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Choose a Dither option to specify how pixels of available colors are combined to simulate colors not available in the current palette. Dithering can improve color quality, but it increases the file size. Choose from the following options: from the table that most closely approximates the specified color. Not dithering can produce smaller files but unsatisfactory colors.

Figure 8-17

lognormal shadowing are the same for all four models. The model parameters can be found in [8, Table 2]. For the remainder of this work, we consider only channels CM1 CM3, where the assumption that the zero padding is longer than the delay spread of the channel impulse response holds (some realizations of channel CM4 violate this assumption). However, we note that the CM4 performance is very similar to that of CM3. Because of the quasi-static nature of the channel, we must consider the performance of MB-OFDM over ensembles of channel realizations. As we will discuss later, the number Nc of realizations we use must be suf ciently large to capture the true behavior of the channel model. This is a problem when performing system simulations since the simulation program must be run separately for all Nc channel realizations, which leads to high computational complexity (see also Section 11.6.3 for a discussion of the computational requirements). 11.3.2 Frequency Domain Channel Description

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Linear regression is used to approximate the relationship between a continuous response variable and a set of predictor variables. However, the response variable is often categorical rather than continuous. For such cases, linear regression is not appropriate, but the analyst can turn to an analogous method, logistic regression, which is similar to linear regression in many ways. Logistic regression refers to methods for describing the relationship between a categorical response variable and a set of predictor variables. In this chapter we explore the use of logistic regression for binary or dichotomous variables; those interested in using logistic regression for response variables with more than two categories may refer to Hosmer and Lemeshow [1]. To motivate logistic regression, and to illustrate its similarities to linear regression, consider the following example.

This expression identi es the past, present and future sequences, and their statistical independence, a fact resulting from the use of the discrete hidden Markov source model This property will be used in following sections The discrete hidden Markov source model is very suitable for describing the behaviour of the output of a trellis encoder, which generates a sequence of related or dependent symbols that are input to a discrete memoryless channel Let B1 , B2 , B3 , be a sequence of branches from the trellis of a given encoder, which assigns values of a discrete alphabet A B each transition or branch, and let X 1 , X 2 , X 3 , be the sequence of values taken from a discrete alphabet A X , such that X j is the output assigned a given transition or branch B j .

Optimal codes for dyadic distributions. For a Huffman code tree, de ne the probability of a node as the sum of the probabilities of all the leaves under that node. Let the random variable X be drawn from a dyadic distribution [i.e., p(x) = 2 i , for some i, for all x X]. Now consider a binary Huffman code for this distribution. (a) Argue that for any node in the tree, the probability of the left child is equal to the probability of the right child. (b) Let X1 , X2 , . . . , Xn be drawn i.i.d. p(x). Using the Huffman code for p(x), we map X1 , X2 , . . . , Xn to a sequence of bits Y1 , Y2 , . . . , Yk(X1 ,X2 ,...,Xn ) . (The length of this sequence will depend on the outcome X1 , X2 , . . . , Xn .) Use part (a) to argue that the sequence Y1 , Y2 , . . . forms a sequence of fair coin ips [i.e., that Pr{Yi = 0} = Pr{Yi = 1} = 1 , independent of 2 Y1 , Y2 , . . . , Yi 1 ]. Thus, the entropy rate of the coded sequence is 1 bit per symbol. (c) Give a heuristic argument why the encoded sequence of bits for any code that achieves the entropy bound cannot be compressible and therefore should have an entropy rate of 1 bit per symbol. Relative entropy is cost of miscoding. Let the random variable X have ve possible outcomes {1, 2, 3, 4, 5}. Consider two distributions p(x) and q(x) on this random variable.

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