ession rate is defined asr = 1 - L/7. The compression rate should not be confused with coding efficiency. The latter measures how close the mean codeword length is to the source entropy, which we know to be the ultimate lower bound. This observation intuitively suggests that efficient codes do not lend themselves to efficient compression. Yet, this correct conclusion does not mean that further compression towards the limits given by the source entropy is impossible, as we will see in the last section in this chapter, which is concerned with block coding. The previous examples with the A-Z English-character source shown in Table 8.5 (Shannon-Fano coding) and Table 9.1 (Huffman coding) represent good illustrations of the data compression concept. Here, we shall take as a comparative reference the codeword length of five bits used by ASCII to designate the restricted set of lower case or upper case letters. With the results from the two aforementioned examples, namely 6 See: R. G. Gallager, Variations on a theme by Huffman. IEEE Trans. Inform. Theory, 24 (1978), 668-74. 9.2 Data compression L** = 4.577 bit/symbol and = bit/symbol, respectively, we obtain: (Shannon-Fano), (Huffman). The above compression rates may look modest, and indeed they are when considering the specific example of the English language. Recall that the mean codeword length cannot be lower than the source entropy H. Thus, there exists no code for which L < H. Since, in this example, the source entropy is H = 4.185 bit/symbol, we see that the compression rate is intrinsically limited to r=1 - 4.185/5 = 16.3%. But this limit cannot be reached, since no code can beat the Huffman code, and r = 15.76%, thus, represents the really achievable compression limit for this source example. Here we come to a fine point in the issue of data compression. It could have been intuitively concluded that, given a source, the compression rate is forever fixed by the coding algorithm that achieves compression. But as it turns out, the compression rate also depends on 