Estimating Rate-Distortion for Multiple Description Coding Based on Zero Padding

In the studies related to multiple description coding (MDC), applying zero padding not only improves the spatial correlation between descriptions but also increases their sizes. However, as we pad more zeros, the spatial correlation does not improve linearly. Therefore, the distortion is not reduced as the same amount when the size increases. In this paper, we focus on how to efficiently find an acceptable trade-off between the number of padded zeros and the increase of distortion in MDC. In this paper, we propose two distortion estimations for MDC with zero padding based on spatial quincunx distribution, which are standard deviation for distortion estimation and triangular linear approximation distortion estimation (TLA-DE) to efficiently calculate the distortion for the number of padded zeros atthe horizontal direction. In order to search for the acceptable number of padded zeros, we propose two search methods, Naïve Search and Best Division Search, which are both based on the proposed rate-distortion trade-off indicator. Our experiments result show that the worst error of distortion estimation by TLA-DE is up to 18%, but the average is 5.5% with 95% confidence level. The executing time of best division search is about two times faster than that of naïve search for 11 test sequences. To sum up, we confirm that the acceptable trade-off between rate and distortion in low computational complexity can be found by using the best division search on TLA-DE.