Optimal Permutation Codes for Uniform SourcesThis work was completed at Bell Labs, Lucent Technologies.
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Permutation codes (PC's) are vector quantizers whose code vectors are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal PC design is identical to optimal entropy-constrained scalar quantizer (ECSQ) design. However, contradicting intuition and previously published assertions, there are finite block length PC's that perform better than the best ones with asymptotically large length; thus, there are PC's whose performances cannot be matched by ECSQ's. Specific counterexamples are created with a memoryless uniform source.
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Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)