Abstract
This paper investigates the design of channel-optimized scalar quantizers with erasure correcting codes over binary symmetric channels (BSC). A new scalar quantizer with uniform decoder and channel-optimized encoder aided by erasure correcting code is proposed. The lower bound for performance of the new quantizer with complemented natural code (CNC) index assignment is given. Then, in order to approach it, the single parity check code and corresponding decoding algorithm are added into the new quantizer encoder and decoder, respectively. Analytical results show that the performance of the new quantizers with CNC is better than that of the original quantizers with CNC and natural binary code (NBC) when crossover probability is at a certain range.
Highlights
1 Introduction For a uniform scalar source, it is well known from [1] that if over a noiseless channel, in terms of the mean squared distortion (MSD), the uniform scalar quantizer is optimal among all quantizers
Joint source and channel coding has attracted much attention in [2,3], which has been seen as a promising scheme for effective data transmission over wireless channels due to its ability to cope with varying channel conditions [4,5,6]
One is that the encoding cells in quantizer’s encoders are designed to be affected by the transmission channel characteristics, for example [7], or the final positioning of the reconstruction in decoders depends on channel characteristics, for example [8], which is called as channel optimized quantizers
Summary
For a uniform scalar source, it is well known from [1] that if over a noiseless channel, in terms of the mean squared distortion (MSD), the uniform scalar quantizer is optimal among all quantizers. The usual goal to design an index It is known from [7] that for uniform decoder and channel-optimized encoder quantizer with CNC index assignment, as crossover probability increases to a certain value, some of the encoding cells appear to be empty, which is discovered in [22,23]. These empty cells can be looked upon as redundancy, just like a form of implicit channel coding.
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