## Introduction to Logplex Encoding

**Authors:** Russell Leidich

Logplex codes are universal codes, that is, bitstrings which map one-to-one
to the whole numbers, regardless of the bits which follow them in memory.
The codes are dense, in the sense that there is no finite series of bits which
does not map to at least one whole number. Their asymptotic efficiency (size
out divided by size in) is one, as with Elias omega codes[1], but they have
some convient features absent in the latter:
Given whole numbers M and N. If (M<N) then (logplex(M)<logplex(N)).
This provides for more efficient searching and sorting, as such tasks can be
done without the need to allocate separate memory for the corresponding
decoded whole numbers.
For all nonzero M, M itself is encoded verbatim in the high bits of its
logplex. In all cases, the high (last) bit of a logplex is one.
Representation of all subparts of logplexes are bitwise little endian. This is in
contrast to Elias omega codes, the endianness of the subparts of which are
opposite to the expansion direction.
Finally, logplexes are scale-agnostic: there is no need to assume that (log 2 M)
has any particular maximum value. This feature stems from their recursive
structure, which is analogous to that of Elias omega codes.

**Comments:** 5 Pages.

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### Submission history

[v1] 2017-05-11 21:28:54

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