Explain Shannon's channel capacity theorem and its implications.

Shannon's theorem states maximum data rate C = B*log2(1 + SNR) bits/second, where B is bandwidth in Hz and SNR is signal-to-noise ratio. Key implications: There is a fundamental limit to error-free transmission rate, increasing bandwidth or SNR increases capacity, capacity approaches limit as SNR increases (diminishing returns), and practical systems operate below this limit. The theorem guides system design trade-offs between bandwidth, power, and complexity. Modern systems like LDPC and turbo codes approach Shannon limit within 1dB.