Introduction DSC using Convolutional Codes DSC Using Turbo Codes Other DSC Work

Consider
a communication system with two correlated signals, **X** and **Y**
(see Figure 1). Assume that
**X** and **Y** come from two separate sources that cannot
communicate
with each other, that is, the signals are encoded independently or are
“distributed”. The receiver,
on the other hand, can see both encoded signals and can perform joint
decoding.
A sensor system composed of low-complexity spatially separated sensor
nodes,
sending correlated information to a central processing receiver, is an
example of such system. What is the minimum encoding rate required such
that **X** and **Y** can still be recovered perfectly?

If a joint encoder
and
a joint decoder are used, the minimum combined rate for probability of
decoding error to approach zero is simply the joint entropy H(**X**,**Y**).
Surprisingly, as proven by Slepian and Wolf in 1973 [1], a combined
rate
of H(**X**,**Y**) is sufficient even if the correlated signals
are
encoded separately. According
to the Slepian-Wolf coding theorem, the achievable rate region for
distributed
sources X and Y is given by

The Slepian-Wolf
theorem
is an encouraging conceptual basis for distributed source coding but
until
today the theoretical limits have not yet been achieved, nor have been
closely approached, by practical applications.
In [6], Pradhan and Ramchandran demonstrate the intuition behind
Slepian-Wolf
coding by providing a solution for **X** and **Y** separated by
a
maximum Hamming distance.
Pradhan and Ramchandran also developed the DISCUS (Distributed Source
Coding
Using Syndromes) method [6][7].
In DISCUS, instead of sending the codeword representing **X**, the
syndrome
of the codeword coset is sent and the receiver decodes by choosing the
codeword in the given coset that is closest to **Y**.
DISCUS, with trellis and lattice encoding, was used in their study to
encode
correlated Gaussian sources.
However, it was not shown that the techniques clearly approached the
information-theoretic
bound. The objective of this
project is to find practical coding techniques that can perform close
to
the Slepian-Wolf achievable rate region and would be effective for
different
types of **X** and **Y** correlation.