Response to the following problem:
In Example 1, repeat the encoding using m = 6. Comment on your results.
Example 1:
We will encode the sequence 1 3 2 1 with parameters shown in Table . First we need to select the word length m. Note that Cum_Count{\) and Cum_Count{2) differ by only 1. Recall that the values of Cum_Count will get translated to the endpoints of the subintervals. We want to make sure that the value we select for the word length will allow enough range for it to be possible to represent the smallest difference between the endpoints of intervals. We always rescale whenever the interval gets small. In order to make sure that the endpoints of the intervals always remain distinct, we need to make sure that all values in the range from 0 to Total_Count, which is the same as Cum_Count(3), are uniquely represented in the smallest range an interval under consideration can be without triggering a rescaling. The interval is smallest without triggering a rescaling when l^"^ is just below the midpoint of the interval and u^"^ is at three-quarters of the interval, or when u^"^ is right at the midpoint of the interval and /^"^ is just below a quarter of the interval. That is, the smallest the interval [/^"\ M^"^] can be is one-quarter of the total available range of 2m values. Thus, m should be large enough to accommodate uniquely the set of values between 0 and Total_Count.
