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The authors consider sources and channels with memory observed through erasure channels. In particular, they examine the impact of sporadic erasures on the fundamental limits of lossless data compression, lossy data compression, channel coding, and denoising. They define the erasure entropy of a collection of random variables as the sum of entropies of the individual variables conditioned on all the rest. The erasure entropy measures the information content carried by each symbol knowing its context. The erasure entropy rate is shown to be the minimal amount of bits per erasure required to recover the lost information in the limit of small erasure probability.
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