From: Arthur Keller <arthur_at_kellers_dot_org>

Date: Tue May 04 2004 - 02:33:49 CDT

Date: Tue May 04 2004 - 02:33:49 CDT

At 3:20 AM -0400 5/4/04, David Mertz wrote:

*>On May 4, 2004, at 2:56 AM, Arthur Keller wrote:
*

*>>You can code in hexadecimal (4 bits, base 16), octal (3 bits, base
*

*>>8), or quad (2 bits, base 4). d is the number of bits in your
*

*>>digital encoding.
*

*>
*

*>I managed to figure out in conversation with Charlie Strauss what
*

*>Arthur was talking about. The missing part of Arthur's description
*

*>is that he is talking about the symbology of a particular barcode.
*

*>I.e. one barcode has a 16-letter alphabet, another has a 4-letter
*

*>alphabet, etc.
*

*>
*

*>So Arthur's "base" is the size of the barcode symbol set.
*

*>Unfortunately, this doesn't allow us to specify in a general way
*

*>what the bit-length required for an optimal self-delimited encoding
*

*>is. It's always relative to the particular alphabet we've already
*

*>chosen. That is, it's of less use in deciding the parameters for
*

*>what is an acceptable barcode to use.
*

*>
*

*>I kinda wish Arthur would have indicated that this was what he was
*

*>talking about... but I guess since it was a hidden assumption in his
*

*>own thinking, it seemed obvious to him (even though it wasn't stated
*

*>on-thread).
*

I thought I did. I learned "base arithmetic" (like binary, base 4,

base 8, etc.) in grade school. What better terminology would you

have preferred?

*>However, we can still produce an example, assuming a priori a
*

*>particular symbology for our yet-undecided barcode. For example, if
*

*>we assume our barcode uses a 16-letter alphabet, applying this to
*

*>the demo election we get:
*

*>
*

*>$ ./election-entropy.py < demo-election.data
*

*>Election summary for OVC demo ballot (write-ins count as candidate)
*

*>
*

*>269995136716800 distinct votes are possible
*

*>Optimal encoding is approximately 48 bits
*

*>Contests at bit-boundaries, approx 53 bits
*

*>Contests self-delimited, approx 88 bits
*

*>
*

*>Vote Space Optimal Self-Delim
*

*>---------- ------- ----------
*

*> 9 4 8
*

*> 9 4 8
*

*> 4 2 4
*

*> 4 2 4
*

*> 5 3 4
*

*> 4 2 4
*

*> 5 3 4
*

*> 4 2 4
*

*> 3 2 4
*

*> 3 2 4
*

*> 3 2 4
*

*> 176 8 12
*

*> 109601 17 24
*

*>
*

*>To me the self-delimited case looks enough less efficient that
*

*>optimal encoding to rule it out if we are still contemplating
*

*>Code128. Especially since Code128 in decimal code includes some
*

*>error-detection of its own. And even more so if we use Karl's
*

*>globally unique identifier for ballots: that ID will include
*

*>reference to the particular ballot template that the ballot refers
*

*>to, i.e. the bit positions of each contest. So self-delimiting
*

*>doesn't get us anything extra.
*

*>
*

*>Yours, David...
*

Thanks, please try a 3-bit (base 8) encoding, for your example. Thanks.

Best regards,

Arthur

-- ------------------------------------------------------------------------------- Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA 94303-4507 tel +1(650)424-0202, fax +1(650)424-0424 ================================================================== = The content of this message, with the exception of any external = quotations under fair use, are released to the Public Domain ==================================================================Received on Mon May 31 23:17:09 2004

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