By Wu F.

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Instead, we try to highlight the core ideas behind the theory and make them more intuitively understood for further practical research on visual data compression and communication. The readers, who are interested in the entire information theory, can find information on this subject by Shannon [4] and Cover and Thomas [5]. Let us assume a finite symbol alphabet A = fa0 , a1 , , aq 1 g, whose probabilities of occurrence are p = fp0 , p1 , , pq 1 g, satisfying ∑i pi = 1. These probabilities are known.

It is from a finite alphabet and satisfies the AEP. The sequence of symbols Sn = fS1 , S2 , , Sn g is sent over the channel so that the receiver can reconstruct the sequence. Assume the one stage coding is considered. We map the sequence onto a codeword Y n (Sn ) and send the codeword over the channel. The receiver looks at his received sequence Yˆ n and makes an estimation Sˆn of the sequence Sn that was sent. The receiver makes an error if (n) Sˆn 6= Sn . 66) yˆn sn where I is the indicator function and g(yˆn ) is the decoding function.

13) Ω where Ω is the support set of the random variable. If S is a zero-mean Gaussian variable, that is, S h(S) = = f (s) ln f (s)ds, f (s) s2 2σ 2 ES2 1 + ln 2πσ 2 , 2σ 2 2 1 1 = + ln 2πσ 2 , 2 2 1 1 = ln e + ln 2πσ 2 , 2 2 1 = ln 2πeσ 2 . 19) Changing the base of the logarithm, the differential entropy for a zero-mean Gaussian variable is h(S) = 1/2 log 2πeσ 2 . 2 Source Coding With the above basic information theory definitions, we are ready to discuss source coding. The objective of the so-called source coding is to find a source code C mapping all possible values of a random variable S in the alphabet A to a set of finite length of binary strings (also called codewords).