## 1 Introduction  
As explicitly stated in the Abstract, the algebraic code-excited linear-prediction (ACELP)-based speech coding technique [1; 2; 3; 4; 5; 6] has the double advantage of low bit rate and high speech quality. Accordingly, it is most widely used in speech communication systems, and adopted in many speech codec standards, such as G.723.1, G.729 [1] in International Telecommunication Union (ITU), adaptive multi-rate narrowband (AMR-NB) [2] and wideband (AMR-WB) [3], and in the codec for enhanced voice services (EVS) [4; 5] in the 3 rd Generation Partnership Project (3 GPP). Among such standards, the AMR-WB speech codec with a 16 kHz sampling rate is applied to modern mobile communication systems as a way to improve the speech quality in handheld devices, e.g., smartphones. The AMR-WB codec [3; 6; 7; 8] is a multi-mode speech codec with nine wideband speech coding modes with bitrates of 23.85, 23.05, 19.85, 18.25, 15.85, 14.25, 12.65, 8.85 and 6.6 kbps. The ACELP-based coding technique is developed as an excellent speech coding technique, but a price paid is a high computational complexity required in the AMR-WB codec. Using the AMR-WB speech codec, the speech quality of a smartphone can be improved but at the cost of high power consumption on a smartphone battery. A vector quantization (VQ) of immittance spectral frequency (ISF) coefficients [9; 10; 11; 12; 13] occupies the second largest part of the total computation load required in the AMR-WB encoder. The VQ structure in AMR-WB adopts a combination of split VQ (SVQ) and multi-stage VQ (MSVQ) techniques, referred to as split-multistage VQ (S-MSVQ), to quantize the 16-order ISF coefficients. Conventionally, VQ conducts a full search to ensure that a codeword is best matched with an arbitrary input vector, but the full search requires an enormous computational load. Thus, a continuous effort has been made to simplify the search complexity of an encoding process in a great volume of published studies [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. These approaches are further classified into three types in terms of the way the complexity is simplified, including the tree-structured VQ (TSVQ) techniques [14; 15; 16], the TIE-based approaches [18; 19; 20] and the equal-average equal-variance equal-norm nearest neighbor search (EEENNS) based algorithms [21; 22; 23; 24; 25]. A TIE algorithm was proposed in [18] as a solution to a VQ-based image coding problem in the aspect of computational load reduction. Improved versions of TIE approaches are presented in [19; 20] to downsize a search space, giving rise to further reduction in computational load. However, there exists a high correlation between ISF coefficients of neighboring frames in AMR-WB, that is, ISF coefficients evolve smoothly over successive frames. This feature benefits TIE-based VQ encoding, according to which a remarkable computational load reduction is demonstrated, while a moving average (MA) filter is required to smooth the data in advance of VQ encoding of ISF coefficients. As a consequence of data smoothing, the high correlation feature is gone, resulting in a poor performance in computational load reduction. On the other hand, an EEENNS algorithm was derived from equal-average nearest neighbor search (ENNS) and equal-average equal-variance nearest neighbor search (EENNS) approaches. The EEENNS algorithm, as opposed to TIE-based approaches, uses three significant features of a vector, i.e., mean value, variance, and norm, as a three-level elimination criterion to reject impossible codewords. In view of this, a TIE algorithm equipped with a dynamic and an intersection mechanism, DI-TIE for short, is presented as an efficient way to quantize the ISF coefficients in AMR-WB. Both mechanisms are designed in a way that recursively enhances the performance of the TIE algorithm. On the other hand, a major motivation behind this paper is to meet the energy saving requirement on handheld devices for an extended operation time period. This paper is outlined as follows.