Extremely Low-Delay Coding of Gaussian Sources with Side Information at the Decoder
One of the innovations brought about by the emerging and thriving of wireless sensor networks is Wyner-Ziv (WZ) coding, in other words, lossy source coding with side information at the decoder. While previous work mostly focuses on using capacity-achieving codes to approach the Wyner-Ziv bound, which naturally introduces huge block lengths and huge delay, we study extremely low-delay Wyner-Ziv coding of Gaussian sources. Three related but distinct problems are considered. The first involves scalar quantization and scalar noiseless coding of the quantization indices when only decoder has access to side information. Under high-resolution assumptions and appropriately defined decodability constraints, the optimal quantization level density is conjectured to be periodic. The performance of variable-length coding with uniform quantization is also characterized. The results are then incorporated in predictive Wyner-Ziv coding for Gaussian sources with memory, and optimal prediction filters are numerically designed so as to strike a balance between maximally exploiting both temporal and spatial correlation and limiting the propagation of distortion due to occasional decoding errors. Finally, zero-delay schemes are also employed in transform coding with small block lengths, where the Gaussian source and side information are transformed separately with the premise that corresponding transform coefficient pairs exhibit good spatial correlation and minimal temporal correlation. For the specific source-side information pairs studied, it is shown that transform coding, even with a small block-length, outperforms predictive coding.
In the second part, we study the zero-delay joint source-channel coding (JSCC) problem of transmitting a Gaussian source over a Gaussian channel in Wyner-Ziv scenario. To achieve zero-delay, after applying scalar quantization to the source, the properly scaled analog information, namely the quantization error, is superimposed on the scaled digital information, i.e., the quantized source, and then transmitted. At the decoder, several decoding schemes are proposed. It is shown that all the schemes, when optimized over all related parameters, are superior to pure analog transmission for high enough correlation between source and side information. The robustness of one of the proposed Hybrid Digital Analog (HDA) schemes against varying channel and side information conditions is also compared with that of the purely analog scheme.
Since JSCC WZ problem is intimately related with JSCC without side information but with bandwidth expansion factor 2, in the third part we investigated the mapping method from 1-D source space to 2-D channel space which integrates HDA schemes into spiral mapping or pure analog mapping. The performance comparison with existing coding algorithms is also presented.