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The compression-complexity trade-off of lossy compression algorithms that arebased on a random codebook or a random database is examined. Motivated, inpart, by recent results of Gupta-Verd\'{u}-Weissman (GVW) and their underlyingconnections with the pattern-matching scheme of Kontoyiannis' lossy Lempel-Zivalgorithm, we introduce a non-universal version of the lossy Lempel-Ziv method(termed LLZ). The optimality of LLZ for memoryless sources is established, andits performance is compared to that of the GVW divide-and-conquer approach.Experimental results indicate that the GVW approach often yields bettercompression than LLZ, but at the price of much higher memory requirements. Tocombine the advantages of both, we introduce a hybrid algorithm (HYB) thatutilizes both the divide-and-conquer idea of GVW and the single-databasestructure of LLZ. It is proved that HYB shares with GVW the exact samerate-distortion performance and implementation complexity, while, like LLZ,requiring less memory, by a factor which may become unbounded, depending on thechoice or the relevant design parameters. Experimental results are alsopresented, illustrating the performance of all three methods on data generatedby simple discrete memoryless sources. In particular, the HYB algorithm isshown to outperform existing schemes for the compression of some simplediscrete sources with respect to the Hamming distortion criterion.

Lossy Compression in Near-Linear Time via Efficient Random Codebooks and Databases