The formula to calculate the channel capacity is:
\[ \text{C} = B \times \log_2(1 + \text{SNR}) \]
Where:
Channel capacity, in information theory, refers to the maximum rate at which data can be transmitted over a communication channel without error, given certain constraints such as signal noise and interference. It is typically measured in bits per second (bps) and depends on the bandwidth of the channel and the signal-to-noise ratio. The concept of channel capacity was introduced by Claude Shannon in his foundational work on information theory.
Let's consider an example:
Using the formula to calculate the channel capacity:
\[ \text{C} = 1000 \times \log_2(1 + 10) \approx 1000 \times 3.32 \approx 3459.4 \text{ bps} \]
This means that the channel capacity for this scenario is approximately 3459.4 bps.