Shannon's channel capacity: C = B log₂(1 + S/N) bits per second

What does the Shannon-Hartley theorem convey about the maximum data rate for a noisy channel in communication systems?

It states the channel capacity in bits per second, given bandwidth and signal-to-noise ratio

What is the formula for calculating the mutual information between two discrete random variables X and Y?

I(X;Y) = ∑∑ P(x,y) log(P(x,y)/(P(x)P(y)))

Time complexity of binary search: O(log n) — halves search space each step

Binary search reduces search space by half with each iteration, achieving O(log n) complexity

What a qubit is: a quantum bit that exists in superposition of |0⟩ and |1⟩

A qubit: a quantum bit in simultaneous |0⟩ and |1⟩ states

How does the concept of information entropy, as described by Claude Shannon, contribute to understanding the complexity and unpredictability of communication systems?

Information entropy quantifies uncertainty and complexity in communication systems, aiding in efficient data encoding and transmission

Reed-Solomon error correction: What is the mathematical formula representing the minimum number of redundant symbols required to correct a given number of symbol errors in a Reed-Solomon code?

Minimum redundant symbols = (2t + 1) * k, where t = (number of symbol errors)/(2t + 1) and k = (codeword length - data length)