646 research outputs found
Compressing Sparse Sequences under Local Decodability Constraints
We consider a variable-length source coding problem subject to local
decodability constraints. In particular, we investigate the blocklength scaling
behavior attainable by encodings of -sparse binary sequences, under the
constraint that any source bit can be correctly decoded upon probing at most
codeword bits. We consider both adaptive and non-adaptive access models,
and derive upper and lower bounds that often coincide up to constant factors.
Notably, such a characterization for the fixed-blocklength analog of our
problem remains unknown, despite considerable research over the last three
decades. Connections to communication complexity are also briefly discussed.Comment: 8 pages, 1 figure. First five pages to appear in 2015 International
Symposium on Information Theory. This version contains supplementary materia
Prefix Codes: Equiprobable Words, Unequal Letter Costs
Describes a near-linear-time algorithm for a variant of Huffman coding, in
which the letters may have non-uniform lengths (as in Morse code), but with the
restriction that each word to be encoded has equal probability. [See also
``Huffman Coding with Unequal Letter Costs'' (2002).]Comment: proceedings version in ICALP (1994
Pure Asymmetric Quantum MDS Codes from CSS Construction: A Complete Characterization
Using the Calderbank-Shor-Steane (CSS) construction, pure -ary asymmetric
quantum error-correcting codes attaining the quantum Singleton bound are
constructed. Such codes are called pure CSS asymmetric quantum maximum distance
separable (AQMDS) codes. Assuming the validity of the classical MDS Conjecture,
pure CSS AQMDS codes of all possible parameters are accounted for.Comment: Change in authors' list. Accepted for publication in Int. Journal of
Quantum Informatio
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