Computer Science – Information Theory
Scientific paper
2004-08-02
Proceedings of the 41st Annual Allerton Conference on Communication, Control, and Computing; Monticello, IL; 2004
Computer Science
Information Theory
10 pages
Scientific paper
We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We show that duals of capacity achieving codes for the BEC yield codes which approach the minimum possible rate for the BEQ. In contrast, low density parity check codes cannot achieve the minimum rate unless their density grows at least logarithmically with block length. Furthermore, we show that duals of efficient iterative decoding algorithms for the BEC yield efficient encoding algorithms for the BEQ. Hence our results suggest that graphical models may yield near optimal codes in source coding as well as in channel coding and that duality plays a key role in such constructions.
Martinian Emin
Yedidia Jonathan S.
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