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Shannon Capacity (Shannon Limit)

The Shannon capacity is a concept from information theory, introduced by Claude Shannon in his 1948 paper A Mathematical Theory of Communication. It defines the maximum rate at which information can be transmitted over a communication channel without error, given a certain level of noise and bandwidth.

Key Formula (for AWGN channel):

\(\(C = B \log_2(1 + \frac{S}{N})\)\) (bits per second)

Where: - C: Channel capacity (maximum data rate) - B: Bandwidth of the channel (Hz) - S: Signal power - N: Noise power - S/N: Signal-to-noise ratio (SNR)

Key Insights:

  • Theoretical Limit: Shannon capacity is the upper bound of reliable communication. It tells us what is possible, not necessarily how to achieve it.
  • Error-Free Communication: Below this limit, it's theoretically possible to transmit data with an arbitrarily low error rate using appropriate coding.
  • Beyond Capacity: If you try to send data faster than this capacity, errors are inevitable regardless of the coding scheme.
  • Bandwidth vs. Power Trade-off: Capacity can be increased by increasing either bandwidth or SNR, showing a trade-off between the two.

Applications:

  • Used in wireless communication, data compression, and network design
  • Basis for evaluating performance of modern coding techniques like Turbo Codes, LDPC, and 5G/6G standards

_Last updated: June 06, 2025