Kivanc Ozonat
ozonat@stanford.edu

Project Topic: Distributed Source Coding Schemes for Highly
               Correlated Still Images

Project Description: 

The encoder-decoder schemes used in practice are symetric in the sense
that either both the encoding and the decoding are done separately or both 
the encoding and decoding are done jointly. Naturally, the joint
encoding-decoding scheme is preferred as it results in coding with lower 
bit rates for highly correlated image data. On the other hand, joint
encoding requires higher complexity, as well as communication between
encoders. Hence, it is highly desirable to come up with a coding scheme
that does the encoding separately and the decoding jointly, provided that    
the achieved bit rate is close to that of the joint encoding-decoding
scheme.

The research paper, " Noiseless Coding of Correlated Information Sources," 
written by D. Slepian and J.K. Wolf in 1973 shows that, at least
theoratically, it is possible to achieve the same bit rate with the
asymetric scheme (separate encoding-joint decoding) that the symetric
joint coding scheme (joint encoding-joint decoding) achieves. Further,
this theoratical work has been tried to turn into practical use within the
last few years through the use of error correcting codes. This project
aims to use a scheme with the error correcting codes to provide a low bit
rate (close to that achieved by the symetric joint coding scheme) in
asymetric coding of still images.

The work to be carried out for this project includes providing a general
scheme for the coding of images, as well as making use of error correcting
codes to achieve a desirable bit rate within this scheme. 

The general scheme is as below:

(i) Production of a highly correlated still image through subsampling a
still image (preferably by 2) and filtering it. This image is to be used
only in the decoder, not in the encoder.

(ii) Encoding the original image by gray code and bit plane encoding. The
gray code will prevent the problems with the large number of bit changes 
in passing from one gray level value to the next one, such as 127 to 128.

(iii) Using an error correcting code, such as the Hamming code, to divide
the original image pixel values into cosets so that the members of each
coset is to have the maximum possible Hamming distance between them. This
is going to be the key in achieving the low bit rate. Note that it is the 
coset value that is to be transmitted.

It should be noted that the actual problem is to be able to define a
measure for and a trade-off between "correlatedness" of images and the 
bit rate achieved. Given that the correlated image is formed through a 
linear combination of the original image in this project, it may be
possible to use linear prediction filters to figure out the linearity
relationship between the two images by sending the first few values of the
original image without error correcting codes. Then, having the decoder
supported with this relationship, it will be possible for the decoder to
always find the right value in the transmitted coset.      


 References:

 D. Sleepian and J.K. Wolf, "Noiseless Coding of Correlated Information
Sources," IEEE Trans. Information Theory, July 1973

 S. Pradhan and K. Ramchandran, "Distributed Source Coding Using Syndromes  
Design and Construction"

 S. Pradhan and K. Ramchandran, "Distributed Source Coding: Symetric Rates
and Applications to Sensor Networks"