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2 is not the same as the 4-tuple in Figure 111 They are different because the rst component in Figure 111 ( Alice ) is not the same as the rst component in Figure 112 ( 100 ) and the second component in each tuple is also different A domain is de ned as a set of possible values We typically think of the values as being conceptually similar rather than completely random, but this depends on the semantics of the problem being considered For example, a domain could be all the possible values for an hourly pay rate, all the possible colors of paint used in a manufacturing process, all the possible rst and last names for our employees, or even the textual content of all the possible suggestions written on scraps of paper and placed in a suggestion box.

Up to this point,7 the applications described were never really dynamic they were either static (civil engineering, time-related, and so on) or very slow moving (maritime or agriculture for instance). When switching to the road sector, or more generally to the transportation sector (see Fig. 11.5), the speed of the mobile increases and this piece of data has to be taken into account. The rst terrestrial application of GNSS technology to the car industry was the navigation system this will be described in the following sections. Another way to use GNSS receivers has been in eet management systems, still in use today. The idea is to integrate a GNSS (GPS for the rst trials) receiver and a telecommunication system; the satellite navigation part allows individual locations of the equipped trucks or vehicles to be obtained, and the telecommunication part is designed to get all the positioning data from the mobiles back to a central management unit. Thus, the central controller has a real-time visibility of the status and positioning reports of the eet. The rst implementations concerned truck eets used for various delivery tasks, soon followed by taxi companies or bus eets. In the case of trucks, the main objective was to follow the goods and to check the route for both surveillance purposes and retrieval after theft. As presented later in this chapter, these rst trials led to well developed auto systems. In the case of a taxi eet, the goal was to optimize the service to customers, as what they want is to optimize their time and to be sure the taxi will arrive quickly. Knowing the location of all the taxis in your eet is bound to help in getting one to the customer s place as quickly as possible. Once again,

In this churn example, the voice mail members were coded as 1 and the nonmembers coded as 0. This is an example of reference cell coding, where the reference cell refers to the category coded as zero. Odds ratios are then calculated as the comparison of the members relative to the nonmembers or with reference to the nonmembers. In general, for variables coded as a and b rather than 0 and 1, we have ln [OR(a, b)] = g(x = a) g(x = b) = (b0 + b1 a) (b0 + b1 b) = b1 (a b)

Average length of an optimal code. Prove that L(p1 , . . . , pm ), the average codeword length for an optimal D-ary pre x code for probabilities {p1 , . . . , pm }, is a continuous function of p1 , . . . , pm . This is true even though the optimal code changes discontinuously as the probabilities vary. Unused code sequences. Let C be a variable-length code that satis es the Kraft inequality with an equality but does not satisfy the pre x condition. (a) Prove that some nite sequence of code alphabet symbols is not the pre x of any sequence of codewords. (b) (Optional ) Prove or disprove: C has in nite decoding delay. Optimal codes for uniform distributions. Consider a random variable with m equiprobable outcomes. The entropy of this information source is obviously log2 m bits. (a) Describe the optimal instantaneous binary code for this source and compute the average codeword length Lm . (b) For what values of m does the average codeword length Lm equal the entropy H = log2 m (c) We know that L < H + 1 for any probability distribution. The redundancy of a variable-length code is de ned to be = L H . For what value(s) of m, where 2k m 2k+1 , is the redundancy of the code maximized What is the limiting value of this worst-case redundancy as m Optimal codeword lengths. Although the codeword lengths of an optimal variable-length code are complicated functions of the message probabilities {p1 , p2 , . . . , pm }, it can be said that less probable

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