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Topic: Fast Trellis Search for optimal ANMR (Read 1699 times)
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## Fast Trellis Search for optimal ANMR

##### 2009-07-28 18:51:49
I have a few question on trellis searches for ANMR optimal SF and HCB selection:

1) In Claus Bauer's paper The choice of Scale Factors and Huffman Code Books for MPEG-4 AAC as a direct function of the perceptual entropy of the audio signal (and longer form Joint Optimization of Scale Factors and and Huffman Code Books for MPEG-4 AAC) he writes:

Λ^R_{final} = c*ln(10)/(10M) * 10^(c(PE-R)/10M) (eq 16)

[blockquote]For a fixed value of R, and assuming that c is a positive
constant, we see from (16) that Λ^R_{final} increases with in-
creasing P E. This can be intuitively explained as follows:
For increasing P E, the minimum number of bits needed by
the encoder to encode an audio sample increases, such that
the transmission rate tends to increase and potentially vi-
olates the rate constraint. However, for an unconstrained
cost function defined as in (5), if the transmission rate is
high, the value of Λ must be large in order to strongly pe-
nalize a violation of the rate constraint.sectionApplications
and Simulation results[/blockquote]

Later in equation 17, he splits the constant c into 3 parts:

Λ^R_{final} = c1*ln(10)/(10M) * 10^((c2*PE-c3*R)/10M) (eq 17)

He goes on:

[blockquote]...we use the experimental data to
determine the constants c1 , c2 and c3 as a two-dimensional
least square problem. We obtain the values c1 = -9248.3,
c2 = 11.712, and c3 = 8.897. We see that the constants c1 -
c3 differ significantly from the value c = 6.02 in (10). This
can be expected as the relation (10) is only a very rough
approximation for non-uniform quantization. In order to
evaluate the formula (17) with the constant values chosen
as above, we compared the formula (17) with experimen-
tal values for Λ_{final} obtained by iterating over all initial Λ
values. Figure 2 shows that the actual values for Λ_{final} are
indeed very well approximated by the formula (17). Fig.[/blockquote]

However the strange fact that c1 is negative is never discussed. Does anyone have any thoughts on that?

2) Can anyone give any guidance on lambda selection for a full trellis search?

3) Both papers cite Anish Aggarwal's Ph.D. dissertation:
Aggarwal. A., Towards weighted mean-squared optimality of scalable audio coding. Dissertation, UCSB, Dec. 2002.

Any idea where I can find a copy of this?