1 research outputs found
Coding for Computing Irreducible Markovian Functions of Sources with Memory
One open problem in source coding is to characterize the limits of
representing losslessly a non-identity discrete function of the data encoded
independently by the encoders of several correlated sources with memory. This
paper investigates this problem under Markovian conditions, namely either the
sources or the functions considered are Markovian. We propose using linear
mappings over finite rings as encoders. If the function considered admits
certain polynomial structure, the linear encoders can make use of this
structure to establish "implicit collaboration" and boost the performance. In
fact, this approach universally applies to any scenario (arbitrary function)
because any discrete function admits a polynomial presentation of required
format.
There are several useful discoveries in the paper. The first says that linear
encoder over non-field ring can be equally optimal for compressing data
generated by an irreducible Markov source. Secondly, regarding the previous
function-encoding problem, there are infinitely many circumstances where linear
encoder over non-field ring strictly outperforms its field counterpart. To be
more precise, it is seen that the set of coding rates achieved by linear
encoder over certain non-field rings is strictly larger than the one achieved
by the field version, regardless which finite field is considered. Therefore,
in this sense, linear coding over finite field is not optimal. In addition, for
certain scenarios where the sources do not possess the ergodic property, our
ring approach is still able to offer a solution