By Toby Berger, Lee D. Davisson (auth.)
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Upon observing an output block of length N, among the Variable Rate Coding with Distordon 67 codewords of distortion less than D- e /2, fmd the one of minimum rate, ifany. If there is no codeward with distortion less than D- e /2, make a random choice. P rJ. ) e/2 PM j J Qn M + 2 + N I\ (D -e) + e + (sup r. ) e /2PM , j which is abritrarily close to ~ (D) for small enough distortion for 0 = k is /2 ~D """'-e +PM J €, large enough N. The average Prob [no codeward of distortion less than D in the kth code J Further details can be found in [ 9) .
The conccpt of trcc cncoding of sourccs is most readily introduced by means of an cxamplc. Thc trcc codc dcpictcd in Figure 5 provides a means for encoding the binary sourcc of Examplc 1 of Lccturc 4. 00 l· l ·~· 00 Iu... 000000 000 000001 001 000110 1110 000111 Oll 111000 100 lt1001 101 111110 110 111111 111 ...... -·· Figure 5. A Binary Tree Code "''h mapl Thc codc consists of the 2 3 = 8 different words of length n = 6 that can bc formcd by concatenating the three pairs of binary digits encountered along a path from the root to a leaf.
Figure 5. A Binary Tree Code "''h mapl Thc codc consists of the 2 3 = 8 different words of length n = 6 that can bc formcd by concatenating the three pairs of binary digits encountered along a path from the root to a leaf. The code word corresponding to each such path is indicated in Figurc 5 directly to the right of the leaf at which the path terminates. Since thcrc arc 26 = 64 different words of length 6 that might be produced by ·the source, thcre usually will not be a code word that matches the source word exactly.