## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 8 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*