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Volume of elements mapped to the same codeword is $2^{H(X|\hat{X})}$

In this paper by Tishby, Pereira and Bialek they mention on page 4 in the Relevant quantization chapter the setting is the following; Given some signal space $X \sim p(x)$ and a quantized codebook $\...
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How to choose a correct prior

Consider a Bernoulli experiment, such as flipping a not necessarily fair coin, which results in a positive outcome (heads) with probability $p$ and with a negative outcome (tails) with probability $(1-...