2WT,

CD = 2WT* 1/2 * log2(1 + Pxx/NoW) bits/channel use

where we used NoW instead of Pxx. No is the spectral density of the
noise having a bandwidth of W Hz.

In the limit T -> Infinity

C = lim (T->oo) (CD/T) = W*log2(1 + Pxx/NoW) bits/sec.

The noise power Pxx maybe expressed as

Pxx = Eb*Rb

where, Eb is the energy per bit, and Rb is the bit rate.

Now, using optimal coding we can have Rb = C.

Therefore,

C = W*log2(1+Eb/No * C/W)

We can now express Eb/No as:

               2^(C/W) - 1
Eb/No =  ------------------
                  (C/W)

and in the limit of (C/W) -> 0, we get

Eb/No = ln(2) = -1.6 dB.

That is, if we have an infinite bandwidth and we use an optimal coding
scheme, we can communicate errorless when the bits energy is 1.6 dB
less than the noise energy !!!

Tsachi.