Shannon's Capacity Formula | Generated by AI

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Shannon’s capacity formula is actually written as:

C = B log₂(1 + S/N)

Where:

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:

  1. Bandwidth factor (B): The bandwidth directly scales the capacity - doubling the bandwidth doubles the capacity.

  2. 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
  3. 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.

Would you like me to explain any particular aspect of this formula in more detail?


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