access icon free Linear filtering methods for fixed rate quantisation with noisy symmetric error channels

© The Institution of Engineering and Technology
Received 26/01/2013, Accepted 28/03/2013, Revised 09/03/2013, Published

This study considers linear filtering methods for minimising the end-to-end average distortion of a fixed-rate source quantisation system. For the source encoder, both scalar and vector quantisation are considered. The codebook index output by the encoder is sent over a noisy discrete memoryless channel whose statistics could be unknown at the transmitter. At the receiver, the code vector corresponding to the received index is passed through a linear receive filter, whose output is an estimate of the source instantiation. Under this setup, an approximate expression for the average weighted mean-square error (WMSE) between the source instantiation and the reconstructed vector at the receiver is derived using high-resolution quantisation theory. Also, a closed-form expression for the linear receive filter that minimises the approximate average WMSE is derived. The generality of framework developed is further demonstrated by theoretically analysing the performance of other adaptation techniques that can be employed when the channel statistics are available at the transmitter also, such as joint transmit–receive linear filtering and codebook scaling. Monte Carlo simulation results validate the theoretical expressions, and illustrate the improvement in the average distortion that can be obtained using linear filtering techniques.

Inspec keywords: filtering theory; receivers; statistics; transmitters; Monte Carlo methods; vector quantisation

Other keywords: end-to-end average distortion; channel statistics; linear filtering methods; linear receive filter; approximate expression; vector quantisations; receiver; Monte Carlo simulation; WMSE; scalar quantisations; codebook scaling; noisy discrete memoryless channel; noisy symmetric error channels; weighted mean square error; codebook index output; transmitter; joint transmit–receive linear filtering; fixed-rate source quantisation system; high-resolution quantisation theory

Subjects: Filtering methods in signal processing; Codes; Other topics in statistics; Monte Carlo methods

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