Commit 57feffc1 authored by Jean-Marc Valin's avatar Jean-Marc Valin
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CELT encoder

parent 154486bb
......@@ -448,6 +448,318 @@ Copy from SILK draft.
Copy from CELT draft.
<section anchor="forward-mdct" title="Forward MDCT">
<t>The MDCT implementation has no special characteristics. The
input is a windowed signal (after pre-emphasis) of 2*N samples and the output is N
frequency-domain samples. A <spanx style="emph">low-overlap</spanx> window is used to reduce the algorithmic delay.
It is derived from a basic (full overlap) window that is the same as the one used in the Vorbis codec: W(n)=[sin(pi/2*sin(pi/2*(n+.5)/L))]^2. The low-overlap window is created by zero-padding the basic window and inserting ones in the middle, such that the resulting window still satisfies power complementarity. The MDCT is computed in mdct_forward() (mdct.c), which includes the windowing operation and a scaling of 2/N.
<section anchor="normalization" title="Bands and Normalization">
The MDCT output is divided into bands that are designed to match the ear's critical bands,
with the exception that each band has to be at least 3 bins wide. For each band, the encoder
computes the energy that will later be encoded. Each band is then normalized by the
square root of the <spanx style="strong">non-quantized</spanx> energy, such that each band now forms a unit vector X.
The energy and the normalization are computed by compute_band_energies()
and normalise_bands() (bands.c), respectively.
<section anchor="energy-quantization" title="Energy Envelope Quantization">
It is important to quantize the energy with sufficient resolution because
any energy quantization error cannot be compensated for at a later
stage. Regardless of the resolution used for encoding the shape of a band,
it is perceptually important to preserve the energy in each band. CELT uses a
coarse-fine strategy for encoding the energy in the base-2 log domain,
as implemented in quant_bands.c</t>
<section anchor="coarse-energy" title="Coarse energy quantization">
The coarse quantization of the energy uses a fixed resolution of
6 dB and is the only place where entropy coding is used.
To minimize the bitrate, prediction is applied both in time (using the previous frame)
and in frequency (using the previous bands). The 2-D z-transform of
the prediction filter is: A(z_l, z_b)=(1-a*z_l^-1)*(1-z_b^-1)/(1-b*z_b^-1)
where b is the band index and l is the frame index. The prediction coefficients are
a=0.8 and b=0.7 when not using intra energy and a=b=0 when using intra energy.
The time-domain prediction is based on the final fine quantization of the previous
frame, while the frequency domain (within the current frame) prediction is based
on coarse quantization only (because the fine quantization has not been computed
yet). We approximate the ideal
probability distribution of the prediction error using a Laplace distribution. The
coarse energy quantization is performed by quant_coarse_energy() and
quant_coarse_energy() (quant_bands.c).
The Laplace distribution for each band is defined by a 16-bit (Q15) decay parameter.
Thus, the value 0 has a frequency count of p[0]=2*(16384*(16384-decay)/(16384+decay)). The
values +/- i each have a frequency count p[i] = (p[i-1]*decay)>>14. The value of p[i] is always
rounded down (to avoid exceeding 32768 as the sum of all frequency counts), so it is possible
for the sum to be less than 32768. In that case additional values with a frequency count of 1 are encoded. The signed values corresponding to symbols 0, 1, 2, 3, 4, ...
are [0, +1, -1, +2, -2, ...]. The encoding of the Laplace-distributed values is
implemented in ec_laplace_encode() (laplace.c).
<!-- FIXME: bit budget consideration -->
</section> <!-- coarse energy -->
<section anchor="fine-energy" title="Fine energy quantization">
After the coarse energy quantization and encoding, the bit allocation is computed
(<xref target="allocation"></xref>) and the number of bits to use for refining the
energy quantization is determined for each band. Let B_i be the number of fine energy bits
for band i; the refinement is an integer f in the range [0,2^B_i-1]. The mapping between f
and the correction applied to the coarse energy is equal to (f+1/2)/2^B_i - 1/2. Fine
energy quantization is implemented in quant_fine_energy()
If any bits are unused at the end of the encoding process, these bits are used to
increase the resolution of the fine energy encoding in some bands. Priority is given
to the bands for which the allocation (<xref target="allocation"></xref>) was rounded
down. At the same level of priority, lower bands are encoded first. Refinement bits
are added until there are no unused bits. This is implemented in quant_energy_finalise()
</section> <!-- fine energy -->
</section> <!-- Energy quant -->
<section anchor="allocation" title="Bit Allocation">
<t>Bit allocation is performed based only on information available to both
the encoder and decoder. The same calculations are performed in a bit-exact
manner in both the encoder and decoder to ensure that the result is always
exactly the same. Any mismatch would cause an error in the decoded output.
The allocation is computed by compute_allocation() (rate.c),
which is used in both the encoder and the decoder.</t>
<t>For a given band, the bit allocation is nearly constant across
frames that use the same number of bits for Q1, yielding a
pre-defined signal-to-mask ratio (SMR) for each band. Because the
bands each have a width of one Bark, this is equivalent to modeling the
masking occurring within each critical band, while ignoring inter-band
masking and tone-vs-noise characteristics. While this is not an
optimal bit allocation, it provides good results without requiring the
transmission of any allocation information.
For every encoded or decoded frame, a target allocation must be computed
using the projected allocation. In the reference implementation this is
performed by compute_allocation() (rate.c).
The target computation begins by calculating the available space as the
number of whole bits which can be fit in the frame after Q1 is stored according
to the range coder (ec_[enc/dec]_tell()) and then multiplying by 8.
Then the two projected prototype allocations whose sums multiplied by 8 are nearest
to that value are determined. These two projected prototype allocations are then interpolated
by finding the highest integer interpolation coefficient in the range 0-8
such that the sum of the higher prototype times the coefficient, plus the
sum of the lower prototype multiplied by
the difference of 16 and the coefficient, is less than or equal to the
available sixteenth-bits.
The reference implementation performs this step using a binary search in
interp_bits2pulses() (rate.c). The target
allocation is the interpolation coefficient times the higher prototype, plus
the lower prototype multiplied by the difference of 16 and the coefficient,
for each of the CELT bands.
Because the computed target will sometimes be somewhat smaller than the
available space, the excess space is divided by the number of bands, and this amount
is added equally to each band. Any remaining space is added to the target one
sixteenth-bit at a time, starting from the first band. The new target now
matches the available space, in sixteenth-bits, exactly.
The allocation target is separated into a portion used for fine energy
and a portion used for the Spherical Vector Quantizer (PVQ). The fine energy
quantizer operates in whole-bit steps. For each band the number of bits per
channel used for fine energy is calculated by 50 minus the log2_frac(), with
1/16 bit precision, of the number of MDCT bins in the band. That result is multiplied
by the number of bins in the band and again by twice the number of
channels, and then the value is set to zero if it is less than zero. Added
to that result is 16 times the number of MDCT bins times the number of
channels, and it is finally divided by 32 times the number of MDCT bins times the
number of channels. If the result times the number of channels is greater than than the
target divided by 16, the result is set to the target divided by the number of
channels divided by 16. Then if the value is greater than 7 it is reset to 7 because a
larger amount of fine energy resolution was determined not to be make an improvement in
perceived quality. The resulting number of fine energy bits per channel is
then multiplied by the number of channels and then by 16, and subtracted
from the target allocation. This final target allocation is what is used for the
<section anchor="pitch-prediction" title="Pitch Prediction">
This section needs to be updated.
<section anchor="pvq" title="Spherical Vector Quantization">
<t>CELT uses a Pyramid Vector Quantization (PVQ) <xref target="PVQ"></xref>
codebook for quantizing the details of the spectrum in each band that have not
been predicted by the pitch predictor. The PVQ codebook consists of all sums
of K signed pulses in a vector of N samples, where two pulses at the same position
are required to have the same sign. Thus the codebook includes
all integer codevectors y of N dimensions that satisfy sum(abs(y(j))) = K.
In bands where neither pitch nor folding is used, the PVQ is used to encode
the unit vector that results from the normalization in
<xref target="normalization"></xref> directly. Given a PVQ codevector y,
the unit vector X is obtained as X = y/||y||, where ||.|| denotes the
L2 norm.
<section anchor="bits-pulses" title="Bits to Pulses">
Although the allocation is performed in 1/16 bit units, the quantization requires
an integer number of pulses K. To do this, the encoder searches for the value
of K that produces the number of bits that is the nearest to the allocated value
(rounding down if exactly half-way between two values), subject to not exceeding
the total number of bits available. The computation is performed in 1/16 of
bits using log2_frac() and ec_enc_tell(). The number of codebooks entries can
be computed as explained in <xref target="cwrs-encoding"></xref>. The difference
between the number of bits allocated and the number of bits used is accumulated to a
<spanx style="emph">balance</spanx> (initialised to zero) that helps adjusting the
allocation for the next bands. One third of the balance is subtracted from the
bit allocation of the next band to help achieving the target allocation. The only
exceptions are the band before the last and the last band, for which half the balance
and the whole balance are subtracted, respectively.
<section anchor="pvq-search" title="PVQ Search">
The search for the best codevector y is performed by alg_quant()
(vq.c). There are several possible approaches to the
search with a tradeoff between quality and complexity. The method used in the reference
implementation computes an initial codeword y1 by projecting the residual signal
R = X - p' onto the codebook pyramid of K-1 pulses:
y0 = round_towards_zero( (K-1) * R / sum(abs(R)))
Depending on N, K and the input data, the initial codeword y0 may contain from
0 to K-1 non-zero values. All the remaining pulses, with the exception of the last one,
are found iteratively with a greedy search that minimizes the normalized correlation
between y and R:
J = -R^T*y / ||y||
The search described above is considered to be a good trade-off between quality
and computational cost. However, there are other possible ways to search the PVQ
codebook and the implementors MAY use any other search methods.
<section anchor="cwrs-encoding" title="Index Encoding">
The best PVQ codeword is encoded as a uniformly-distributed integer value
by encode_pulses() (cwrs.c).
The codeword is converted to a unique index in the same way as specified in
<xref target="PVQ"></xref>. The indexing is based on the calculation of V(N,K) (denoted N(L,K) in <xref target="PVQ"></xref>), which is the number of possible combinations of K pulses
in N samples. The number of combinations can be computed recursively as
V(N,K) = V(N+1,K) + V(N,K+1) + V(N+1,K+1), with V(N,0) = 1 and V(0,K) = 0, K != 0.
There are many different ways to compute V(N,K), including pre-computed tables and direct
use of the recursive formulation. The reference implementation applies the recursive
formulation one line (or column) at a time to save on memory use,
along with an alternate,
univariate recurrence to initialise an arbitrary line, and direct
polynomial solutions for small N. All of these methods are
equivalent, and have different trade-offs in speed, memory usage, and
code size. Implementations MAY use any methods they like, as long as
they are equivalent to the mathematical definition.
The indexing computations are performed using 32-bit unsigned integers. For large codebooks,
32-bit integers are not sufficient. Instead of using 64-bit integers (or more), the encoding
is made slightly sub-optimal by splitting each band into two equal (or near-equal) vectors of
size (N+1)/2 and N/2, respectively. The number of pulses in the first half, K1, is first encoded as an
integer in the range [0,K]. Then, two codebooks are encoded with V((N+1)/2, K1) and V(N/2, K-K1).
The split operation is performed recursively, in case one (or both) of the split vectors
still requires more than 32 bits. For compatibility reasons, the handling of codebooks of more
than 32 bits MUST be implemented with the splitting method, even if 64-bit arithmetic is available.
<section anchor="stereo" title="Stereo support">
When encoding a stereo stream, some parameters are shared across the left and right channels, while others are transmitted separately for each channel, or jointly encoded. Only one copy of the flags for the features, transients and pitch (pitch period and gains) are transmitted. The coarse and fine energy parameters are transmitted separately for each channel. Both the coarse energy and fine energy (including the remaining fine bits at the end of the stream) have the left and right bands interleaved in the stream, with the left band encoded first.
The main difference between mono and stereo coding is the PVQ coding of the normalized vectors. In stereo mode, a normalized mid-side (M-S) encoding is used. Let L and R be the normalized vector of a certain band for the left and right channels, respectively. The mid and side vectors are computed as M=L+R and S=L-R and no longer have unit norm.
From M and S, an angular parameter theta=2/pi*atan2(||S||, ||M||) is computed. The theta parameter is converted to a Q14 fixed-point parameter itheta, which is quantized on a scale from 0 to 1 with an interval of 2^-qb, where qb = (b-2*(N-1)*(40-log2_frac(N,4)))/(32*(N-1)), b is the number of bits allocated to the band, and log2_frac() is defined in cwrs.c. From here on, the value of itheta MUST be treated in a bit-exact manner since
both the encoder and decoder rely on it to infer the bit allocation.
Let m=M/||M|| and s=S/||S||; m and s are separately encoded with the PVQ encoder described in <xref target="pvq"></xref>. The number of bits allocated to m and s depends on the value of itheta. The number of bits allocated to coding m is obtained by:
<t>imid = bitexact_cos(itheta);</t>
<t>iside = bitexact_cos(16384-itheta);</t>
<t>delta = (N-1)*(log2_frac(iside,6)-log2_frac(imid,6))>>2;</t>
<t>qalloc = log2_frac((1&lt;&lt;qb)+1,4);</t>
<t>mbits = (b-qalloc/2-delta)/2;</t>
<t>where bitexact_cos() is a fixed-point cosine approximation that MUST be bit-exact with the reference implementation
in mathops.h. The spectral folding operation is performed independently for the mid and side vectors.</t>
<section anchor="synthesis" title="Synthesis">
After all the quantization is completed, the quantized energy is used along with the
quantized normalized band data to resynthesize the MDCT spectrum. The inverse MDCT (<xref target="inverse-mdct"></xref>) and the weighted overlap-add are applied and the signal is stored in the <spanx style="emph">synthesis buffer</spanx> so it can be used for pitch prediction.
The encoder MAY omit this step of the processing if it knows that it will not be using
the pitch predictor for the next few frames. If the de-emphasis filter (<xref target="inverse-mdct"></xref>) is applied to this resynthesized
signal, then the output will be the same (within numerical precision) as the decoder's output.
<section anchor="vbr" title="Variable Bitrate (VBR)">
Each CELT frame can be encoded in a different number of octets, making it possible to vary the bitrate at will. This property can be used to implement source-controlled variable bitrate (VBR). Support for VBR is OPTIONAL for the encoder, but a decoder MUST be prepared to decode a stream that changes its bit-rate dynamically. The method used to vary the bit-rate in VBR mode is left to the implementor, as long as each frame can be decoded by the reference decoder.
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