MLow LSF and LPC

Encodings - mlow-lsf-lpc

ENC-08 - status: review - audio

MLow carries an internal frame's spectral envelope as range-coded LSF indices, reconstructed into an order-16 quantized NLSF vector and interpolated per-subframe to LPC coefficients.

LSF coding is MLow-specific, NOT stock SILK codebook coding. Order is 16. All symbols are read with the cumulative-CDF primitive (decode_cdf, u16 cumulative tables), not the ICDF path. Symbols are read from the range coder (see mlow-rangecoder).

Wire read order (per internal frame).

1. stage-1 selector   ; 1 symbol, CDF = lsf_sel[sel]
2. stage-1 grid        ; 1 symbol, CDF chosen by (match, stage1)
3. stage-2 residuals   ; 16 symbols, coeff k from lsf_stage2[stage1][config][grid][k]
4. extra               ; 1 symbol, 3-symbol static CDF lsf_extra

Stage-1 selector. Row index sel:

sel = 0   if intf == 0          (first internal frame)
sel = 2   if prev_stage1 != 0
sel = 1   otherwise

intf is the internal-frame index (0,1,2) within the 60 ms packet; prev_stage1 is the stage-1 value of the previous internal frame. Decoded value is stage1.

Match / predictor reset.

match = (intf != 0) AND (stage1 == prev_stage1)

When match is false, the cross-frame pitch/LTP predictor state (gain index, filter index, lag, fractional lag) MUST be reset to -1 before decoding the rest of the frame. prev_stage1 MUST then be set to the current stage1.

Stage-1 grid. CDF selected as:

match  && stage1 != 0   -> lsf_grid.match1
match  && stage1 == 0   -> lsf_grid.match1_alt
!match && stage1 != 0   -> lsf_grid.match0_alt
!match && stage1 == 0   -> lsf_grid.match0

Stage-2 residuals. Exactly 16 symbols, coefficient k using CDF lsf_stage2[stage1][config][grid][k], where config is the MLow config (0/1). Per coefficient, raw-symbol count nraw = len(CDF) - 2.

Extra read. One extra symbol from the 3-symbol static CDF lsf_extra. Always fires on the standard decode path (num_subfr >= 2).

NLSF reconstruction. Map (stage1, grid, stage2[16]) plus the previous internal frame's NLSF to qlsf[0..16] (radians, 0..PI). The wire grid is the stage-1 codebook index; value 16 denotes the conditional ("cond") centroid derived from the previous frame:

qlsf = 2*cbhalf[grid] + we^T * qlvls(stage2)

i.e. twice the selected stage-1 half-centroid plus the weighted stage-2 levels, with conditional prediction from the previous NLSF when the cond centroid is selected.

LSF -> LPC interpolation. For each of the 4 subframes interpolate between the previous frame's NLSF (prev) and current qlsf using interpolation row 0:

w = [0.55, 0.88, 1.0, 1.0]   (per subframe j)
ilsf[k] = (1-w[j]) * prev[k] + w[j] * qlsf[k]   ; ilsf = qlsf when w == 1.0

On reset (no valid previous NLSF) prev MUST be initialized from current qlsf. Each interpolated NLSF MUST be converted to monic LPC coefficients A[0..16] (A[0] = 1) via the NLSF->A transform, then bandwidth-expanded until it forms a stable all-pole filter (chirp factor 1 - iter*0.001 per iteration; stability bound |reflection| <= 0.9995).

Encoder side (LSF quantization). Select wire indices so the decoder reconstructs the same qlsf the encoder synthesizes with. Compute the analysis NLSF (forward A->NLSF) from the analysis LPC, then run the LSF vector quantizer:

• RD weights per LSF are the inverse spectral-envelope magnitude 1/sqrt(|A(e^jw)|^2 * scale), scale = 1/min.
• A Mahalanobis shortlist (VQ_temp) over the stage-1 centroids (plus the cond centroid for conditional coding) selects surv survivors.
• Per survivor, stage-2 residuals qerr = wie^T*(lsf - 2*cbhalf[qi1]) / qstep, rounded and per-coefficient clamped to [min_qi, max_qi]; an RD beam then refines one coefficient at a time minimizing 0.5*order*log2(werr)*RDw_adj + bits.
• Reconstructed LSFs MUST be spaced so consecutive distances exceed the per-coefficient min_dist table before the RD metric is evaluated.

The chosen qi[0] is the wire grid (stage-1 index, or 16 for the cond centroid); qi[1..16] are the 16 stage-2 indices.

Notes. The selector, grid, and stage-2 CDFs are runtime-built (not static rodata), carried as a table blob alongside the decoder; the stage-2 CDF is indexed [stage1][config][grid][coeff]. The forward A->NLSF is the fixed-point silk_A2NLSF transform (Q16 coefficients -> Q15 NLSF, scaled to radians).

Parent: mlow
Requires: mlow, mlow-rangecoder, mlow-frame
Breakdown: mlow-decoder, mlow-encoder, mlow-excitation, mlow-noise, mlow-synthesis

Implemented by

Flavor	Status	Source	Notes
whatsapp-rust	working	history - blame - commits ed12f35 c697c36 674e851	—
meowcaller	partial	history - blame - commits 011af47 1c62c52 b0b3263 d572d2f 99c55e2 5ab3e3d 0246dbb d88663a b0fe93c e362783	LSF decode/reconstruction KAT-verified; encoder-side LSF VQ not in scope

Annotation wacrg:ENC-08 — a flavor marks its implementation site in source with this comment; a script clones the source, finds it, and attaches the commit blame/permalink.

Contributors

Contributor	Role
Rajeh Taher	wrote initial spec

protocol history / diff - blame

Open questions - The selector/grid/stage-2 CDF tables and the stage-1/stage-2 codebooks (cbhalf, we, wie, qstep, min_qi/max_qi, min_dist, means, reg_cond) are carried as opaque table blobs; their generating procedure inside the codec is not specified here. - Whether interpolation rows other than row 0 ([0.55,0.88,1.0,1.0]) are ever signalled/used on the decode path, or only chosen encoder-side.

References - RFC 6716 — Opus (SILK NLSF/LSF background)

Changelog

• 2026-06-21 — Initial spec entry.

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