M-CELP — technical documentation

The Mitsubishi CELP speech codec: a 3.6 kbit/s analysis-by-synthesis coder for 8 kHz telephony speech. This directory describes how it works, stage by stage, at the level of detail needed to read or modify the implementation in src/.

At a glance

Sample rate	8 kHz, mono
Audio format	μ-law, 8 bits per sample
Frame	320 samples = 40 ms
Bit stream	18 bytes per frame = 3.6 kbit/s
Structure	1 frame = 2 half-frames = 4 subframes of 80 samples
Prediction	10th-order short-term, one long-term (pitch) predictor
Excitation	adaptive codebook + fixed codebook, both gain-scaled

CELP means code-excited linear prediction. A short-term linear predictor models the vocal tract; what it cannot predict — the excitation — is chosen from two codebooks by synthesising every candidate and keeping the one whose output sounds closest to the input. "Closest" is measured through a perceptual weighting filter, so the coder spends its bits where the ear will notice.

Two things distinguish this codec from the ITU-T G.729 family it otherwise resembles. Its frame is four times longer, which buys the low bit rate at the cost of delay. And its encoder carries a full spectral noise-suppression front end: the signal that reaches the analysis has already been cleaned.

Reading order

Start with architecture for the shape of both pipelines, then follow the signal. If the vocabulary is unfamiliar, keep glossary.md open alongside; if you would rather see the thing before the theory, walkthrough.md takes one real frame apart.

document	subject
architecture.md	frame structure, the two pipelines, what state survives a frame
bitstream.md	the 18-byte frame and its fourteen fields
noise-suppression.md	the encoder front end: spectrum, critical bands, voice activity, suppression
lpc.md	short-term prediction, line spectral frequencies, their quantiser
weighting.md	the perceptual weighting filter — how "closest" is measured
encoder-loop.md	analysis by synthesis: the target, the impulse response, the memories
pitch.md	long-term prediction: the adaptive codebook and its two searches
fixed-codebook.md	the six innovation structures and the 16-bit index that selects one
gain.md	the conjugate gain codebook and the energy predictor behind it
synthesis.md	the decoder: synthesis, postfiltering, concealment
fixed-point.md	the arithmetic model everything is computed in
tables.md	reference data: band edges, class layout, quantiser dimensions
testing.md	how the implementation is verified, and what is not covered
walkthrough.md	one real frame, field by field, with the values it decodes to
glossary.md	the vocabulary, as used in this codebase

Bit budget

One frame carries 138 bits of parameters plus a suppression flag:

parameter	per frame	bits
Line spectrum, predictor mode + first stage	1	8
Line spectrum, second stage (two halves)	1	12
Pitch lag, absolute (first subframe of each half)	2	8 each
Pitch lag, relative (second subframe of each half)	2	5 each
Fixed-codebook index	4	16 each
Gain index	4	7 each
Frame suppression flag	1	1
		139

The remaining 5 bits of the 144 transported are framing. The fixed codebook takes 64 of the 138 parameter bits — nearly half the frame — which is where a CELP coder's quality comes from at this rate.

Per second, that is 25 frames of: one line spectrum, 100 pitch lags and codebook indices, and 100 gains. The spectral envelope is updated 25 times a second and the excitation 100 times — a ratio that reflects how much faster the excitation changes than the vocal tract does.

Conventions in these documents

Fixed-point quantities are written in Q notation: Q15 means a signed 16-bit value scaled by 2¹⁵, so 1.0 is not representable and 32767 stands for 0.99997. See fixed-point.md.

Frame always means 320 samples, half-frame 160, subframe 80. Several stages work per half-frame rather than per frame or per subframe, and the distinction matters.