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From: Mok-Kong Shen on 14 Jul 2010 08:59
[Addendum] One could also treat in a similar way homophones of digrams
or even trigrams. The space of trigram is 26^3=17576. Since 2^16=65536,
a homophone mapping of trigrams to 16 bits could presumably be fairly
satisfactorily done. However, the large table size 2^16 is obviously
a substantial disadvantage. A conceivable compromise is first to
assign each individual trigram T a numerical range Tr in [0, 2^16-1]
and choose a function f(x) that does a bijective pseudo-random
mapping in [0, 2^16-1] and obtain f(Tr) as the homophones of T. A
permutation polynomial f(x) mod 2^16 could obviously be chosen to
serve this purpose, noting that f^(-1)(x), for given x, can be
numerically computed.

M. K. Shen
From: Maaartin on 14 Jul 2010 12:16
On Jul 14, 2:59 pm, Mok-Kong Shen <mok-kong.s...(a)t-online.de> wrote:
> [Addendum] One could also treat in a similar way homophones of digrams
> or even trigrams.

Continuing this idea you reinvent compression.
From: Mok-Kong Shen on 14 Jul 2010 16:06

> Continuing this idea you reinvent compression.

Homophone is in the counter direction of compression!!

M. K. Shen
From: Maaartin on 14 Jul 2010 17:17
On Jul 14, 10:06 pm, Mok-Kong Shen <mok-kong.s...(a)t-online.de> wrote:
> > Continuing this idea you reinvent compression.
>
> Homophone is in the counter direction of compression!!

Single character homophone in fact do expand the text. Trigram
homophones as you described them pack 3 chars into 2, this is a
compression, at least when compared to the most straightforward
representation using 3 bytes. Using good compression always leads to
homophony, otherwise the compressed text would be still compressible.
From: Mok-Kong Shen on 14 Jul 2010 17:25
Maaartin wrote:
> Mok-Kong Shen wrote:
>>> Continuing this idea you reinvent compression.
>>
>> Homophone is in the counter direction of compression!!
>
> Single character homophone in fact do expand the text. Trigram
> homophones as you described them pack 3 chars into 2, this is a
> compression, at least when compared to the most straightforward
> representation using 3 bytes. Using good compression always leads to
> homophony, otherwise the compressed text would be still compressible.

I wrote "The space of trigram is 263=17576. Since 216=65536, ....".
The space of 3 characters of the normal alphabet is 'expanded' to the
full space of 16 bits.

M. K. Shen
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