9,483 research outputs found
Optimal prefix codes for pairs of geometrically-distributed random variables
Optimal prefix codes are studied for pairs of independent, integer-valued
symbols emitted by a source with a geometric probability distribution of
parameter , . By encoding pairs of symbols, it is possible to
reduce the redundancy penalty of symbol-by-symbol encoding, while preserving
the simplicity of the encoding and decoding procedures typical of Golomb codes
and their variants. It is shown that optimal codes for these so-called
two-dimensional geometric distributions are \emph{singular}, in the sense that
a prefix code that is optimal for one value of the parameter cannot be
optimal for any other value of . This is in sharp contrast to the
one-dimensional case, where codes are optimal for positive-length intervals of
the parameter . Thus, in the two-dimensional case, it is infeasible to give
a compact characterization of optimal codes for all values of the parameter
, as was done in the one-dimensional case. Instead, optimal codes are
characterized for a discrete sequence of values of that provide good
coverage of the unit interval. Specifically, optimal prefix codes are described
for (), covering the range , and
(), covering the range . The described codes produce the expected
reduction in redundancy with respect to the one-dimensional case, while
maintaining low complexity coding operations.Comment: To appear in IEEE Transactions on Information Theor
A construction for balancing non-binary sequences based on gray code prefixes
Abstract: We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on a generalization of Knuth’s parallel balancing approach, which can handle very long information sequences. However, the overall sequence—composed of the information sequence, together with the prefix—must be balanced. This is reminiscent of Knuth’s serial algorithm. The encoding of our construction does not make use of lookup tables, while the decoding process is simple and can be done in parallel
Properties of optimal prefix-free machines as instantaneous codes
The optimal prefix-free machine U is a universal decoding algorithm used to
define the notion of program-size complexity H(s) for a finite binary string s.
Since the set of all halting inputs for U is chosen to form a prefix-free set,
the optimal prefix-free machine U can be regarded as an instantaneous code for
noiseless source coding scheme. In this paper, we investigate the properties of
optimal prefix-free machines as instantaneous codes. In particular, we
investigate the properties of the set U^{-1}(s) of codewords associated with a
symbol s. Namely, we investigate the number of codewords in U^{-1}(s) and the
distribution of codewords in U^{-1}(s) for each symbol s, using the toolkit of
algorithmic information theory.Comment: 5 pages, no figures, final manuscript to appear in the Proceedings of
the 2010 IEEE Information Theory Workshop, Dublin, Ireland, August 30 -
September 3, 201
A generalization of Girod's bidirectional decoding method to codes with a finite deciphering delay
International audienceGirod"s encoding method has been introduced in order to efficiently decode from both directions messages encoded by using prefix codes. In the present paper, we generalize this method to codes with a finite deciphering delay. In particular, we show that our decoding algorithm can be realized by a deterministic finite transducer. We also investigate some properties of the corresponding unlabeled graph
A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay
Girod's encoding method has been introduced in order to efficiently decode from both directions messages encoded by using finite prefix codes. In the present paper, we generalize this method to finite codes with a finite deciphering delay. In particular, we show that our decoding algorithm can be realized by a deterministic finite transducer. We also investigate some properties of the underlying unlabeled graph
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