# Mutual Information, the Linear Prediction Model, and CELP Voice Codes
## 9 Estimated versus Actual CELP Codec Performance
Grab every dish of sugar,\" spoken by a female [6]. Therefore, we use 4 bits/sample as our reference point for toll quality speech for these two sentences. We then subtract from the rate of 4 bits/sample the rates in bits/sample we associate with each of the CELP codec components as estimated from Sections 7 and 8. For \"We were away...,\" we see from Table 4 that the 10 th order model of the voiced mode has a \(MMSPE=0.078\), which corresponds to a mutual information reduction of 1.84 bits/sample. For this highly voiced sentence, we estimate the mutual information corresponding to the adaptive codebook as 0.5 bits/sample, and at a codec rate of 8000 bits/s, the fixed codebook mutual information would correspond to 0.5 bits/sample. Silence corresponds to about only 1 percent of the total utterance. If we sum these contributions up and subtract them from 4 bits/sample, we obtain \(4-2.84=1.16\) bits/sample. Inspecting Table 5, the rates for the AMR and G.729 codecs at this MOS are 1.1 bits/sample, so there is surprisingly good agreement. From Table 4, we see that for the utterance, \"A lathe is...,\" there is broader mix of speech modes, including significant silence and unvoiced components. Neither of these modes had to be dealt with for the sentence \"We were away... \". Since silence is almost never perfect silence and usually consists of low level background noise, we associate the bits/sample for silence with a silence detection/comfort noise generation (CNG) method [25]. From Table 6, we see that G.726 with CNG is about 1.2 bits/sample lower than G.726, even though it occurs for only a 0.3685 portion of the utterance. For the short-term prediction, the \(MMSPE=0.0656\), which corresponds to a mutual information of 1.96 bits/sample. The adaptive codebook contribution at 8 kbits/s can again be estimated as 0.5 bits/sample, and the fixed codebook component estimated at 0.5 bits/sample. If we now combine all of these estimates with their associated relative frequencies of occurrence as indicated in Table 4, we obtain a total mutual information of \(0.5265(1.96+0.5)+1.2+0.5(0.0771)=2.5\) bits/sample. Subtracting this from 4 bits/sample, we estimate that the CELP codec rate in bits/sample for an MOS = 4.0 would be 1.5 bits/sample. We see from Table 6 that for AMR and G.729, their rate is 1.0 bits/sample. This gap can be narrowed if the adaptive codebook contribution \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sequence**} & \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Autocorrelation Coefficients for V, ON, H**} & \multicolumn{2}{c}{**Mean Square**} \\  & & \multicolumn{2}{c}{**Average Frame Energy for UV**} & \multicolumn{2}{c}{**Prediction Error**} & \multirow{2}{*}{**Probability**} \\ \hline \multirow{6}{*}{(active speech level: \(-18.1\) dBov) (sampling rate: 8 kHz)} & V & [1.0 8217 0.5592 0.3435 0.1498 0.0200 & \multirow{2}{*}{0.0656} & \multirow{2}{*}{0.5265} \\  & & \(-0.0517\)\(-0.0732\)\(-0.0912\)\(-0.1471\)\(-0.2340\)] & & \\ \cline{2-5}  & ON & [1.0 8495 0.5962 0.3979 0.2518] & & 0.0432 & 0.0093 \\ \cline{2-5}  & H & [1.0 2.0709 0.2808 0.1576 0.1182] & & 0.7714 & 0.0186 \\ \cline{2-5}  & UV & 0.1439 & 0.1439 & 0.0771 \\ \cline{2-5}  & S & & & 0.3685 \\ \hline \multirow{6}{*}{(active speech level: \(-16.5\) dBov) (sampling rate: 8 kHz)} & V & [1.0 8014 0.5176 0.2647 0.0432 \(-0.1313\) & \multirow{2}{*}{0.0780} & \multirow{2}{*}{0.9842} \\  & & \(-0.2203\)\(-0.3193\)\(-0.3934\)\(-0.4026\)\(-0.3628\)] & & \\ \cline{1-1} \cline{2-5}  & ON & [1.0 8591 0.7215 0.6128 0.5183] & & 0.0680 & 0.0053 \\ \cline{1-1} \cline{2-5}  & H & & & 0 \\ \cline{1-1} \cline{2-5}  & UV & & & 0 \\ \cline{1-1} \cline{2-5}  & S & & & 0.0105 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Composite source models for narrowband speech sentences [6]. V, voiced; UV, unvoiced; ON, onset; H, hangover; S, silence.