Shannon Channel Capacity

Shannon’s channel capacity gives the highest theoretical bit rate that can be sent over a noisy communication link with arbitrarily low error if the right coding scheme is used. It grows linearly with bandwidth, but only logarithmically with signal-to-noise ratio, which means doubling bandwidth helps more directly than trying to endlessly boost power. The log term appears because information is limited by how reliably the receiver can distinguish signal variations from noise; once noise is present, each extra increase in SNR yields diminishing returns.

Use this when estimating the ultimate throughput of a radio link, fiber-optic channel, Wi‑Fi system, or any digital communication channel under additive noise. It is especially useful for comparing whether a design problem should be solved by increasing bandwidth, improving SNR, or both.

• Using SNR in decibels directly instead of converting it to a linear ratio first
• Forgetting that B must be in Hz if you want C in bits per second
• Treating Shannon capacity as a guaranteed real-world data rate rather than an ideal upper bound