ords, a cumulative density function of the probabilities is constructed, as seen in Figure 3.14. Imagine now that we wish to send the sequence of codewords ASZ. Arithmetic coding achieves this by scaling each interval after the generation of each individual codeword. This is shown in Figure 3.15. The rules are straightforward: When you code a word, the new interval is the interval occupied in the previous iteration according to the symbol probability. For example, at the first step when coding the word A, you will notice from Figure 3.14 that it occupies the interval 0.4 to 0.72; therefore, the interval in the next iteration of coding is 0.4 to 0.72. To subsequently code the word S, given that the interval is now only 0.4 to 0.72, the next interval must lie somewhere in between. Therefore, the lower value is 0.4 + 0.72 X (0.72 - 0.42) = 0.6304, and the upper is 0.4 + 0.92 X (0.72 - 0.42) = 0.6944. The same rule continues: Calculate the width of the interval and work out the relative positions of the symbols within it at each stage. Finally, conveying a number between 0.69312 and 0.6944 uniquely identifies the code sequence ASZ. The sequence can be calcu- lated by the decoder if it has a copy of the original cumulative density function. In practice, binary rather than floating-point arithmetic is used (Ghanbari, 2003). Hybrid Codecs: Exploiting Spatial, Temporal, and Statistical Redundancy Hybrid codecs employ spatial temporal, and statistical redundancy. Spatial and statistical redundancy is employed in image codecs, such as JPEG. Spatial temporal, and statistical redundancy is employed in standard video codecs, such as MPEG-1, MPEG-2, MPEG-4, H.261, H.263, H.264, and H.26L. The block diagram of a hybrid spatial temporal and statisti- cal DCT codec is shown in Figure 3.16. Bitrate and Quality Variations Great progress has been made in the last few decades in techniques for the data reduction or compression of digital video signals. The challenge has been to find techniques that provide high compression ratios wit