/ˈʃænən ˈlɪmɪt/
noun … “Maximum reliable information rate of a channel.”
Shannon Limit, named after Claude Shannon, is the theoretical maximum rate at which information can be transmitted over a communication channel with a specified bandwidth and noise level, while achieving error-free transmission. Formally defined in information theory, it sets the upper bound for channel capacity (C) given the signal-to-noise ratio (SNR) and bandwidth (B) using the Shannon-Hartley theorem: C = B * log2(1 + SNR).
Key characteristics of the Shannon Limit include:
- Channel capacity: represents the absolute maximum data rate achievable under ideal encoding without error.
- Dependence on noise: higher noise reduces the capacity, requiring more sophisticated error-correcting codes to approach the limit.
- Fundamental bound: no coding or modulation scheme can exceed the Shannon Limit, making it a benchmark for communication system design.
- Practical significance: real-world systems aim to approach the Shannon Limit using advanced techniques like LDPC or Turbo Codes to maximize efficiency.
Workflow example: In modern fiber-optic networks, engineers measure the channel’s SNR and bandwidth, then select modulation formats and forward error correction schemes to operate as close as possible to the Shannon Limit. This ensures maximum throughput without exceeding physical constraints.
-- Example: Shannon-Hartley calculation in pseudocode
bandwidth = 1e6 -- 1 MHz
snr = 10 -- Linear ratio
capacity = bandwidth * log2(1 + snr)
print("Max channel capacity: " + capacity + " bits per second")Conceptually, the Shannon Limit is like a pipe carrying water: no matter how clever the plumbing, the flow cannot exceed the pipe’s physical capacity. Engineers design systems to maximize flow safely, approaching the limit without causing overflow (errors).
See LDPC, Turbo Codes, Information Theory, Signal-to-Noise Ratio.