Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02718865 2010-10-26
RATE-DISTORTION OPTIMIZATION FOR ADVANCED AUDIO CODING
FIELD
[0001] Example embodiments herein relate to audio signal encoding,
and in particular to rate-distortion optimization for Advanced Audio Coding
(AAC).
BAC KGROU D
[0002] Advanced Audio Coding (AAC) has been proposed as the
successor to the MPEG-1/2 Layer-3 format (commonly referred to as "MP3")
for high quality multi-channel audio transmission. AAC was first specified in
the standard MPEG-2 Part 7, and later updated in MPEG-4 Part 3. AAC has
found applications in digital audio broadcasting and storage applications such
as in portable digital audio devices, the Internet and wireless
communications.
[0003] Generally, for the AAC standard, the decoding algorithms are
predetermined and fixed. However, there may be opportunities to
manipulate the encoding algorithm while maintaining full decoder
compatibility.
[0004] Some differences between AAC and MP3 include-the AAC ---
standard providing for the selection of quantization step sizes (which are
differentially coded), and selection of Huffman codebooks from a set of 12
Huffman codebooks. Some conventional encoding algorithms are limited to
optimization of these two parameters for optimization of rate-distortion in
AAC encoding. These two parameters may thereafter be used to configure
an encoder.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] Reference will now be made, by way of example, to the
accompanying drawings which show example embodiments of the present
application, and in which:
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[0006]
Figure 1 shows an AAC process to which example embodiments
may be applied;
[0007]
Figure 2 shows an optimization process in accordance with an
example embodiment;
[0008]
Figure 3 shows a detailed example Trellis process to be used in
= the optimization process of Figure 2;
[0009]
Figure 4 shows another detailed example Trellis process to be
used in the optimization process of Figure 2;
[0010]
Figure 5 shows a graph of comparative performance
characteristics of an example embodiment, for encoding of audio file
Waltz.wav;
[0011]
Figure 6 shows a graph of comparative performance
characteristics of an example embodiment for encoding of audio file
Violin.wav;
[0012]
Figure 7 shows a graph of performance characteristics of an
example embodiment, having an alternate configuration, for encoding of
' audio file Waltz.wav;
[0013]
Figure 8 shows a graph of comparative performance
characteristics of an example embodiment, having another alternate
configuration, for encoding of audio file Waltz.wav;
[0014]
Figure 9 shows a method for optimizing performance of AAC in
accordance with an example embodiment; and
[0015]
Figure 10 shows an encoder for optimizing performance of MC
in accordance with an example embodiment.
[0016]
Similar reference numerals may have been used in different
figures to denote similar components.
DESCRIPTION OF EXAMPLE EMBODIMENTS'
[0017]
It would be advantageous to provide for the optimization of
additional parameters for optimization of rate-distortion in MC encoding.
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[0018] In one aspect, the present application provides for the
optimization of rate-distortion for AAC encoding based on quantized spectral
coefficient sequences.
[0019] In another aspect, the present application provides for joint
optimization of scale factors, Huffman codebooks and quantized spectral
coefficient sequences for optimization of rate-distortion.
[0020] In another aspect, the present application provides a method
having an iterative rate-distortion optimization algorithm for AAC encoding
based on a method of Lagrangian multipliers. In each iteration, the method
first finds the optimal values of scale factors and quantized spectral
coefficients when Huffman codebooks are fixed, and then updates the values
of Huffman codebooks and quantized spectral coefficients given the
optimized scale factors. The iterations may be applied until a predetermined
threshold is attained.
[0021] In another aspect, the present application provides a method for
optimizing performance of Advanced Audio Coding of an audio source
sequence, the Advanced Audio Coding being dependent on a quantized
spectral coefficient sequence, wherein the quantized spectral coefficient
sequence is a quantized sequence of the audio source sequence. The
method includes determining values of the quantized spectral coefficient
sequence which minimize a cost function of an encoding of the audio source
sequence within a predetermined threshold, by using soft decision
quantization, the cost function being dependent on the quantized spectral
coefficient sequence, and performing Advanced Audio Coding of the audio
source sequence using the determined quantized spectral coefficient
sequence.
[0022] In another aspect, the present application provides a method for
optimizing performance of Advanced Audio Coding of an audio source
sequence, the Advanced Audio Coding being dependent on a quantized
spectral coefficient sequence, on a scale factor sequence, and on Huffman
codebooks, wherein the quantized spectral coefficient sequence is a
quantized sequence of the audio source sequence, the scale factor sequence
corresponds to quantization step sizes of the quantized spectral coefficient
sequence, and the Huffman codebooks are from a set of selectable Huffman
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codebooks. The method includes determining values of the quantized
spectral coefficient sequence, the scale factor sequence, and the Huffman
codebooks which minimize a cost function of an encoding of the audio source
sequence within a predetermined threshold, the cost function being
dependent on the quantized spectral coefficient sequence, the scale factor
sequence, and the Huffman codebooks, and performing Advanced Audio
Coding of the audio source sequence using the determined quantized spectral
coefficient sequence, the determined scale factor sequence, and the
determined Huffman codebooks.
[0023] In another aspect, the present application provides an encoder
for optimizing performance of Advanced Audio Coding of an audio source
sequence, the Advanced Audio Coding being dependent on a quantized
spectral coefficient sequence, wherein the quantized spectral coefficient
sequence is a quantized sequence of the audio source sequence. The
encoder includes a controller, a memory accessible by the controller, and a
predetermined threshold stored in the memory. The controller is configured
to: access the predetermined threshold from memory, determine values of
the quantized spectral coefficient sequence which minimize a cost function
within the predetermined threshold, by using soft decision quantization, the
cost function being dependent on the quantized spectral coefficient sequence,
and store the determined quantized spectral coefficient sequence in memory
for Advanced Audio Coding of the audio source sequence.
[0024] In another aspect, the present application provides an encoder
for optimizing performance of Advanced Audio Coding of an audio source
sequence, the Advanced Audio Coding being dependent on a quantized
spectral coefficient sequence, a scale factor sequence, and Huffman
codebooks, wherein the quantized spectral coefficient sequence is a
quantized sequence of the audio source sequence, the scale factor sequence
corresponds to quantization step sizes of the quantized spectral coefficient
sequence, and the Huffman codebooks are from a set of selectable Huffman
codebooks. The encoder includes a controller, a memory accessible by the
controller; and a predetermined threshold stored in the memory. The
controller is configured to: access the predetermined threshold from
memory, determine values of the quantized spectral coefficient sequence,
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the scale factor sequence, and the Huffman codebooks which minimize a cost
function of an encoding of the audio source sequence within the
predetermined threshold, the cost function being dependent on the quantized
spectral coefficient sequence, the scale factor sequence, and the Huffman
codebooks, and store the determined quantized spectral coefficient
sequence, the scale factor sequence, and the Huffman codebooks in memory
for Advanced Audio Coding of the audio source sequence.
[0025] Reference is now made to Figure 1, which shows an AAC
process 20 to which example embodiments may be applied. The AAC process
20 may for example be implemented by a suitably configured encoder, for
example by a computer having a memory with suitable instructions stored
thereon. The AAC process generally processes digital audio and produces an
encoded or compressed bit stream for storage and transmission. In Figure 1,
the continuous lines denote the time or spectral domain signal flow, and the
dash lines denote the control information flow. As shown, the AAC process
20 includes audio input 22 for input to a time/frequency (T/F) mapping
module 24 and a psychoacoustic model module 26. Also shown are a
quantization and entropy coding module 28 and a frame packing module 30.
The AAC process 20 results in an encoded output 32 of the audio input 22,
for example for sending to a decoder for subsequent decoding.
[0026] The audio input 22 may for example be time domain audio
samples which are first preprocessed (as is known in the art; not shown) and
sent into the T/F mapping module 24 which converts the audio input 22 into
spectral coefficients. The T/F mapping module 24 shown is for example a
time-variant modified discrete cosine transform (MDCT). The transform
length could be set to 1024 (long block) or 128 (short block) time samples.
The long block is used to address stationary audio signals. This may ensure a
higher frequency resolution, but may also cause quantization errors
spreading over the 1024 time samples in the process of quantization. The
short block is used to reduce temporal noise to spread for the signals
containing transients/attacks. In order to ensure a smooth transition from a
long block to a short block and vice versa, two transition blocks, long-short
(start) and short-long (stop), which have the same size as a long block, may
be employed. The time-variant MDCT is used to generate a frame of 1024
CA 02718865 2010-10-26
spectral coefficients. One spectral frame may contain one long block
sequence (including long-short and short-long) and eight short block
sequences.
[0027] The
psychoacoustic model module 26 is generally used to
generate control information for the T/F mapping module 24 and the
quantization and entropy coding module 28. Based
on the control
information from the psychoacoustic model module 26, spectral coefficients
received from the T/F mapping module 24 are sent to the quantization and
entropy coding module 28, and are quantized and-entropy coded, resulting in
quantized spectral coefficients. These encoded bit streams are packed up
along with format information, control information and other auxiliary data in
AAC frames, and are sent as encoded output 32.
[0028]
Generally, the AAC syntax leaves the selection of quantization
step sizes and Huffman codebooks to the encoder implementing the AAC
process 20. The spectral coefficients received at the quantization and
entropy coding module 28 are first quantized using the selected quantization
step sizes and then further encoded using Huffman codebooks from a set of
selectable Huffman codebooks. The AAC syntax for example specifies twelve
fixed Huffman codebooks. In addition, the indices of scale factors (SFs) and
Huffman codebooks are coded and transmitted as side information. In AAC,
the SFs are differentially coded relative to the previous SF, and then Huffman
coded using a fixed Huffman codebook. The indices of Huffman codebooks
used for the encoding of the quantized spectral coefficients are coded by run-
length codes.
[0029] In
some conventional AAC algorithms, optimization of rate-
distortion has been limited to these two parameters of quantization step sizes
and Huffman codebooks. In
such systems, to optimize those two
parameters, a two nested loop search (TNLS) algorithm is commonly used.
The TNLS search in such applications uses a heuristic search, which may not
be guaranteed to converge. In addition, quantization and Huffman coding
are considered separately.
[0030] Therefore, referring still to Figure 1, in conventional systems
the
AAC quantization and entropy coding module 28 first groups an entire frame
of 1024 spectral coefficients into a number of scale factor bands. Each
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coefficient xr,, 1=0 to 1023, is quantized by the following non-uniform
quantizer:
xri I
y = ninta (2.1)
cAliylobal _gain-scale _ factor[sb]) .75 ¨ 0.0946]
where y, denotes the quantized index, flint denotes the nearest non-negative
integer, global gain determines the overall quantization step size for the
entire frame, and scale factor[sb] is used to determine the actual
quantization step size for scale factor band (SFB) sb where the spectral
coefficient xri lies to make the perceptually weighted quantization noise as
small as possible. In AAC encoding global gain is usually set to be equal to
scale factor[0]. The formulaic calculation of y, may conveniently be referred
to as "hard decision quantization".
[0031] In
some conventional algorithms, to minimize the quantization
noise, a noise shaping method needs to be applied to find the proper global
quantization step size global gain and scale factors before the actual
quantization. Some conventional algorithms use the TNLS algorithm to
jointly control the bit rate and distortion. The TNLS algorithm may require
quantization step sizes so small to obtain the best perceptual quality. On the
other hand, it has to increase to the quantization step sizes to enable coding
at the required bit-rate. These two requirements are conflicting. Therefore,
this algorithm does not guarantee to converge. Moreover, the scale factors
and Huffman codebooks are considered separately in the TNLS algorithm.
[0032] In
some example embodiments described, herein, it is identified
to use quantized spectral coefficients as another free parameter to which an
AAC encoder can optimize. Generally, in some example embodiments, a
method is provided to jointly optimize the quantized coefficients,
quantization
step sizes and Huffman codebooks. The method may for example be based
on the method of Lagrangian multipliers, as can be implemented by those
skilled in the art.
[0033] In
some example embodiments, one purpose is to achieve the
minimum perceptual distortion for a given encoding rate. Mathematically,
the following minimization problem is to be solved:
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,
. .
{minyAhD,Okr,rxr), subject to
R(s)+R(h)+R(y) RI
(3.1)
where xr is the original spectral signal sequence, rxr is the reconstructed
signal sequence, y is the quantized spectral coefficient sequence, s= {so,
si....} is the scale factor sequence, h is the Huffman codebook index sequence
("Huffman codebooks"), R(s), R(y) and R(h) are the bit rates for transmitting
s, y and h respectively, R1 is the rate constraint, and Dw (xr, rxr) denotes
the weighted distortion measure between xr and rxr. Generally, average
noise-to mask ratio (ANMR) may be used as the distortion measure.. The
noise-to mask ratio (NMR), the ratio of the quantization noise to the masking
threshold, is the mostly widely used objective measure for the evaluation of
an audio signal. ANMR is expressed as:
N
ANMR = 1 ¨Ew[sb] = d[sh]
(3.2)
N sb=1
where N is the number of scale factor bands, w[sb] is the inverse of the
masking threshold for scale factor band sb, and d[sb] is the quantization
distortion, mean squared quantization error for scale factor band sb.
[0034]
The above constrained optimization problem could be converted
into the following minimization problem:
minyAb J A, (y ,s,h) = D., (xr, rxr) + .1., = (R(s) + R(h) + R(y))
(3.3)
where A is a fixed parameter that represents the tradeoff of rate for
distortion, and JA is commonly referred to as the "Lagrangian cost", as can be
understood by those skilled in the art. From the rate-distortion theoretic
point of view, one object of audio compression design is to find a set of
encoding and decoding schemes to minimize the actual rate-distortion cost
given by (3.3).
However, for the standard-constrained optimization
described herein, in some example embodiments, the decoding algorithms
have already been selected and fixed. What may be optimized is the '
encoding algorithm while maintaining full decoder compatibility.
[0035]
Since AAC employs differential coding of scale factors and run-
length coding of Huffman codebook indices, this may introduce significant
inter-band dependencies in coding of the side information. The absolute
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CA 02718865 2010-10-26
difference between the scale factor values of two neighboring scale factor
bands should be restricted within a dynamic range of 60, and the scale factor
value is differentially encoded relative to the one of the preceding band (or
the global gain for the first band) by a fixed Huffman codebook. The whole
quantized spectrum is segmented into sections whose boundaries are aligned
with those of scale factor bands, such that a single Huffman codebook is used
to code each section. The indices of Huffman codebooks are coded by run-
length codes: Therefore, R(s) can be decomposed as
N-1
R(s)=ERs(s,¨ s1_1) (3.4)
i=o
and R(h) as
R(h)=ERk(hõrun(hi)) (3.5)
where N denotes the total number of scale factor bands of one spectral
frame, Rs determines the number of side information bits needed to encode
the scale factor si of band i as a function of si and ski, Rh represents the
number of bits to encode Huffman codebook index hi for band i as a function
of hi and the length of hi, run(hd, and the summation in (3.5) is over all
pairs
of (hi, run(hd) along with the Huffman codebook index sequence. Here s_1 is
equal to global gain.
[0036] In (3.3) the bit rates to transmit the scale factors, R(s) and
Huffman codebook indices R(h), depend on the actual scale factors and
Huffman codebook indices transmitted, and the bit rate to transmit the
quantized coefficients R(y) is determined by the actual Huffman codebook.
[0037] Some conventional systems have limited the optimization
algorithms to the two above-mentioned parameters of scale factors and
Huffman codebooks. The conventional hard decision quantization methods
consider y solely determined by scale factors given xr, i.e., y=Q(xr, s) (e.g.
(2.1)). On the other hand, in some example embodiments, some of the
methods described herein also consider the optimization of the quantized
spectral coefficient sequence y. This may be referred to herein as "soft-
decision quantization" (rather than hard decision quantization), such that y
is
chosen as a parameter to minimize the rate-distortion cost (3.3).
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[0038]
Reference is now made to Figures 2, 3 and 4, wherein Figure 2
shows an optimization process 50 in accordance with an example
embodiment, and Figure 3 shows a detail of an example Trellis process 66 to
be used in the optimization process 50 of Figure 2, and Figure 4 shows a
detail of another example Trellis process 68 to be used in the optimization
process 50 of Figure 2. The Trellis process 66 is an example Trellis-based
implementation of step 56 of the optimization process 50. The Trellis process
68 is an example Trellis-based implementation of step 58 of the optimization
process 50. Generally, the optimization process 50 includes an alternating
minimization procedure to optimize the scale factors s and Huffman
codebooks h alternatively to minimize the Lagrangian cost. The exact order
of steps may vary from those shown in Figures 2 and 3 in different
applications and embodiments. It can also be appreciated that some steps
may not be required in some example embodiments.
[0039] The
optimization process 50 is as follows. At step 52, specify a
threshold or tolerance E as the convergence criterion for the Lagrangian cost.
At step 54, initialize a set of scale factors so and quantized indices yo from
the given frame of spectral domain coefficients xr with a Huffman codebooks
selection mode ho; and set t=0. Compute MY, s, h), and denote is as 4.
[0040] At step 56, ht is fixed or given for any t Find
the optimal
quantized spectral coefficient sequence Temp and scale factors st+i where
Ytemp and st+i achieve the minimum
min, = Dw(xr, Q-' (s, y)) + A = (R(s) + R(h) + R(y)) (3.6)
where Q-1(s,y) is the inverse quantization function to generate the
reconstructed signal rxr. This step may for example be implemented by a
Trellis process 66 (Figure 3), which is described in greater detail below.
[0041] At
step 58, given st+i, find the optimal quantized coefficients
yt+i and Huffman codebooks ht+i where yt+i and ht+1 achieve the minimum
miny,h J a = D (xr , Q-1 (s, y)) + A = (R(s)+ R(h) + R(y)) (3.7)
This step 58 may for example be implemented by a Trellis process 68 in a
similar manner as Trellis process 66. Compute JA(Yt+1., st+i, ht+1), and
denote
is as fp.
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[0042] At step 60, query whether Ja"-'
= J. . If so, the optimization
process 50 proceeds to step 70 and outputs the final y, $ and h, and ends at
step
72. If not, proceed to step 64 wherein t=t+/, and repeat steps 56 and 58 for
t=0,
1, 2, ... until JA' 8
Since the Lagrangian cost function may be non-
increasing at each step, the convergence is guaranteed. The final y, s and h
may
thereafter be provided for AAC coding of xr.
[0043]
Steps 56 and 58 will now be explained in greater detail, which may for
example be solved by applying dynamic programming for the soft decision
quantization. Reference is now made to Figure 3, which shows the Trellis
process
66 to be used for step 56. The number of states at each stage is Als (or any
suitable Aix, depending on the parameter used for minimization). Each state at
the
ith stage represents an SF candidate (i.e., s) for the ith SFB. Denote these
states
as rk,, where 0
< Ns and 0 5 i < N. Denote Jki as the minimum accumulative
cost from stage 0 to yk,, . The state transition cost from ro_i to r is A = Rs
(s,
The optimization procedure for the Trellis process 66 (step 56) is described
as
follows:
1) For each state in the Trellis, find the best yk,, to minimize the
incremental cost in the state by applying soft decision quantization. The
minimum incremental cost Cki is equal to
C;()=minyk, {Dõ,(xr0Q-1(swyk,ki)}. (3.8)
Thus, each state of the Trellis is associated with each minimal incremental
cost Ck,,. The determination of yk,, may for example be found by searching all
possible and allowable quantized coefficients as determined by the particular
Huffman codebook. In other example embodiments, the search range for yk,1
is limited to [yhj - a, yhj + a], where yhj is the jth quantized coefficient
from
hard decision quantization (e.g., using (2.1)) and a is a fixed integer.
2) Initialize all the states and start Trellis search from the initial
stage.
-1k,o =Ck,,-F A = Rs(0), for all k and 1=0.
3) For each state at the ith stage, find the best accumulative cost to the
ith stage by examining all the states at the (i-/)th stage leading
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to the current state. The best path ending at yo is the one that has
the minimum accumulative cost Ai. Jki is defined as
min/{J0-1+C" 2=12,(so¨so_)} . (3.9)
4) Check the index I. If i < N-1, set i = 1+1 and go to 3).
[0044] After
traversing all the states in the Trellis, the optimal path can
be extracted by tracing backward from the state with the minimum
Lagrangian cost at the last stage. As a result, for a fixed or given ht, the
optimal quantized spectral coefficient sequence y and SFs s for all SFBs that
minimize the Lagrangian cost are determined.
[0045]
Reference is now made to Figure 4, which shows the Trellis
process 68 to be used for step 58. The Trellis process 68 follows a similar
procedure to Trellis process 66. It is used to attain a solution for step 58
for
the optimal quantized spectral coefficient sequence y and Huffman
codebooks h for a fixed or given s. The number of states at each stage is
now nix = AIN as shown. Each state at the ith stage represents a Huffman
codebook candidate (i.e., h) for the ith SFB. Denote these states as yo
where 0 < Nh
and 0 i < N. Denote 41 as the minimum accumulative
cost from stage 0 to yki. As in Trellis process 66, there are transition paths
between any of two states in neighboring stages. In addition, there are
transition paths between any of two states which, have identical state
numbers (There two states are not restricted within neighboring stages). The
optimization procedure for the Trellis process 68 (step 58) is described as
follows:
1) For each state in the Trellis, find the best yKi to minimize the
incremental cost in the state by applying soft decision quantization.
The minimum incremental cost Cici is equal to
=ffinyki fpw (xri)Q4(SkilYk,i) 11.R6rk,i)} = (3.10)
Thus, each state of the Trellis is associated with each minimal
incremental cost Ck,i.
2) Initialize all the states and start Trellis search from the initial
stage. Jko =Ck,O+ A = R5(0), for all k..
3) For each state k at the ith stage, find the best accumulative cost
from the initial stage by examining all the states at the (i-/)th stage
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leading to the kth state at the ith stage, and by examining states rk,
(0 < n < 1-1) leading to the current state. The best path ending at
yo is the one that has the minimum accumulative cost Jk,i. - 1,I is
defined as
J kj = min{ min /E{01 {../1, 1 + A(R5(so¨s1,,_1)+ Rh (h1,_1, kin} ,
= N h- 1)
1 1 (3.11)
min2) {Jk n+ E Co + A(Rh(hch,h0)-i- E Rs(sk,r¨ s1,_1))} }
= t-- '
t=n+1 t=n+1
wherein Rh( = ) denotes the bits to encode the Huffman codebooks for
the transition path.
4) Check the index i. If i < N-1, set i = 1+1 and go to 3).
[0046] After
traversing all the states in the Trellis, the optimal path can
be extracted by tracing backward from the state with the minimum
Lagrangian cost at the last stage. As a result, for fixed or given SFs, the
optimal quantized spectral coefficient sequence y and Huffman codebooks for
all SR3s that minimize the Lagrangian cost are determined.
[0047] To
develop an intuition for the optimization process 50 using
soft-decision quantization described above, consider the following example.
Consider a scale factor band of spectral coefficient sequence in AAC
encoding:
xr = (-1442687.48668, 257886.45517, -363544.22677, -967991.05298)
with scale factor equal to 1, global gain equal to 63, and masking threshold
equal to 9.8776 X 106. The quantization indices given the hard decision
quantization are
yh= (5, 1, 2, 4)
which needs 17 bits to encode assuming Huffman codebook 10 is applied. An
optimized quantization output, obtained from the soft-decision quantization
optimization process 50 described above could be
y, = (5, 2, 2, 4)
which needs 16 bits to encode assuming the same Huffman codebook is
applied. The extra weighted distortion introduced by y, is 0.00402, based on
the de-quantizer/decoder defined in the standard. This
brings a rate
reduction of 1 bit. For A >0.00402, this directly leads to a better rate-
distortion tradeoff defined by (3.3).
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[0048] Implementation and simulation results of the optimization process
50
will now be described, referring now to Figures 5 to 8. Figures 5 and 6 show
graphs
80, 90 of comparative performance characteristics of an example embodiment
using the above-described optimization process using a specified configuration
for
encoding of audio files Waltz.wav and Violin.wav, respectively. Figures 7 and
8
show graphs 100, 110 of performance characteristics, having alternate
configurations, for encoding of audio file Waltz.wav.
[0049] The estimation of lambda (A) will now be briefly described. For a
fixed
value of A, the optimization process 50 may be applied to minimize the
encoding
cost. As can be understood by those skilled in the art, the following
relationship
between Perceptual Entropy, signal to noise ratio, signal to mask ratio,
encoding
rate and the number of audio samples to be encoded:
AR =c x10c2PE-c3R
final (4.1)
where PE is Perceptual Entropy of an encoded frame, and R is the encoding
rate.
c2 and c3 are determined from the experimental data using the least square
criterion. This is for example described in C. Bauer and M. Vinton, "Joint
optimization of scale factors and Huffman codebooks for MEPG-4 AAC," in Proc.
of
the 2004 IEEE workshop on Multimedia Signal Processing, pp. 111-114, 2004; and
C. Bauer and M. Vinton, "Joint optimization of scale factors and Huffman
codebooks
for MEPG-4 AAC," in IEEE Trans. on Signal Processing, vol. 54, pp. 177-189,
Jan.
2006. Therefore, given a fixed rate, one could use Afinai determined by the
above
formula as an initial value for an iterative Lagrangian multiplier search. Due
to the
close guess of Afinai, significantly less iterations are required than that
randomly
picks an initial A value.
[0050] The simulations may for example be implemented by a FAAC encoder,
which is an open source simulation tool for implementing AAC. In some example
simulations, Faac_src_26102001 is used, which adopts ISO perceptual model. The
optimization process 50 also uses the original FAAC encoder output as the
initial
point.
[0051] The optimization process 50 is implemented as explained above. In
the
simulation, the search range for yi is set to [yh3-2, yhj +2], where yhj
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is the jth quantized coefficient from hard decision quantization (e.g., using
(2.1)). The number of possible SFs for each Trellis stage is set to 60. For
each case, the perceptual model, joint stereo encoding mode and window
switching decision are kept intact, as can be implemented by those skilled in
the art.
[0052] Figure 5 depicts a graph 80 showing the rate-distortion
performance for the audio test file Waltz.wav. The test file may for example
be configured at 48khz, 2 channel, 16 bits/sample, 30 seconds. In Figure 5,
FAAC 82 represents the results obtained by using the FAAC encoder, Trellis
84 represents the conventional Trellis-based optimized AAC encoder using
hard-decision quantization, and Trellis+SQ 86 represents the results from the
optimization process 50 (Figure 2) using soft-decision quantization, as
described above. The vertical axes denote the average noise to mask ratio
(i.e., distortion) over all audio frames, while the horizontal axes denote the
rate in kbps. From Figure 5, it may be observed that the optimization
process 50 achieves a performance gain over the FAAC reference encoder.
At 98kbps, the proposed optimization algorithm achieves 1.858 dB and 0.67
dB ANMR gains over the FAAC reference encoder and Trellis-based optimized
AAC encoder respectively, which is equivalent to 22.6% and 8% compression
rate gains respectively.
[0053] Figure 6 shows a graph 90 of another simulation, performed in a
similar manner as the simulation shown in Figure 5, for the audio coding of
test file Violin.wav. The test file may for example be configured at 48khz, 2
channel, 16 bits/sample, 30 seconds. Improvements in rate-distortion are
shown in the graph 90. Similar results may be achieved for other test music
files.
[0054] The computational complexity and additional methods of
reducing thereof will now be described, referring still to Figures 5 and 6.
Given the value of A, the number of iterations in the optimization process 50
has a direct impact on the computational complexity. Experiments show that
by setting the convergence tolerance e to 0.005, the iteration process is
observed to converge after 3 loops in most cases, that is, most of the gain
achievable from full joint optimization is obtained within 3 iterations.
Compared with the direct search using dynamic programming, for example,
CA 02718865 2010-10-26
"Joint optimization of scale factors and Huffman codebooks for MEPG-4 AAC,"
in IEEE Trans. on Signal Processing, vol. 54, pp. 177-189, Jan. 2006, the
computational complexity has been reduced from 0((Ns. Nh)2 N) to O((N52 +
Nh2) .3N). This is equivalent to 46 times faster if N=60, Nh=12 and N=49.
As described in the previous subsection, the search range for yi in soft-
decision quantization is set to [yty a, yhi + a], where yhi is the jth
quantized
coefficient from hard decision quantization, and a is a fixed integer (e.g. a
=
2 for simulation purposes). The number of possible SFs at each stage is set
to 60. In some example embodiments, further expansion of the search range
for yi and SFs would not significantly improve the compression performance.
[0055] Reference is now made to Figures 7 and 8, which show
simulation results in alternate configurations, which may for example be used
to reduce computational complexity.
[0056]
Bit rates 36 50 66 80 98 128 160 192
(kbps)
FAAC 14 14 45 15 15 15 15 11
encoder
Trellis 77 78 80 80 79 71 64 57
Trellis+SQ 255 276 318 337 306 447 433 426
TABLE 1: Computation time in seconds for different AAC encoders
[0057] Table 1 lists the computation time in seconds on a Pentium PC,
2.16GHZ, 1G bytes of RAM to encode waltz.wav at different bit rates for
three different encoders. Figures 7 and 8 represent simulations configured to
further improve the computation speed in two aspects. First, the number of
possible SFs could be reduced to 50. In some example embodiments, this
does not contribute significantly to any performance loss. Second, as the
interim outputs from the iterative algorithm converge to the final output
gradually, it is possible and reasonable to decrease the number of SFs for the
dynamic programming search one iteration after another. In the simulation,
the number of SFs is set to 16 and 8 respectively during the second and third
iterations.
[0058]
16
CA 02718865 2010-10-26
Bit rates 36 50 66 80 98 128 160 192
(kbps)
Fast Trellis 42 42 42 42 40 36 33 30
Fast 169 186 190 184 185 195 173 168
Trellis+SQ
TABLE 2: Computation time in seconds for fast optimized AAC
encoders
[0059] Table 2 lists the computation time in seconds to encode
Waltz.wav for the two optimized encoders after applying the above changes.
Fast Trellis refers to implementing the above two changes on conventional
hard-decision quantization. Figure 7 accordingly shows the performance for
Fast Trellis versus Trellis (conventional hard-decision quantization). Fast
Trellis+SQ refers to implementing the above two changes on the optimization
process 50 using soft-decision quantization. Figure 8 accordingly shows the
performance for Fast Trellis+SQ versus Trellis+SQ. As shown, the
computational complexity may be reduced significantly after reducing the
number of possible scale factors. At the same time, the performance loss is
relatively small. In particular, the fast Trellis-based optimized AAC encoder
may realize near real time throughput.
[0060] As can be appreciated, the two above-mentioned configurations
for improving computational time (for providing "fast" implementation) may
be implemented by other methods, and are not limited to the Fast Trellis and
Fast Trellis+SQ simulations described herein.
[0061] Reference is now made to Figure 9, which shows a method 200
for optimizing performance of AAC of a source sequence in accordance with
an example embodiment. At step 202, the method 200 defines and
initializes a quantized spectral coefficient sequence (y) as a quantized
sequence of the source sequence to be determined, Huffman codebooks (h)
from a set of selectable Huffman codebooks, and a scale factor sequence (s)
corresponding to quantization step sizes of the quantized spectral coefficient
sequence. At step 204, there is provided a cost function (3) based on
distortion and bit rate transmission of an encoding of the source sequence,
the cost function being dependent on the quantized spectral coefficient
17
CA 02718865 2010-10-26
sequence (y), the scale factor sequence (s), and the Huffman codebooks (h).
A tolerance E is also specified as a tolerance for the cost function (J).
[0062] At step 206, the method 200 determines the quantized spectral
coefficient sequence (y) which minimizes the cost function (3) within the
predetermined tolerance E. As shown, the method may also minimize the
scale factor sequence (s) and the Huffman codebooks (h). At step 208, the
method outputs y, s and h as parameters for performing of Advanced Audio
Coding of the source sequence.
[0063] Reference is now made to Figure 10, which shows an encoder
300 in accordance with an example embodiment. The encoder 300 may for
example be implemented on a suitable configured computer device. The
encoder 300 includes a controller such as a microprocessor 302 that controls
the overall operation of the encoder 300. The microprocessor 302 may also
interact with other subsystems (not shown) such as a communications
subsystem, display, and one or more auxiliary input/output (I/O) subsystems
or devices. The encoder 300 includes a memory 304 accessible by the
microprocessor 302. Operating system software 306 and various software
applications 308 used by the microprocessor 302 are, in some example
embodiments, stored in memory 304 or similar storage element. For
example, AAC software application 310, such as the FAAC encoder software
described above, may be installed as one of the various software applications
308.. The microprocessor 302, in addition to its operating system functions,
in example embodiments enables execution of software applications 308 on
the device.
[0064] The encoder 300 may be used for optimizing performance of
AAC of a source sequence. Specifically, the encoder 300 may enable the
microprocessor 302 to determine a quantized spectral coefficient sequence as
a quantized sequence of the source sequence. The memory 304 may contain
a cost function of an encoding of the source sequence, wherein the cost
function is dependent on the quantized spectral coefficient sequence. The
memory 304 may also contain a predetermined threshold of the cost function
stored in the memory 304. Instructions residing in memory 304 enable the
micrbprocessor 302 to access the cost function and predetermined threshold
from memory 304, determine the quantized spectral coefficient sequence
18
CA 02718865 2010-10-26
=
which minimizes the cost function within the predetermined threshold, and
store the determined quantized spectral coefficient sequence in memory 304
for AAC of the source sequence. For example, AAC software application 310
may be used to perform AAC using the determined quantized spectral
coefficient sequence.
[0065] In another example embodiment, the encoder 300 may be
configured for optimizing of quantized spectral coefficient sequences, in a
manner similar to the example methods described above.
[0066] In another example embodiment, the encoder 300 may further
be configured for jointly optimizing performance of scale factors, Huffman
codebooks and quantized spectral coefficient sequences, in a manner similar
to the example methods described above.
[0067] While example embodiments have been described in detail in
the foregoing specification, it will be understood by those skilled in the art
that variations may be made without departing from the scope of the present
application.
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