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Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality
arXiv:2512.11322v1 Announce Type: new
Abstract: We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion coding. These refinements and extensions include sharper bounds for one-to-one codes and $D$-semifaithful codes, a Shannon lower bound for distortion measures based on sliding-window functions, and an individual-sequence counterpart of the Shannon lower bound.
Abstract: We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion coding. These refinements and extensions include sharper bounds for one-to-one codes and $D$-semifaithful codes, a Shannon lower bound for distortion measures based on sliding-window functions, and an individual-sequence counterpart of the Shannon lower bound.
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