Coding theory

Unary coding

Unary coding, or the unary numeral system and also sometimes called thermometer code, is an entropy encoding that represents a natural number, n, with a code of length n + 1 ( or n ), usually n ones followed by a zero (if natural number is understood as non-negative integer) or with n − 1 ones followed by a zero (if natural number is understood as strictly positive integer). For example 5 is represented as 111110 or 11110. Some representations use n or n − 1 zeros followed by a one. The ones and zeros are interchangeable without loss of generality. Unary coding is both a prefix-free code and a self-synchronizing code. Unary coding is an optimally efficient encoding for the following discrete probability distribution for . In symbol-by-symbol coding, it is optimal for any geometric distribution for which k ≥ φ = 1.61803398879…, the golden ratio, or, more generally, for any discrete distribution for which for . Although it is the optimal symbol-by-symbol coding for such probability distributions, Golomb coding achieves better compression capability for the geometric distribution because it does not consider input symbols independently, but rather implicitly groups the inputs. For the same reason, arithmetic encoding performs better for general probability distributions, as in the last case above. (Wikipedia).

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(IC 5.11) Finite-precision arithmetic coding - Rescaling

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From playlist Information theory and Coding

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From playlist The Internet

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From playlist Cryptography

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(IC 5.6) Encoder for arithmetic coding (infinite-precision)

Pseudocode for the arithmetic coding algorithm, assuming addition and multiplication can be done exactly (i.e. with infinite precision). Later we modify this to work with finite precision. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837

From playlist Information theory and Coding

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From playlist Sequences

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(IC 5.5) Rescaling operations for arithmetic coding

Certain rescaling operations are convenient for the infinite-precision algorithm, and are critical for the finite-precision algorithm. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

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(IC 5.7) Decoder for arithmetic coding (infinite-precision)

Pseudocode for the arithmetic coding algorithm, assuming addition and multiplication can be done exactly (i.e. with infinite precision). Later we modify this to work with finite precision. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

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From playlist Random Access Memory

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From playlist Geometric Algebra, First Course, in STEMCstudio

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From playlist Los Angeles Ruby Conf 2011

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Related pages

Geometric distribution | Natural number | Unary numeral system | Instantaneously trained neural networks | Probability distribution | Golden ratio | Prefix code | Without loss of generality