By Toby Berger, Lee D. Davisson (auth.)

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Moreover, since the optimum quantizer has nearly uniformly spaced Ievels, some of these Ievels become many times more probable than others, which Ieads to difficult buffering problems. Furthermore, when the buffer overflows it is usually because of an inordinately high local density of large-magnitude source outputs. This means that the per-letter MSE incurred when buffer overflows occur tends to be even bigger than o2. 34 Rate Distordon Theory and Data Compression As a result, the performance of coded quantizers with buffer overflow properly taken into account may be considerably poorer than that shown in Figure 6, especially at high rates.

This specification requires at most log(N + 1) bits. The second part of the codeward gives the location of the w(xN ) ones by indexing the ( ~(xN ) ) possible location patterns given w(xN ). 1 bits. (xN))] + 1- \(N)). The N-t (log (N + 1) + 2) term clearly vanishes as N ..... Using Stirling's approximation and the ergodie theorem. N- t log (N N ) = N-t log N N! (N-w(x ))! l- 0 logO- (1-0)log(l-0) The last step also follows from the strong law of large numbers (a special case of the ergodie theorem, N-1 w(x N) N7..

There is no general relation between li 8 (R,A,N) and D 8 (R,A,N). Analogaus to redundancy in the noiseless case, define the discrepancy of a rate R code C N as the difference between actual performance for the given dass of codes: We next consider source coding for a dass of sources. A sequence of codes {C N}~ =1 will be said to be universal if d6 ( C N) ~ 0 in some sense for a1l (} • The various types of universal fixed rate codes with a fidelity criterion are defined by the type of convergence exactly as in the noiseless case.

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