Eurospeech 2001 - Scandinavia
Joint Source-Channel Coding for Low Bit-Rate Coding of LSP Parameters Jos´e L. P´erez-C´ordoba, Antonio J. Rubio, Antonio M. Peinado, Angel de la Torre Dpto. Electr´onica y Tecnolog´ıa de Computadores Facultad de Ciencias. Universidad de Granada (Spain) E-mail:jlpc/rubio/amp/
[email protected] Abstract
2. COMQ Technique
This work presents a quantization technique for LSP parameters which results in a low bit-rate transmission while providing protection against channel errors. As a generalization of the so called Channel Optimized Vector Quantization (COVQ), Channel Optimized Matrix Quantization (COMQ) can remove intraframe and interframe LSP redundancy with the target of protecting the information sent through a channel in the presence of noise. Split COMQ is used in order to reduce storage requirements and complexity. Results show that Split COMQ gives better performance under certain error conditions and a lower bit rate transmission in all channel conditions compared to the reference quantization techniques.
In this Section we present the fundamentals of COMQ technique and the necessary optimal conditions are presented. To introduce COMQ technique, let us consider a real-valued independent and identically distributed (i.i.d.) source = Xi 1 i=1 with probability density function (pdf) p(x). The source is to be encoded by means of a matrix quantizer (MQ) whose output is transmitted over a waveform channel. We consider a k N matrix quantization process with M levels. The COMQ system, as depicted in Figure 1, consists of a encoder mapping , a signal selection module and a decoder mapping . The encoder : IRN IRk , where = 1; 2; : : : ; M , is described in terms of a partition = S1 ; S2 ; :::; SM of IRN IRk according to
1. Introduction
(X ) = i; if X 2 Si ; i 2 I (1) where X = (x1 ; x2 ; :::; xN ) is a typical source output matrix and xi ; i = 1; : : : ; N is a source vector. The signal selection module maps an index i to a signal s that is transmitted over the
Efficient LPC quantization is a key question on speech coding. Many techniques have been proposed with the objective of reducing the bit-rate while maintaining a good quality of the corresponding synthesized speech. One approach to achieve these objectives is applying vector quantization (VQ). To reduce storage requirements and complexity Split VQ (SVQ) was proposed [4]. VQ removes the intraframe correlation of LSP parameters. One way to remove also interframe correlations is to apply matrix quantization (MQ) [8]. However, MQ introduces bigger delays, storage requirements and complexity. Split MQ (SMQ) was proposed [9] to reduce these bigger requirements. The performance of these quantization techniques degrades with the presence of channel errors. To mitigate the effect of channel errors without increasing the bit rate, joint sourcechannel coding techniques are used. For example, Channel Optimized Vector Quantization (COVQ) [1] was proposed in the context of VQ and, as a generalization of COVQ, Channel Optimized Matrix Quantization (COMQ) [5] was proposed in the context of MQ. In [5] the application of Split COMQ to LSP quantization is studied with the objective of removing the intraframe LSP redundancy maintaining the same number bits per frame as in the reference quantization technique. In the present work we extend the application of Split COMQ to remove the interframe redundancies of LSP parameters in addition to the intraframe ones, resulting in a coder with a low bit-rate transmission while protecting the parameters against channel errors. This paper is organized as follows. In Section 2 COMQ is presented. Expressions for necessary optimal conditions are given. Section 3 discusses the application of Split COMQ to LSP quantization and summarizes characteristics of the coders. In Section 4 results on the performance evaluation of the COMQ are presented and the discussion about these results are reported. Finally, Section 5 contains conclusions.
X f g
I f
f
g
g
!I
S
channel. The details of this module can be find in [5]. First, we consider that the channel is a AWGN channel. Therefore, the random channel output vector r = (r1 ; r2 ; : : : ; rL ) is related to the input vector s = (s1 ; s2 ; : : : ; sL ) through
rl = sl + nl ;
l = 1; 2; :::; L
(2)
where L is the dimension of the signal constellation and nl ’s are i.i.d. zero-mean Gaussian random variables with common variance 2 = N0 =2. b of the source Finally, the decoder makes an estimate X matrix based on the received vector (channel output) r. We will restrict our study to hard-decision decoder, that is, the de{, of the index transmitted, i, repcoder makes an estimate, ^ resented by the signal s, based on the received vector r. Given
X N
k
Rx R
^ X
Encoder
i
γ
Decoder β
Signal Selection
r Channel
Figure 1: Block diagram of the COMQ system.
s
Eurospeech 2001 - Scandinavia b is selected from a finite reproduction alphabet ^{, the estimate X (codebook) C = fC1 ; C2 ; :::; CM g that described the decoder
through
(^{) = (^{(r)) = C^{ ; C^{ 2 IRN IRk ^{ 2 I
(3)
The performance of this system is generally measured by the average distortion per sample ( ; ) and the encoding rate R. The average distortion is given by
DSC
D(S ; C ) = k1 E [D (X; (^{(r)))]
(4)
where E [ ] means the expectation value and D(X; Y ) means the distortion measure used in the Generalized Linde-BuzoGray (GLBG) algorithm [8] defined by
D(X; Y ) = with d(xn ; y n ) =
N 1 X
N
n=1
d(xn ; y n )
(5)
kxn yn k . The encoding rate is given by 2
1
R=
kN
log2 M bits/sample
D (S ; C ) = k
Z
i=1 Si
p(X )
8 M 4 dB 12.66 0.23 12.66 0.23 30.97 19.97 10.50 88.25 0.37 0.00 0.46 0.03 21.90 18.95 14.74 82.38 45.07 1.33 46.57 1.40 52.06 28.75 7.64 92.23 45.14 1.29 45.24 1.35 52.43 28.31 7.92 91.93 45.25 1.35 45.34 1.41 52.48 28.35 7.95 91.89 60.53 4.12 60.57 4.15 65.78 16.77 20.26 79.26 63.36 26.38 63.38 26.39 60.66 32.07 31.10 67.92
CSNR (in dB) 21 12 6 0 21 12 6 0 21 12 6 0 21 12 6 0 21 12 6 0 21 12 6 0 21 12 6 0
Av. SD (in dB) 1.70 3.01 5.30 7.97 1.10 2.53 4.97 7.58 2.87 3.49 5.43 7.46 2.27 3.33 5.09 7.02 2.46 3.05 4.30 6.11 2.90 3.23 4.09 5.69 3.82 3.96 4.39 5.45
(a)
Outliers (in %) 2-4 dB > 4 dB 16.69 2.83 33.76 26.59 24.93 66.39 3.60 96.35 4.99 3.00 23.48 21.42 26.16 60.19 8.42 90.82 49.23 5.65 50.89 32.21 22.51 75.92 3.51 96.47 49.29 5.15 53.78 28.08 27.45 70.55 4.57 95.40 61.28 5.70 65.38 17.85 43.98 53.11 11.41 88.39 66.43 13.87 65.50 21.91 49.68 46.65 17.20 82.52 57.09 37.61 54.29 41.45 43.39 54.41 22.10 77.54 (b)
Table 2: Average spectral distortion for different CSNR and different coders: (a) AWGN Channel, (b) Slow-fading Rayleigh Channel.
9
9 SQ SVQ SMQ COMQ-21 COMQ-12 COMQ-6 COMQ-0
Average SD (dB)
7 6 5
8
SQ SVQ SMQ COMQ-21 COMQ-12 COMQ-6 COMQ-0
7 Average SD (dB)
8
4 3
6 5 4 3
2
2
1
1
0
0 0
3
6
9
12
CSNR (dB)
(a)
15
18
21
0
3
6
9
12
CSNR (dB)
(b) Channel
Figure 2: Average SD: (a) AWGN Channel, (b) Slow-fading Rayleigh Channel.
15
18
21
