Shannon Channel Capacity Calculator: The Fundamental Limit of Data Rate

simulator intermediate ~10 min
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C ≈ 133 Mbps — 20 MHz at 20 dBm

A 20 MHz channel with 20 dBm signal power and 5 dB noise figure at 290 K yields roughly 133 Mbps theoretical maximum — close to real-world Wi-Fi 5 performance.

Formula

C = B × log₂(1 + S/N)
N = k × T × B × NF  (thermal noise power)
η = log₂(1 + SNR)  bits/s/Hz

The Ultimate Speed Limit

In 1948, Claude Shannon published a theorem that stunned the engineering world: every communication channel has a maximum data rate, determined solely by its bandwidth and signal-to-noise ratio, below which error-free transmission is theoretically possible — and above which it is not. This capacity limit, C = B·log₂(1 + S/N), is the most important equation in telecommunications, guiding the design of every modern wireless and wired system.

Bandwidth vs. Power

The Shannon formula reveals two paths to higher capacity: increase bandwidth or increase signal power. In the power-rich, bandwidth-limited regime (like urban spectrum), capacity grows logarithmically with power — each additional 3 dB yields only one more bit/s/Hz. In the power-limited, bandwidth-rich regime (like deep-space links), spreading the signal over more bandwidth helps linearly. Real systems operate somewhere between these extremes.

Approaching the Limit

For decades after Shannon's theorem, practical codes fell far short of the limit. The breakthrough came in 1993 with turbo codes and in 1996 with the rediscovery of LDPC codes, both achieving performance within a fraction of a decibel of capacity. Today, 5G NR and Wi-Fi 6 use LDPC codes that operate within 0.5 dB of the Shannon limit — engineering has essentially closed the gap that information theory predicted.

From Theory to Practice

This simulation computes the Shannon capacity for realistic parameters: you set the bandwidth, signal power, receiver noise figure, and temperature, and see the theoretical maximum throughput alongside the SNR and spectral efficiency. Compare the results to real-world systems — Wi-Fi, LTE, satellite links — to see how close modern technology comes to the fundamental bound.

FAQ

What is Shannon channel capacity?

Shannon channel capacity is the theoretical maximum rate at which information can be transmitted over a communication channel with arbitrarily low error probability. Derived by Claude Shannon in 1948, C = B·log₂(1 + S/N) sets an inviolable ceiling that no real system can exceed.

Can you exceed the Shannon limit?

No. The Shannon limit is a mathematical bound proved from information theory. Modern codes like turbo codes and LDPC codes come within 0.1 dB of the limit, but exceeding it is provably impossible without errors.

How does bandwidth affect capacity?

Capacity grows linearly with bandwidth when SNR is constant. However, wider bandwidth also captures more thermal noise (N = kTB), so in power-limited scenarios there are diminishing returns — doubling bandwidth does not double capacity.

What is spectral efficiency?

Spectral efficiency η = C/B measures bits per second per Hertz of bandwidth. It depends only on SNR: η = log₂(1 + SNR). 5G NR achieves up to 7.8 bits/s/Hz in ideal conditions, approaching practical limits.

Sources

Embed

<iframe src="https://homo-deus.com/lab/telecommunications/channel-capacity/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub