PPMZ v7.6 by Charles Bloom cbloom@mail.utexas.edu

report is in output-bits-per-input-byte on the Calgary Corpus

* indicates the Best item

Coder   :    0      1      2      3      4      5      6     Guess
Order   :    8      5      4      3      2      1      0     varies

BIB     :  1.801  1.798* 1.823  2.075  2.618  3.442  5.208   1.798*
BOOK1   :  2.305  2.267* 2.272  2.438  2.889  3.595  4.531   2.267*
BOOK2   :  1.925  1.923* 1.961  2.241  2.874  3.765  4.758   1.923*
GEO     :  4.639  4.640  4.629  4.598  4.476* 4.620  5.648   4.476*
NEWS    :  2.306* 2.315  2.346  2.619  3.233  4.114  5.084   2.306*
OBJ1    :  3.718  3.713  3.711* 3.740  3.844  4.435  5.668   3.711*
OBJ2    :  2.287* 2.334  2.392  2.696  3.070  4.069  6.056   2.287*
PAPER1  :  2.284* 2.290  2.299  2.441  2.888  3.797  4.948   2.284*
PAPER2  :  2.286  2.276* 2.282  2.405  2.842  3.612  4.600   2.276*
PIC     :  0.811* 0.814  0.816  0.835  0.833  0.840  1.017   0.811*
PROGC   :  2.316* 2.330  2.339  2.466  2.869  3.814  5.177   2.316*
PROGL   :  1.518* 1.566  1.601  1.866  2.371  3.292  4.580   1.518*
PROGP   :  1.568* 1.603  1.622  1.802  2.252  3.340  4.841   1.568*
TRANS   :  1.282* 1.331  1.366  1.716  2.331  3.461  5.401   1.282*
AVERAGE :                                                    2.202

Local Order Estimating (LOE) Coders
Coder   :    9     10     11     12     13       Best

BIB     :  1.771* 1.776  1.791  1.777  1.833    1.771
BOOK1   :  2.235* 2.243  2.265  2.258  2.251    2.235
BOOK2   :  1.886* 1.890  1.907  1.894  1.942    1.886
GEO     :  4.581  4.590  4.601  4.604  4.475*   4.475
NEWS    :  2.280* 2.281  2.293  2.285  2.371    2.280
OBJ1    :  3.731  3.726  3.729  3.723* 3.877    3.723
OBJ2    :  2.302  2.297* 2.302  2.291  2.453    2.297
PAPER1  :  2.265  2.263* 2.269  2.266  2.393    2.263
PAPER2  :  2.244* 2.246  2.260  2.257  2.302    2.244
PIC     :  0.798  0.800  0.803  0.804  0.793*   0.793
PROGC   :  2.297  2.295* 2.306  2.295* 2.446    2.295
PROGL   :  1.505* 1.506  1.519  1.505* 1.574    1.505
PROGP   :  1.552  1.552  1.562  1.550* 1.653    1.550
TRANS   :  1.273* 1.276  1.291  1.277  1.347    1.273
AVERAGE :  2.194  2.196  2.207  2.199  2.265    2.185


Technical Notes:

The LOE coders use this heuristic:

each assigns an Order Rating (OR) to each PPM Order
the Order with the highest OR is coded from
All higher orders are updated, lower ones are not

the OR heuristics for each coder are:

 let P = probability of Most Probable Symbol in context
 let E = probability of Escape

Coder9  : OR = P
Coder10 : OR = 20*ln(P) + ln(E)
Coder11 : OR =  6*ln(P) + ln(E)
Coder12 : OR = P*ln(P) + (1-P)*( ln(E) - 10*ln(2) )
Coder13 : OR = P*ln(P) + (P-E-1)*8*ln(2)

These are equivalent to using the Lowest Order Entropy (H)
with

Coder9  : H =  log2(1/P)
Coder10 : H =  log2(1/P) + (1/20)*log2(1/E)
Coder11 : H =  log2(1/P) + (1/6)*log2(1/E)
Coder12 : H =  P*log2(1/P) + (1-P)*( log2(1/E) + 10 )
Coder13 : H =  P*log2(1/P) + (1-P)*8 + E*8

I think it should be easy to see from each of these how
they are trying to minimize output length.

i.e. Coder12 guesses there is a probability P for a length of log2(1/P)
to be output, and if P is not output, then an Escape of length log2(1/E)
is written followed by 10 bits from lower orders.