Shannon's Capacity Formula | Generated by AI
Shannon’s capacity formula is actually written as:
C = B log₂(1 + S/N)
Where:
- C is the channel capacity in bits per second
- B is the bandwidth in Hertz
- S/N is the signal-to-noise ratio (power ratio)
- log₂ is the logarithm with base 2
This formula represents the theoretical maximum data rate that can be reliably transmitted over a communications channel with bandwidth B and a signal-to-noise ratio of S/N.
To understand why this is correct:
-
Bandwidth factor (B): The bandwidth directly scales the capacity - doubling the bandwidth doubles the capacity.
- Logarithmic relationship: The log₂ shows that capacity increases logarithmically with S/N, not linearly. This means:
- Doubling S/N doesn’t double capacity
- Each additional “bit” of capacity requires doubling the S/N
- 1 + S/N term: The addition of 1 ensures that capacity is always positive, even with very small S/N values.
This formula is fundamental to information theory because it establishes the theoretical upper limit for how much information can be transmitted through a noisy channel, regardless of the coding scheme used.
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