An Upgraded Version of the Binary Search SpaceStructured VQ Search Algorithm for AMRWB Codec
Abstract
:1. Introduction
2. ISF Quantization in AMRWB
2.1. Linear Prediction Analysis
2.2. Quantization of ISF Coefficients
3. Proposed Search Algorithm
3.1. The BSSVQ Search Algorithm
Algorithm1 Encoding procedure of BSSVQ 
Step 1. Given a TQA, M_{k}(TQA) satisfying (12) is found directly in the lookup table in bss_{k}. 
Step 2. Referencing Table 2 and by means of (9) and (10), an input vector is assigned to a subspace bss_{k} in an efficient manner. 
Step 3. A full search for the bestmatched codeword is performed among the top M_{k}(TQA) sorted codewords in bss_{k}, and then the index of the found codeword is output. 
Step 4. Repeat Steps 2 and 3 until all the input vectors are encoded. 
3.2. The ITIE Search Algorithm
Algorithm2 Search procedure of ITIE 
Step 1. Build a TIE lookup table. 
Step 2. Given a c_{r}, compute d(c_{r}, x), and then CSG(c_{r}) is found directly in the TIE lookup table, that is, 
CSG(c_{r}) = {c_{k}  k = 1,2,...,N(c_{r})},

Step 3. Starting at k = 1, obtain d(c_{r}, c_{k}) from the lookup table. 
Step 4. If (d(c_{r}, c_{k}) < 2d(c_{r}, x)), then compute d(c_{k}, x), and perform Step 5. 
Otherwise, let k = k + 1, and then repeat Step 4, until k = N(c_{r}). 
Step 5. If (d(c_{k}, x) < d(c_{r}, x)), then replace c_{r} with c_{k}, update new CSG(c_{r}), let k = 1, and repeat Step 3. 
Otherwise, let k = k + 1, and then repeat Step 4, until k = N(c_{r}). 
3.3. Upgraded Version of the BSSVQ Search Algorithm
Algorithm3 Search mechanism of the upgraded version 
Step 1. Initial setting: Given a TQA, M_{k}(TQA) satisfying (12) is found directly in the lookup table in bss_{k}. A TIE lookup table is also built. 
Step 2. Referencing Table 2 and through (9) and (10), an input vector is efficiently assigned to a subspace bss_{k}. And then a set, composed of the top M_{k}(TQA)sorted codewords in bss_{k}, is denoted by CSG(bss_{k}) and formulated as 
CSG(bss_{k}) = {c_{k}  k = 1,2,...,M_{k}(TQA)}.

Step 3. Starting at k = 1, set c_{r} = c_{k}  k = 1 in (15), then compute d(c_{r}, x). 
Step 4. Let k = k + 1, then obtain d(c_{r}, c_{k}) from the TIE lookup table. 
Step 5. If (d(c_{r}, c_{k}) < 2d(c_{r}, x)), then compute d(c_{k}, x), and perform Step 6. 
Otherwise, let k = k + 1, and then repeat Step 5, until k = M_{k}(TQA). 
Step 6. If (d(c_{k}, x) < d(c_{r}, x)), then replace c_{r} with c_{k}, and repeat Step 4. 
Otherwise, let k = k + 1, and then repeat Step 5, until k = M_{k}(TQA). 
4. Experimental Results
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
 3rd Generation Partnership Project (3GPP). Adaptive MultiRate—Wideband (AMRWB) Speech Codec; Transcoding Functions; TS 26.190; 3GPP: Valbonne, France, 2012. [Google Scholar]
 Ojala, P.; Lakaniemi, A.; Lepanaho, H.; Jokimies, M. The adaptive multirate wideband speech codec: System characteristics, quality advances, and deployment strategies. IEEE Commun. Mag. 2006, 44, 59–65. [Google Scholar] [CrossRef]
 Varga, I.; De Lacovo, R.D.; Usai, P. Standardization of the AMR wideband speech codec in 3GPP and ITUT. IEEE Commun. Mag. 2006, 44, 66–73. [Google Scholar] [CrossRef]
 Bessette, B.; Salami, R.; Lefebvre, R.; Jelínek, M.; RotolaPukkila, J.; Vainio, J.; Mikkola, H.; Järvinen, K. The adaptive multirate wideband speech codec (AMRWB). IEEE Trans. Speech Audio Process. 2002, 10, 620–636. [Google Scholar] [CrossRef]
 Salami, R.; Laflamme, C.; Adoul, J.P.; Kataoka, A.; Hayashi, S.; Moriya, T.; Lamblin, C.; Massaloux, D.; Proust, S.; Kroon, P.; et al. Design and description of CSACELP: A toll quality 8 kb/s speech coder. IEEE Trans. Speech Audio Process. 1998, 6, 116–130. [Google Scholar] [CrossRef]
 Wang, L.; Chen, Z.; Yin, F. A novel hierarchical decomposition vector quantization method for highorder LPC parameters. IEEE Trans. Audio Speech Lang. Process. 2015, 23, 212–221. [Google Scholar] [CrossRef]
 SalahEddine, C.; Merouane, B. Robust coding of wideband speech immittance spectral frequencies. Speech Commun. 2014, 65, 94–108. [Google Scholar] [CrossRef]
 Ramirez, M.A. Intrapredictive switched split vector quantization of speech spectra. IEEE Signal Process. Lett. 2013, 20, 791–794. [Google Scholar] [CrossRef]
 Chatterjee, S.; Sreenivas, T.V. Optimum switched split vector quantization of LSF parameters. Signal Process. 2008, 88, 1528–1538. [Google Scholar] [CrossRef]
 Yeh, C.Y. An Efficient VQ Codebook Search Algorithm Applied to AMRWB Speech Coding. Symmetry 2017, 9, 54. [Google Scholar] [CrossRef]
 Lu, Z.M.; Sun, S.H. Equalaverage equalvariance equalnorm nearest neighbor search algorithm for vector quantization. IEICE Trans. Inf. Syst. 2003, 86, 660–663. [Google Scholar]
 Xia, S.; Xiong, Z.; Luo, Y.; Dong, L.; Zhang, G. Location difference of multiple distances based knearest neighbors algorithm. Knowl. Based Syst. 2015, 90, 99–110. [Google Scholar] [CrossRef]
 Chen, S.X.; Li, F.W. Fast encoding method for vector quantisation of images using subvector characteristics and Hadamard transform. IET Image Process. 2011, 5, 18–24. [Google Scholar] [CrossRef]
 Chen, S.X.; Li, F.W.; Zhu, W.L. Fast searching algorithm for vector quantisation based on features of vector and subvector. IET Image Process. 2008, 2, 275–285. [Google Scholar] [CrossRef]
 Yao, B.J.; Yeh, C.Y.; Hwang, S.H. A search complexity improvement of vector quantization to immittance spectral frequency coefficients in AMRWB speech codec. Symmetry 2016, 8, 104. [Google Scholar] [CrossRef]
 Hwang, S.H.; Chen, S.H. Fast encoding algorithm for VQbased image coding. Electron. Lett. 1990, 26, 1618–1619. [Google Scholar]
 Hsieh, C.H.; Liu, Y.J. Fast search algorithms for vector quantization of images using multiple triangle inequalities and wavelet transform. IEEE Trans. Image Process. 2000, 9, 321–328. [Google Scholar] [CrossRef] [PubMed]
 Yeh, C.Y. An Efficient Iterative Triangular Inequality Elimination Algorithm for Codebook Search of Vector Quantization. IEEJ Trans. Electr. Electron. Eng. 2018, 13, 1528–1529. [Google Scholar] [CrossRef]
 3rd Generation Partnership Project (3GPP). Codec for Enhanced Voice Services (EVS); Detailed Algorithmic Description; TS 26.445; 3GPP: Valbonne, France, 2015. [Google Scholar]
Structure of SMSVQ  

Stage 1  CB1: r_{1} (1–9 order of r) (8 bits)  CB2: r_{2} (10–16 order of r) (8 bits)  
Stage 2  CB11: r^{(2)}_{1,1}_{–3} (6 bits)  CB12: r^{(2)}_{1,4}_{–6} (7 bits)  CB13: r^{(2)}_{1,7}_{–9} (7 bits)  CB21: r^{(2)}_{2,1}_{–3} (5 bits)  CB22: r^{(2)}_{2,4–7} (5 bits) 
jthOrder  Mean 

0  15.3816 
1  19.0062 
2  15.4689 
3  21.3921 
4  26.8766 
5  28.1561 
6  28.0969 
7  21.6403 
8  16.3302 
Codebooks  Full Search  EEENNS  DITIE  ITIE  

Stage 1  CB1  256  58.82  42.46  58.01 
CB2  256  63.87  42.79  62.03  
Stage 2  CB11  64  14.17  12.31  13.10 
CB12  128  22.91  14.40  15.32  
CB13  128  21.01  13.50  14.40  
CB21  32  11.08  8.95  9.48  
CB22  32  17.44  12.42  13.21 
TQA  Average Number of Searches in Various Codebooks  

CB1  CB2  CB11  CB12  CB13  CB21  CB22  
0.90  15.40  26.45  12.47  19.96  19.93  7.11  6.66 
0.91  16.10  27.52  12.86  20.84  20.62  7.11  6.72 
0.92  16.80  28.85  12.99  21.50  21.19  7.64  6.91 
0.93  17.79  30.23  13.52  21.84  22.02  7.64  7.15 
0.94  18.87  31.71  14.04  22.85  22.72  8.00  7.57 
0.95  20.03  33.58  14.61  23.85  23.72  8.26  7.84 
0.96  21.36  35.81  15.04  24.76  24.95  8.87  8.21 
0.97  23.18  38.37  15.86  25.93  26.24  9.27  8.51 
0.98  25.71  41.82  16.73  27.60  27.86  10.00  9.33 
0.99  29.71  47.12  18.21  29.61  29.99  10.49  10.15 
TQA  Average Number of Searches in Various Codebooks  

CB1  CB2  CB11  CB12  CB13  CB21  CB22  
0.90  10.56  15.82  6.55  8.48  8.21  4.06  4.69 
0.91  10.99  16.26  6.62  8.56  8.30  4.06  4.72 
0.92  11.40  16.79  6.63  8.65  8.38  4.22  4.82 
0.93  11.86  17.36  6.73  8.70  8.49  4.22  4.90 
0.94  12.40  17.89  6.80  8.76  8.54  4.28  5.10 
0.95  13.00  18.57  6.89  8.84  8.60  4.34  5.19 
0.96  13.67  19.44  6.95  8.91  8.68  4.41  5.32 
0.97  14.53  20.27  7.10  8.98  8.73  4.50  5.43 
0.98  15.71  21.50  7.16  9.09  8.85  4.68  5.74 
0.99  17.46  23.28  7.33  9.22  8.97  4.75  6.04 
Method  LR in CB1 (%)  LR in CB2 (%)  Overall Search Load  Overall LR (%)  

Full Search  Benchmark  Benchmark  5280  Benchmark  
EEENNS  77.03  75.05  1253.76  76.26  
DITIE  83.42  83.29  878.88  83.36  
ITIE  77.34  75.77  1165.99  77.92  
Original version of BSSVQ (TQA)  0.90  93.98  89.67  528.78  89.99 
0.91  93.71  89.25  548.77  89.61  
0.92  93.44  88.73  570.76  89.19  
0.93  93.05  88.19  595.34  88.72  
0.94  92.63  87.61  624.92  88.16  
0.95  92.18  86.88  657.95  87.54  
0.96  91.66  86.01  696.62  86.81  
0.97  90.95  85.01  743.15  85.93  
0.98  89.96  83.66  808.06  84.70  
0.99  88.39  81.60  902.67  82.90  
Upgraded version (TQA)  0.90  95.88  93.82  306.41  94.20 
0.91  95.71  93.65  314.19  94.05  
0.92  95.55  93.44  323.09  93.88  
0.93  95.37  93.22  332.32  93.71  
0.94  95.15  93.01  342.42  93.51  
0.95  94.92  92.75  353.80  93.30  
0.96  94.66  92.40  367.20  93.05  
0.97  94.32  92.08  382.26  92.76  
0.98  93.86  91.60  404.15  92.35  
0.99  93.18  90.91  435.10  91.76 
TQA  BSSVQ (Benchmark)  Proposed  LR (%) 

0.90  528.78  306.41  42.05 
0.91  548.77  314.19  42.75 
0.92  570.76  323.09  43.39 
0.93  595.34  332.32  44.18 
0.94  624.92  342.42  45.21 
0.95  657.95  353.80  46.23 
0.96  696.62  367.20  47.29 
0.97  743.15  382.26  48.56 
0.98  808.06  404.15  49.99 
0.99  902.67  435.10  51.80 
Memory Size (Byte)  BSS Space  Dichotomy Position  TIE  Sum 

CB1  524,288  36  326,400  850,724 
CB2  131,072  28  326,400  457,500 
CB11  2048  12  20,160  22,220 
CB12  4096  12  81,280  85,388 
CB13  4096  12  81,280  85,388 
CB21  1024  12  4960  5996 
CB22  2048  16  4960  7024 
Sum  668,672  128  845,440  1,514,240 
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Yeh, C.Y.; Huang, H.H. An Upgraded Version of the Binary Search SpaceStructured VQ Search Algorithm for AMRWB Codec. Symmetry 2019, 11, 283. https://doi.org/10.3390/sym11020283
Yeh CY, Huang HH. An Upgraded Version of the Binary Search SpaceStructured VQ Search Algorithm for AMRWB Codec. Symmetry. 2019; 11(2):283. https://doi.org/10.3390/sym11020283
Chicago/Turabian StyleYeh, ChengYu, and HungHsun Huang. 2019. "An Upgraded Version of the Binary Search SpaceStructured VQ Search Algorithm for AMRWB Codec" Symmetry 11, no. 2: 283. https://doi.org/10.3390/sym11020283