Locally decodable source coding

Abstract

Source coding is accomplished via the mapping of consecutive source symbols (blocks) into code blocks of fixed or variable length. The fundamental limits in source coding introduces a tradeoff between the rate of compression and the fidelity of the recovery. However, in practical communication systems many issues such as computational complexity, memory capacity, and memory access requirements must be considered. In conventional source coding, in order to retrieve one coordinate of the source sequence, accessing all the encoded coordinates are required. In other words, querying all of the memory cells is necessary. We study a class of codes for which the decoder is local. We introduce locally decodable source coding (LDSC), in which the decoder need not to read the entire encoded coordinates and only a few queries suffice to retrieve a given source coordinate. Both cases of having a constant number of queries and also a scaling number of queries with the source block length are studied. Also, both lossless and lossy source coding are considered. We show that with constant number of queries, the rate of (almost) lossless source coding is one, meaning that no compression is possible. We also show that with logarithmic number of queries in block length, one can achieve Shannon entropy rate. Moreover, we provide achievability bound on the rate of lossy source coding with both constant and scaling number of queries.