This is fundamentally an issue of information theory
http://en.wikipedia.org/wiki/Information_theory
The problem is, you can only do so much compression before you start getting losses. That said, a good academic library should have some journals on the topic which would discuss current research.
If you can get online access, try ProQuest. Here's a sample abstract.
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Low-Complexity Approaches to Slepian-WoIf Near-Lossless Distributed Data Compression
T P Coleman, A H Lee, M Medard, M Effros. IEEE Transactions on Information Theory. New York: Aug 2006. Vol. 52, Iss. 8; pg. 3546
Abstract (Summary)
This paper discusses the Slepian-Woif problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple "source-splitting" strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover,when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian-WoIf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML)sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the "mm-sum" iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions,we show that selecting easily constructable "expander"-style low-density parity check codes (LDPC5) as syndrome-formers admits a positive error exponent and therefore provably good performance. [PUBLICATION ABSTRACT]
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Nope, I don't claim to understand what they're saying. But it certainly sounds impressive!
