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The Multivariate Covering Lemma and its Converse

Noorzad, Parham and Effros, Michelle and Langberg, Michael (2015) The Multivariate Covering Lemma and its Converse. . (Unpublished)

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The multivariate covering lemma states that given a collection of k codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one codeword from each codebook such that the resulting k-tuple of codewords is jointly typical with respect to the joint distribution. We give a proof of this lemma for weakly typical sets. This allows achievability proofs that rely on the covering lemma to go through for continuous channels (e.g., Gaussian) without the need for quantization. The covering lemma and its converse are widely used in information theory, including in rate-distortion theory and in achievability results for multi-user channels.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Noorzad, Parham0000-0002-0201-3791
Langberg, Michael0000-0002-7470-0718
Record Number:CaltechAUTHORS:20190402-145646746
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94381
Deposited By: George Porter
Deposited On:02 Apr 2019 22:49
Last Modified:02 Apr 2019 22:49

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