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ined to analyse the general case.

(5.2)
H(X) denotes the entropy of the output signal X and H(X|Y) denotes the conditional entropy of the input signal (X) given the output signal (Y). Equation 5.2 states that the average information conveyed per symbol equals the source entropy minus conditional entropy.

The solution for rate and distortion problem can be achieved by minimising the rate-distortion function given below:

(5.3)
Where R is the information rate and D is an average distortion. I(X;Y) which describes the average mutual information between an original source (X : where the source selects symbols from an alphabet X) and a reconstructed data (Y),. Equation 5.1 says that for a given maximum average distortion Dmax, the rate distortion function R(D) defines the lower bound for the transmission bit-rate. The minimization is over all conditional probability distributions P (yj|xi) for which the joint distribution P (yj ; xi) satisfies the expected distortion constraint. The set of defines all the conditional distributions of P (yj|xi)

Conditional probability p(y | x) is considered as an inherent and fixed property of the communicational channel defined by the characteristics of the noise in the channel. The joint probability distribution of X and Y is entirely determined by the nature of the channel and the distribution of messages, f(x), to be transmitted over the channel. Under these constraints, the objective is to maximize the rate of information communicating over the noisy channel. The appropriate measure for this is known as the mutual information, The theoretical upper bound of mutual information is know as the channel capacity and is given by:

C = \max_{f} I(X;Y).\!

Channel capacity has the subsequent property related to transmitting information at rate R, where R is generally bits per message or symbol. For a communication system where the information rate R is < C and coding error ε is > 0, it is always possible to transmit with an arbitrarily small error, such that the maximal probability of error is less than an acceptable level ε. In addition, for any rate R > C, it is unachievable to transmit with arbitrarily small block error. The objective of channel coding is to find nearly optimal codes that can be used to transmit data over an error pone channels with an acceptable error at a rate close to channel capacity. However, in most practical video communication systems, the quality of transmitted video varies due to variations in the allowable bandwidth limitations. Thus, the maximum perceptual quality, under the rate constraint, can be achieved by the solving the following:

(5.4)
The set of Φ is defines the solution space of conditional distributions P (yj|xi) for which the joint distribution P (yj;xi) satisfies the expected rate constraint.

1.33D视频的联合信源信道编码——1.3 Joint Source and Channel Coding for 3D Video

In this section, the frame work of the proposed JSCC to improve the performance of colour-plus-depth 3D video transmission over wireless channels is discussed. The difference between the JSCC for 2D video and the JSCC for 3D video is that the traditional 2D video has only one source component while the 3D video consists of two source components: colour video and depth map.

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