 code is that the codewords are not calculated symbol by symbol (or by symbol blocks of predefined length), but by symbol sequences having any arbitrary length. The max- imum sequence length is defined by the precision of the coding arithmetic, namely the maximum number of bits that the machine can handle for any given codeword. As we have seen, the use of m-bit codewords makes it possible to represent proba- bilities with an accuracy of 1 x 2-m. Referring to Fig. 10.1, for instance, the five- bit codewords define subintervals having a minimum width of 2-5 = 1/32 = 0.03125, exactly. This number defines the minimum difference allowed between ymbol-sequence probabilities. As previously explained, the source's probability distribution, including joint proba- bilities up to some maximum order, must be calculated at first by the encoding machine. As soon as this initial calibration round is complete, encoding can then be performed on the fly, meaning that the codeword assignment (encoding) is performed almost at the same rate as the message-sequence symbols a1, A2. input encoder. Such a construction consists of building up the right codeword prefix corresponding to the beginning of the received sequence. Referring to Fig. 10.1, for instance, the reception of a = b as the first sequence symbol does not make it possible to conclude between 00, 01, or 10 as possible two-bit prefixes. If the next symbol is a2 = b, the machine can make the choice of 01, since the interval of the sequence bb is described by this prefix, as the figure indicates. If the next symbol is a3 = a, the prefix is changed to 011, and SO on. This shows that the encoder builds the codeword prefix practically at the same rate as symbols come in, because more than one symbol may be required to make the choice of the next prefix bit. If the choice is unique, this means that the codeword is complete, and basically, that the sequence is ended. For instance, the three-symbol sequence bbc in Fig. 10.1 yields the final five-bit codeword 01001. In contrast, the