# Network data compression

Our research in the area of network data compression has been mainly on the following:

## Network scalable data compression

In wireless sensor networks, one could have multiple sensors measuring correlated information. In these cases, for efficient data collection, we would like to opportunistically utilize the dependencies between multiple observations, even when we may not have complete access to these dependent observations. Moreover, we may want to collect this information in a scalable manner, by asking for a better approximation (higher quality) of the sensory information in multiple stages, with the receivers having access to some correlated sensory information (side-information) which is not available to the encoder. In particular, the side-information scalability could be such that the node with access to the better quality side-information can decode with minimum delay. In a sense, this is an opportunistic scheme since we want to aggressively deliver the source to the better decoder, which should not be jeopardized simply because of the existence of worse decoders in the network. We posed this problem and have solved this completely for Gaussian sources with quadratic distortion measures.

We have solved an open problem (posed by Steinberg and Merhav, 2004) on multi-stage successive refinement with side information, when successive stages are for decoders with improving quality side-information. In solving this problem, we identified the general notion of successive refinability of data compression with side-information.

We studied the multi-user successive refinement problem (posed in Pradhan and Ramchandran, 2002), where the users are connected to a central server through links with different noiseless capacities. Each user requires to reconstruct the source in a scalable manner. We provided the best known achievable strategy for the two-user, two-layer case and the complete characterization of the rate-distortion region for the Gaussian source under the mean-squared error (MSE) distortion measure.

## Compression with encoder side-informations

Suppose that one wants to distribute data to two receivers, each of which have a correlated version (side-information) of the data to be sent. Suppose further that the encoder has access to these side-informations. If the data is to be sent losslessly, then there is a classical result using Slepian-Wolf coding that shows that encoder knowledge is not useful in reducing transmission rate (though it might help encoding complexity). We investigated the case where the data is only needed approximately (with distortion). In this case, we have shown that encoder knowledge actually helps in transmission rate for Gaussian sources and quadratic distortion measures (also see longer version).

If the source was binary and the receivers had (different) partial knowledge of the source i.e., they had erased” versions of the source) then we have also shown a complete characterization for some special cases of the problem. This also shows the value of encoder knowledge and leads to some interesting analogies between the Gaussian and the erasure cases.