Audio Signal Processing and Coding

3.5 BIT-ALLOCATION ALGORITHMS

Until now, we discussed various scalar and vector quantization algorithms without emphasizing how the number of quantization levels are determined. In this section, we review some of the fundamental bit allocation techniques. A bit-allocation algorithm determines the number of bits required to quantize an audio frame with reduced audible distortions. Bit-allocation can be based on certain perceptual rules or spectral characteristics. From Figure 3.1, parameters typically quantized include the transform coefficients, x, scale factors, S, and the residual error, e. For now, let us consider that the transform coefficients, x, are to be quantized, i.e.,

where N_f represents the total number of transform coefficients. Let the total number of bits available to quantize the transform coefficients be N bits. Our objective is to find an optimum way of distributing the available N bits across the individual transform coefficients, such that a distortion measure, D, is minimized. The distortion, D, is given by

where x_i and denote the i-th unquantized and quantized transform coefficients, respectively; and E[.] is the expectation operator. Let n_i be the number of ...