Shannon's source coding theorem is a fundamental result in information theory, established by Claude Shannon in his groundbreaking 1948 paper "A Mathematical Theory of Communication." The theorem provides a formal framework for understanding how to optimally encode information in a way that minimizes the average length of the code while still allowing for perfect reconstruction of the original data.

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For a discrete memoryless source of entropy , every uniquely decodable binary code has expected length at least . Shannon code lengths satisfy , and block coding can make the expected length per source symbol arbitrarily close to .