An Efficient Codebook for the SCELP Low Delay Audio Codec Hauke Kr¨ uger and Peter Vary Institute of Communication Systems and Data Processing RWTH Aachen University, D-52056 Aachen, Germany email: {krueger,vary}@ind.rwth-aachen.de Abstract— The SCELP (Spherical Code Excited Linear Predic- tion) audio codec has recently been proposed as a new candidate for low delay audio coding based on Linear Prediction (LP). The new codec applies closed-loop vector quantization employing a spherical code in a gain shape manner. The spherical code is based on the apple-peeling code construction rule and in general does not require a codebook table for the encoding and decoding process. In this contribution, however, we propose to employ auxiliary information gathered in advance to reduce the computational encoding and decoding complexity at runtime significantly. This auxiliary information can be considered as the SCELP codebook. Due to the consideration of the characteristics of the apple- peeling code construction principle, this codebook can be stored very efficiently in read-only-memory. With the proposed princi- ple, low computational as well as low memory complexity can be achieved simultaneously in the SCELP codec. I. I NTRODUCTION Lossy compression of audio signals can be roughly subdivided into two principles: Perceptual audio coding is based on transform coding. The signal to be compressed is firstly transformed by an analysis filter bank, and the sub band rep- resentation is quantized in the transform domain. A perceptual model controls the adaptive bit allocation for the quantization. The goal is to keep the noise introduced by quantization below the masking threshold described by the perceptual model. In general, the algorithmic delay is rather high due to large transform lengths, e.g. [3]. Parametric audio coding is based on a source model. One parametric approach is based on linear prediction (LP), the basis for todays highly efficient speech coding algorithms for mobile communications, for example [4]. An all-pole filter models the spectral envelope of the input signal. Based on the inverse of this filter, the input is filtered to produce the LP residual signal which is quantized. Often vec- tor quantization with a sparse codebook is applied according to the CELP (Code Excited Linear Prediction [2]) analysis-by- synthesis approach to achieve very high compression. Due to the sparse codebook and additional modeling of the speaker’s instantaneous pitch period, speech coders perform well for speech but cannot compete with perceptual audio coding for non-speech input. The typical algorithmic delay is around 20 ms. In a previous contribution [1] we presented a new coding scheme for low delay parametric audio coding in which the principle of linear prediction is preserved while a spherical code is used in a gain-shape manner for the quantization of the residual signal at a moderate bit rate. This spherical code is based on the apple-peeling principle introduced in [5] for the purpose of channel coding and referenced in [6] in the context of a spherical code analysis. The apple-peeling code has been revisited in [7] for DPCM. In contrast to that approach, the SCELP codec employs the spherical code in a CELP scheme. The sphere construction principle according to the apple-peeling method in general enables the encoding and decoding of a signal vector without any codebook. In this contribution we propose to use auxiliary information which can be determined in advance during code construction. This auxiliary information is stored in read-only-memory (ROM) and can be considered as a compact vector codebook. At codec runtime it aids the process of transforming the spherical code vector index, used for signal transmission, into the reconstructed code vectors on encoder and decoder side. The compact codebook is based on a representation of the spherical code as a coding tree combined with a lookup table to store all required trigonometric function values for spherical coordinate transformation. Because both parts of this compact codebook are determined in advance the computational complexity for signal compression can be drastically reduced. The properties of the compact codebook can be exploited to store it with only a small demand for ROM compared to an approach that stores a lookup table as often applied for trained codebooks [11]. In this paper, the principle of the SCELP audio coding scheme will be shortly reviewed in Section II. The construction of the spherical code according to the apple-peeling method is described in Section III. A representation of this code construction principle as spherical coding tree for code vector decoding is explained in Section IV. In Section V, the principle to efficiently store the coding tree and the lookup table for trigonometric function values for code vector reconstruction is presented. Results considering the reduction of the compu- tational and memory complexity are given in Section VI. II. THE SCELP AUDIO CODEC The SCELP codec as proposed in [1] is based on block adaptive linear prediction. Linear predictive coding in general exploits correlation immanent to an input signal x(k) by decorrelating it before quantization. For short term block adaptive linear prediction of order N , a windowed segment of the input signal, x w (k), of length L LP C is analyzed 119 0-7803-9752-5/06/$20.00 ©2006 IEEE