# Mutual Information, the Linear Prediction Model, and CELP Voice Codes
## 9 Estimated versus Actual CELP Codec Performance  
The analyses determining the mutual information in bits/sample between the input speech and the short-term linear prediction, the adaptive codebook, and the fixed codebook individually, are entirely new and provide new ways to analyze CELP codec performance by only analyzing the input source. In this section, we estimate the performance of a CELP codec by analyzing the input speech source to find the mutual information provided by each CELP component about the input speech and then subtract the three mutual informations from a reference codec rate in bits/sample for a chosen MOS value to get the final estimate of the rate required in bits/sample to achieve the target MOS. For waveform speech coding, such as differential pulse code modulation (DPCM), for a particular utterance, we can study the rate in bits/sample versus the mean squared reconstruction error or SNR to obtain some idea of the codec performance for this input speech segment [14; 15]. However, while SNR may order DPCM subjective codec performance correctly, it does not provide an indicator of the actual difference in subjective performance. Subjective performance is most accurately available by conducting subjective listening tests to obtain mean opinion scores (MOS). Alternatively, reasonable views of subjective performance can be obtained from software such as PESQ /MOS [12]. We use the latter. In either case, however, MOS cannot be generated on a per-frame basis as listening tests and PESQ values are generated from longer utterances. Therefore, we cannot use the per-frame estimates of mutual information from Section 7 and need to calculate estimates of mutual information over longer sentences. To this end, Table 4 contains autocorrelations for two narrowband (200 to 3400 Hz) utterances sampled at 8000 samples/s, \"We were away a year ago,\" spoken by a male and \"A lathe is a big tool. Grab every dish of sugar,\" spoken by a female, including the decomposition of the sentences into five modes, namely voiced, unvoiced, onset, hangover, and silence, and their corresponding relative frequencies. The two utterances are taken from the Open Speech Repository [27]. These data are excerpted from tables in Gibson and Hu [6] and are not calculated on a per-frame basis but averaged over all samples of the utterance falling in the specified subsource model. From Table 4, the voiced subsource models are set as \(N=10\)th order, with the 1 in the column vector representing the \(a_{0}\)th \(=1\) term. The onset and hangover modes are modeled as \(N=4\)th order autoregressive (AR). We see from this table that the sentence \"We were away... \" is voiced, with a relative frequency of 0.98, and that the sentence \"A lathe is a big...,\" has a breakdown of voiced (0.5265), silence (0.3685), unvoiced (0.0771), onset (0.0093), and hangover (0.0186). The _MMSPEs_ for each mode are also shown in the table. We focus on G.726 as our reference codec. Generally, G.726 adaptive differential pulse code modulation (ADPCM) at 32 kbits/s or 4 bits/sample for narrowband speech is considered to be \"toll quality\". G.726 is selected as the reference codec because ADPCM is a waveform-following codec and is the best-performing speech codec that does not rely on a more sophisticated speech model. In particular, G.726 utilizes only two poles and six zeros, and the parameter adaptation algorithms rely only on polarities. G.726 will track pure tones as well as other temporal waveforms in addition to speech. In G.726, no parameters are coded and transmitted, only the quantized and coded prediction error signal. Finally, both mean squared reconstruction error or SNR and MOS have meaning for G.726, which is useful since SPER plays a role in estimating the change in mutual information from the log ratio of entropy powers. From Tables 5 and 6, G.726 achieves a PESQ/MOS of about 4.0 for 4 bits/sample and for both sentences, \"We were away a year ago,\" spoken by a male speaker and \"A lathe is a big tool.