Receiver Only Optimized Semi-Hard Decision VQ for Noisy Channels

This paper proposes a new receiver optimized semihard-decision vector quantization (SHDVQ) for noisy channels, as a technique to alleviate the drastic increase in distortion incurred when the output of the classical source optimized vector quantizer (SOVQ) is sent over a noisy channel. The advantages of the proposed method are that it is computationally simple, requires minimal extra storage, and can be implemented solely at the receiver; thus allowing the encoder to be independent of channel conditions. Another advantage is that it can be used in conjunction with an index assignment to obtain the benefits of index assignment (IA). The decoder considers errors and erasures based on thresholding the log-likelihood ratio (LLR) of the bits comprising the transmitted index. Then, the proposed decoder computes the output as a linear combination of the codebook vectors based on the erasure bit locations and the IA. A novel performance analysis is presented, where the overall distortion is expressed as a convex combination of the distortion with an ideal IA and the distortion with random IA. The analysis is used to find the erasure threshold that minimizes the overall distortion. Finally, Monte-Carlo simulation results are presented to corroborate the derived theoretical expressions.