Furthermore, analysis and determination of support region for quasilogarithmic
quantizers and the same source were presented in [8].
The superscript u stands for user and may refer to either Alice, in which case the
quantizer is [Q.sup.A] (*) , or to Bob, for which the
quantizer is [Q.sup.B] (*) .
The system is operating on frame-by-frame basis, where the
quantizer is adapted to the short-term estimate of the frame variance.
Section 2 demonstrates the problem discussed and the CHO network; distributed protocol and logarithmic
quantizer are illustrated there in detail.
Q(s) is transfer function of ideal
quantizer and [Q.sub.e](s) is error characteristics of known saw-tooth shape with zero mean and peak-to-peak value of one quantization step q.
Hemami, "Sequential design of multiple description scalar
quantizers," in Proc.
The G.711 standard (G.711
quantizer) defines fixed length coding that provides high quality of reconstructed signal for fixed bit rates [1].
The same bit allocation is utilized in all implemented modifications of the BTC algorithm, so that, for the given fixed bit rates of the three abovementioned
quantizers, the total bit rate depends on the frame size, which is the only variable left in Eq.
for l=1: L [Q.sup.l] = {[c.sup.1.sub.l]} // initialization by using [C.sup.2.sub.1] [M.sup.l] = mean([Q.sup.l]) // [M.sup.l] is the centroid of
quantizer [Q.sup.l] for k=2:K D(i,j) = d{[M.sup.i], // compute the initial distance [c.sup.k.sub.j]) idx = compute indicator(D) // idx(j), an indicator computed as Algorithm 3, for j=1:L [Q.sup.idx(j)] = [Q.sup.idx(j)] // update
quantizers [union] [c.sup.k.sub.j] [M.sup.idx(j)] = // update
quantizer centroids mean([Q.sup.idx(j)]) Algorithm 3 Computing idx from distance matrix D for l = 1: L idx(l) = l //initialize indicator for i = 1:L-1 for j = i +1:L if D(idx(i), i) + D(idx(j), j) < D(idx(j), i) + D(idx(i), j) swap(idx(i), idx(j)) // swap indicator 4.
where N is the average number of quantization levels of
quantizers [Q.sub.1] and [Q.sub.2], whereas f is compression factor.
For each of the k range two
quantizers are designed: 1)
quantizer which provides the smallest quantization error or minimum distortion if the assumed distribution of the amplitude of the signal source is described by Laplacian function and 2)
quantizer which provides the smallest quantization error when assumed distribution of sources is described by Gaussian function.
On our disposal are k
quantizers designed for variances [[??].sup.2.sub.p], p = 1, ..., k, that have been log-uniformly distributed in the dynamic range of variances B = 20 log ([[sigma].sub.max] / [[sigma].sub.min])