A Cognitive Source Coding Scheme for Multiple Description 3DTV Transmission

Abstract

Multiple Description Coding has recently proved to be an effective solution for the robust transmission of 3D video sequences over unreliable channels. However, adapting the characteristics of the source coding strategy (Cognitive Source Coding) permits improving the quality of 3D visualization experienced by the end-user. This strategy has been successfully employed for standard video signals, but it can be applied to Multiple Description video coding for an effective transmission of 3D signals. The chapter presents a novel Cognitive Source Coding scheme that improves the performance of traditional Multiple Description Coding approaches by adaptively combining traditional predictive and Wyner-Ziv coders according to the characteristics of the video sequence and to the channel conditions. The approach is employed for video+depth 3D transmissions improving the average PSNR value up to 2.5 dB with respect to traditional MDC schemes.

Appendix

Given the original pixel $x_m(i,j)=s_m(i,j)+k \ 2^{n_{\max ,m}}$ ($k \in \mathbb Z$) and its reconstructed value $x_{r,m}(i,j)=s_m(i,j)+e_m(i,j)+k \ 2^{n_{\max ,m}}$ after the quantization of the transformed syndromes, a wrongly-decoded pixel $x^\prime _{r,m}(i,j)$ can be written as

$$\begin{aligned} \begin{array}{ll} x^\prime _{r,m}(i,j)&=s_m(i,j)+e_m(i,j)+k^\prime 2^{n_{\max ,m}} \\&=x_m(i,j)+e_m(i,j)+d_k \ 2^{n_{\max ,m}}, \end{array} \end{aligned}$$

(13.8)

with $k^\prime \in \mathbb Z$, $k^\prime \ne k$, and $d_k=k^\prime - k$. In the following, we will omit pixel position indexes $(i,j)$ and description index $m$ for the sake of conciseness.

The probability of a wrong decoding is

$$\begin{aligned} P_W=P\left[x^\prime _r \ne x_r\right]=P\left[ |x_p - x^\prime _r | < |x_p - x_r| \right], \end{aligned}$$

(13.9)

which can be written as

$$\begin{aligned} P_W=P\left[ |-d-e-d_k 2^{n_{\max }} | < |-d -e | \right], \end{aligned}$$

(13.10)

where $d$ is the difference between the current pixel and its predictor. Given $d$ and $d_k$, the probability $P_W$ becomes

$$\begin{aligned} P_W=\left\{ \begin{array}{ll} P[e \le -d - d_k \ 2^{n_{\max }-1}]&\quad \text{ if} \quad d_k>0, \\ P[e > -d - d_k \ 2^{n_{\max }-1}]&\quad \text{ if} \quad d_k \le 0. \\ \end{array} \right. \end{aligned}$$

(13.11)

The error $e$ is modelled with a normal distribution $\mathcal N (0,\sigma _{e,q})$ with mean $0$ and variance $\sigma ^2_{e,q} \simeq A^2 \varDelta ^2/12$ (where $A$ is a scaling factor related to the adopted inverse transform since quantization is perform on the coefficients $\varvec{S}$). The choice of a normal distribution is motivated by the fact that $e$ is a linear combination of independent quantization errors generated in the transform domain and inversely-transformed. From Eq. (13.1) it is possible to infer that $2^{n_{\max }-2} \le |d| < 2^{n_{\max }-1}$, and therefore, the probability of a wrong decoding becomes

$$\begin{aligned} P_W=\displaystyle Q\left( \frac{|d+d_k \ 2^{n_{\max }-1} |}{\sigma _{e,q}}\right). \end{aligned}$$

(13.12)

From Eq. (13.12) it is possible to write the inequalities

$$\begin{aligned} \begin{array}{ll} P_W&\displaystyle \le Q\left( \frac{2^{n_{\max }-2}+|d_k| \ 2^{n_{\max }-1}}{\sigma _{e,q}}\right) \\&\displaystyle \le Q\left( \frac{1.5 \ 2^{n_{\max }-1} }{\sigma _{e,q}}\right) = Q\left( \frac{2.6 \ 2^{n_{\max }} }{A \ \varDelta }\right). \end{array} \end{aligned}$$

(13.13)

As a matter of fact,

$$\begin{aligned} \displaystyle Q\left( \frac{2.6 \ 2^{n_{\max }} }{A \ \varDelta }\right) \le 0.017 \qquad \Rightarrow \qquad \displaystyle \varDelta < \frac{1.24 \cdot 2^{n_{\max }}}{A}=5.6 \cdot 2^{n_{\max }} \end{aligned}$$

(13.14)

where $A$ is assumed to be approximately equal to $1/4$ for the inverse $4 \times 4$ transform defined in the standard H.264/AVC (considering both transform amplification and rescalings).