M-Channel Multiple Description Coding with Two-Rate Predictive Coding and Staggered Quantization
Upul Samarawickrama, Jie Liang
2008
Data Compression Conference (DCC), Proceedings
A low complexity multiple description (MD) coding method is proposed to generate M descriptions. Consider the MD coding of a stationary correlated source. We first fictitiously partition the source into sample blocks of size M , i.e., M polyphases. Each description encodes all input samples, but with a variable bit rate that depends on the indices of the sample and the description. A special DPCM encoder is used in each description, where each sample is predicted from the reconstructed samples
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... n the same description. The prediction error is uniformly scalar-quantized and entropy coded. In the i-th description, the prediction error of the i-th sample in each block is coded with rate R 0 and other errors are coded with rate R 1 , where R 1 < R 0 . As a result, the prediction error for a given sample is quantized at R 0 in one description and at R 1 in M − 1 descriptions. Different DPCM encoders are designed such that the lower rate encodings in different descriptions are mutually refinable. To achieve this, the quantizers for the low rate prediction errors in the M − 1 descriptions are staggered such that they jointly result in a finer uniform quantizer. Since quantization of a prediction error induces a shifted partition on the source sample, to ensure the staggered quantizer partitions on the source samples rather than on the prediction errors, the predictions are also quantized using the same quantization step [1] . At the decoder side, each description uses a separate DPCM decoder to obtain an initial reconstruction of the entire sequence. The final reconstruction is obtained by combining the reconstructions from all received descriptions. When all the descriptions are available, the reconstruction for sample x(n) is obtained from the description in which x(n) is predictively coded at rate R 0 . When only a subset of the descriptions is received, we first try to reconstruct x(n) from the description where it is coded at rate R 0 , if available. Otherwise, x(n) is jointly reconstructed from all received descriptions in which it is coded at rate R 1 . Under high rate quantization assumptions, it can be shown that the average distortion D k when there are k descriptions received is given by where 2 is the entropy power of the prediction error. The constant 2 k is equal to 2 when k = 1 and k = M . For 1 < k < M, it is given by This MD coding method can also be used with memoryless sources. In that case, there is no any prediction and the source samples are directly quantized using unform quantizers. The quantizers for lower rate encoding will be staggered as explained above. When applied to image coding, the proposed method has a performance that is competent with the state-of-the-art MD image coders. Reference [1] V. Vaishampayan and S. John, Balanced interframe multiple descreption video compression, Proc.
doi:10.1109/dcc.2008.57
dblp:conf/dcc/SamarawickramaL08
fatcat:t4sfleieqrax7ilonex5s2rrfu