RESULTS

    Table-1 below summarizes the results of the algorithm developed in this project for the five image sets described in the Data Set Section, using D=128. The H(X) in the first column represents the bit-rate achieved by the bit- plane encoding of the images. The second column shows the joint encoding bit rate minus the individual coding bit-rate for the images, which is the asymptotic bound established by Slepian and Wolf. The third column is the bit-rate achieved by the algorithm developed in this project; while the the final column represents the percentage of pixels incorrectly coded by the algorithm.

    It needs to be noted that for the three images, boats, bridge and harbour, the algorithm comes very close to the established bound with very small errors. It should be recalled that the Slepian-Wolf bound is stated for highly correlated source pairs; and it is obvious that differences greater than +/- 64 in a range of 256 values clearly violate the high correlation (or linear relationship) rule. Hence, for these three images, the algorithm works very efficiently. On the other hand, in airfield and peppers, which are images with many sharp gray level transitions, the algorithm is less successful in reaching the established bound. However, it should be noted the algorithm still does very well compared to the individual coding of these two images, which is the other criterion to analyze the efficiency of the algorithm.

Table-1) The comparison of the individual (only X), joint (X and Y available both at the encoder and the decoder) and the distributed coding bit-rates and the distributed coding error, with D=128 and N=256
                 Note the very low error and the high proximity of distributed coding bit rate to joint coding bit rate.
                 Note that the H(X) with distributed source coding values for airfield and pepper are not as close to the joint entropy rate; however, they are still very much below the individual entropy values.

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Table-2 below is included to show how the entropy values decrease as N increases for a given value of D. The table confirms that the choice of using multiple sub-cosets as described in the Algorithm Section gives better results.

Table-2) Comparison of the H(X) values achieved for different N values at D=128.
                 H((X)) values are the entropy values that the algorithm achieves
                 Note that the H values decrease as N increases.

Tables 3a and 3b below show that the algorithm in most cases can easily achieve the bit rate established by the Slepian-Wolf bound for small D values. This is because as D decreases, the number of cosets constructed decreases, and this translates into fewer bit rates for coset transmission.

Image H(X,Y)-H(Y) H with N=1 H with N=4 H with N=16 H with N=32 Airfield 4.53 4.00 3.99 3.99 3.98 Boats 3.96 3.75 3.82 3.83 3.82 Bridge 4.64 3.22 3.30 3.30 3.30 Harbour 4.07 3.72 3.72 3.71 3.69 Peppers 4.08 3.95 3.97 3.97 3.97

Table-3a) D=16

Image H(X,Y)-H(Y) H with N=1 H with N=4 H with N=16 H with N=32 Airfield 5.14 4.97 4.98 4.98 4.97 Boats 4.12 4.30 4.31 4.29 4.28 Bridge 5.22 4.14 4.15 4.14 4.11 Harbour 4.43 4.46 4.38 4.33 4.31 Peppers 4.18 4.56 4.66 4.67 4.66

Table-3b) D=32

Table-3) The comparison of the Slepian-Wolf bound (H(X,Y)-H(Y)) to the H values achieved by the algorithm for D=16 in Table-3a) and D=32 in Table-3b)
                 Note that for relatively small values of D, the algorithm does as good as the Slepian-Wolf bound very easily

ABSTRACT
INTRODUCTION
PROBLEM DESCRIPTION and PRIOR WORK
DATA SET
ALGORITHM
RESULTS
CONCLUSIONS
REFERENCES