ression than the fourth datafile, corresponding to ordinary English. There is no need to go through tedious statistics to conclude beforehand that increasing the length of such English-text datafiles would give compression ratios increasingly closer to the limit of r = 15.76%. Clearly, this is because the probability distribution of long English-text sequences will duplicate with increasing fidelity the standard distribution for which we have found this compression limit. On the other hand, shorter sequences of only a few characters might have significantly higher compression ratios. To take an extreme example, the datafile "AAA" (for American Automobile Association) takes 1 bit/symbol and, thus, has a compression ratio of = 1 - 1/5 = 80%. If we take the full ASCII code for reference (7 bit/character), the compression becomes r = 1 - 1/7 85.7%. The above examples have shown that for any given datafile, there exists an optimal (Huffman) code that achieves maximum data compression. As we have seen, the code- word assignment is different for each datafile to be compressed. Therefore, one needs to keep track of which code is used for compression in order to be able to recover the orig- inal, uncompressed data. This information, which we refer to as overhead, must then be transmitted along with the compressed data, which we refer to as payload. Since the over- head bits reduce the effective compression rate, it is clear that the overhead size should be the smallest possible relatively to the payload. In the previous examples, the overhead is simply the one-to-one correspondence table between codewords and symbols. Using five-bit (ASCII) codewords to designate each of the character symbols, and a five-bit field to designate the corresponding compressed codewords makes a ten-bit overhead per datafile symbol. Taking, for instance, datafile 3 (Table 9.2), there are 13 symbols, which produces 130 bits of overhead. It is easily calculated that the payload represents 111 bits, which leads to a total of 130 + 111 = 241 bits f