Well I was reading this " A Mathematical Theory of Communication" paper by Claude Shannon. He says that the capacity of a discrete channel is given by(adsbygoogle = window.adsbygoogle || []).push({});

[ tex ] C= \ \lim_{T \to +\infty} \ \frac{\log ( N(T) )} {T} [ \tex ]

Here N(T) is the number of possible sequences in a duration of T seconds.

He gives one example before talking about this capacity formula. Here's the example- Consider 32 symbols. You have a system where you can transmit 2 symbols per second. Now he says it is clear that if each symbol has 5 bits then we can send 2 x 5 =10 bits per second (or 2 symbols per second). This is the capacity of the channel. But when I tried it out using the above expression I couldn't get the answer as 2 symbols/ second. I got it as 3 symbols per second. Can you help me with this?

Thanks in advance.

(As latex doesn't seem to work now I have even attached the image of the formula for Capacity)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Capacity of a discrete channel

**Physics Forums | Science Articles, Homework Help, Discussion**