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Channel-matched hierarchical table-lookup vector quantization for finite-state channels without feedback

The encoder of a vector quantizer (VQ) is usually implemented by computing the distortion between the input vector and each codevector in the codebook and finding the codevector which results in minimum distortion. The decoder however is a simple table-lookup. Chang et al. (1985) have proposed a hierarchical table-lookup vector quantizer (HTVQ) in which the encoder is implemented using a table-lookup in multiple stages. The basic idea behind channel-optimized VQ (COVQ) is to design the VQ encoder and decoder such that the end-to-end average distortion after encoding, transmission over the channel, and decoding is minimized. Like a regular VQ, a COVQ suffers from the high encoding complexity problem. A channel-matched HTVQ (CM-HTVQ) which provides the simplicity of an HTVQ is examined. To investigate the advantage of using the new procedure in designing VQs, we consider three systems. In a fully-adaptive (FA) system, the channel state information (CSI) is available at the encoder and decoder. The CSI is only available at the decoder in a decoder-adaptive system. When there is no access to the CSI at all, we use a non-adaptive system.