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komm.EliasOmegaCode

Elias omega code. It is an integer code with domain the positive integers. The codeword for an integer $n$ is built from right to left: it ends with a single $0$ and, while $n > 1$, the binary representation of $n$ is prepended, and $n$ is replaced by its number of bits minus one. For more details, see Wikipedia: Elias omega coding or MacK03, Ch. 7 (therein called code $C_\omega$).

The table below shows the codewords for the first integers, with a space between the parts.

$n$ Codeword
$1$ 0
$2$ 10 0
$3$ 11 0
$4$ 10 100 0
$5$ 10 101 0
$6$ 10 110 0
$7$ 10 111 0
$8$ 11 1000 0

encode_single()

Encodes a single integer into its codeword.

Parameters:

  • integer (SupportsIndex) –

    The integer to be encoded. Must be in the domain of the code.

Returns:

  • codeword (Word) –

    The codeword of the integer. It is a tuple of bits.

Examples:

>>> code = komm.EliasOmegaCode()
>>> code.encode_single(4)
(1, 0, 1, 0, 0, 0)

decode_single()

Decodes a single codeword from a bit iterator. This method consumes exactly the bits of one codeword, leaving the iterator at the boundary with the next one; any remaining bits are left untouched.

Parameters:

  • bits (Iterator[SupportsIndex]) –

    An iterator of bits starting with a complete codeword. It must be an iterator (as returned by iter), not a general iterable, since advancing it is part of the contract.

Returns:

  • integer (int) –

    The decoded integer.

Notes

A ValueError is raised if the iterator is exhausted mid-codeword or if an invalid bit is found.

Examples:

>>> code = komm.EliasOmegaCode()
>>> bits = iter([1, 0, 1, 0, 0, 0, 1, 1])
>>> code.decode_single(bits)
4
>>> list(bits)  # Iterator is left at codeword boundary
[1, 1]

length()

Returns the codeword length $\ell(n)$ for a given integer $n$ in the domain of the code.

Examples:

>>> code = komm.EliasOmegaCode()
>>> code.length(4)
6

encode()

Encodes a sequence of integers.

Parameters:

  • input (ArrayLike) –

    The sequence of integers to be encoded. Must be a 1D-array of positive integers.

Returns:

  • output (Array1D[integer]) –

    The concatenation of the codewords. It is a 1D-array of bits.

Examples:

>>> code = komm.EliasOmegaCode()
>>> code.encode([4, 1, 3])
array([1, 0, 1, 0, 0, 0, 0, 1, 1, 0])

decode()

Decodes a sequence of bits.

Parameters:

  • input (ArrayLike) –

    The sequence of bits to be decoded. Must be a 1D-array of bits. Also, the sequence must be a concatenation of codewords (i.e., the output of the encode method).

Returns:

  • output (Array1D[integer]) –

    The sequence of decoded integers. It is a 1D-array of positive integers.

Examples:

>>> code = komm.EliasOmegaCode()
>>> code.decode([1, 0, 1, 0, 0, 0, 0, 1, 1, 0])
array([4, 1, 3])