Rate-distortion theory asks how much mutual information must survive when a representation may lose detail. Lossy compression groups different inputs into one reconstruction; a distortion measure specifies which differences matter. The rate-distortion function then gives a quantitative tradeoff between allowed expected distortion and the required number of bits. A smaller file is useful only if its reconstruction retains the distinctions that the application needs.
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Rate-distortion theory is a branch of information theory that deals with the trade-off between the fidelity of data representation (distortion) and the amount of information (rate) used to represent that data. It provides a framework for understanding how to encode data such that it can be reconstructed with a certain level of quality while minimizing the amount of information transmitted or stored. ### Key Concepts: 1. **Rate (R):** This refers to the number of bits per symbol needed to encode the data.