Universal estimation of erasure entropy
IEEE Transactions on Information Theory
Lossy source coding with Gaussian or erased side-information
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Steganography using Gibbs random fields
Proceedings of the 12th ACM workshop on Multimedia and security
Relevance of contextual information in compression-based text clustering
IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
Gibbs construction in steganography
IEEE Transactions on Information Forensics and Security
Is the contextual information relevant in text clustering by compression?
Expert Systems with Applications: An International Journal
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We consider sources and channels with memory observed through erasure channels. In particular, we examine the impact of sporadic erasures on the fundamental limits of lossless data compression, lossy data compression, channel coding, and denoising. We 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. When we allow recovery of the erased symbols within a prescribed degree of distortion, the fundamental tradeoff is described by the erasure rate-distortion function which we characterize. We show that in the regime of sporadic erasures, knowledge at the encoder of the erasure locations does not lower the rate required to achieve a given distortion. When no additional encoded information is available, the erased information is reconstructed solely on the basis of its context by a denoiser. Connections between erasure entropy and discrete denoising are developed. The decrease of the capacity of channels with memory due to sporadic memoryless erasures is also characterized in wide generality.