METHOD AND ARRANGEMENT FOR FINDING AN OPTIMAL RECONSTRUCTION POINT

Abstract: To reduce the complexity of finding reconstruction points in connection with vector quantization, a set of reconstruction points close to a predicted reconstruction point is selected, whereupon a distortion measure is calculated for all the reconstruction points of the selected set, and that reconstruction point that gives the smallest distortion, is chosen as the optimal reconstruction point. Since only a small number of reconstruction points has to be searched, the complexity of the search is significantly reduced.

Description: METHOD AND ARRANGEMENT FOR FINDING AN OPTIMAL RECONSTRUCTION POINT TECHNICAL FIELD The invention relates generally to vector quantization and, more specifically, to a method and an arrangement for finding an optimal reconstruction point for an N- dimensional point to be quantized. BACKGROUND OF THE INVENTION When data are to be quantized, vector quantization is often used. This is due to the fact that the distortion resulting from vector quantization always is less than the distortion resulting from scalar quantization. Moreover, the distortion will decrease further if the data to be quantized are correlated. Vector quantization is computationally complex in the sense that a search for the optimal vector has to be carried out. The optimal vector is usually defined as the vector giving the least residual error. Solutions with a "nearest neighbor" list or similar approaches to find the reconstruction points will reduce the complexity of the search. One technical field where vector quantization is used is speech coding, where several correlated gain parameters are jointly quantized. All CELP (Code Excited Linear Prediction) coders of today minimize the mean square error in the weighted speech domain when quantizing many of the parameters. To achieve the best speech quality, the correlated gain parameters should also be quantized with regard to the distortion in the weighted speech domain and not to the traditional distortion in the gain domain. This makes it impossible to create a "nearest neighbor" list since this list with this distortion measure, is signal dependent, i.e. depends on other values than the ones to be quantized. When the distortion measure is signal dependent, all reconstruction points have to be searched in order to find the best reconstruction point. One example of this is the gain quantization in the newly standardized speech codec IS-641 used in the Digital American Mobile Phone System (D-AMPS). The complexity of the search will be high since all reconstruction points have to be searched. It will be especially complex for the above mentioned CELP coders, since the distortion calculation itself is complex. SUMMARY OF THE INVENTION The object of the invention is to reduce the complexity of the current methods and apparatuses for finding reconstruction points in connection with vector quantization. This is attained by selecting a set of reconstruction points close to a predicted reconstruction point, evaluating a distortion measure for all reconstruction points of the selected set, and choosing, as reconstruction point, the reconstruction point of the selected set that gives the smallest distortion. Since only a small number of the total number of reconstruction points has to be searched with this method, the complexity is significantly reduced. BRIEF DESCRIPTION OF THE DRAWING The invention will be described more in detail below with reference to the appended drawing, on which - Fig. 1 illustrates an example of reconstruction points for a 2-dimensional vector quantizer, where the values in the two dimensions are strongly correlated, - Fig. 2 illustrates a relationship between predicted values and sorted reconstruction points for the reconstruction points illustrated in Fig. 1, - Fig. 3 illustrates another example of reconstruction points for a 2-dimensional vector quantizer, where the values in the two dimensions are evenly distributed, and - Fig. 4 illustrates a further example of reconstruction points for a 2-dimensional vector quantizer, where the values in the two dimensions are grouped along the border of a circle. PREFERRED EMBODIMENTS Fig. 1 illustrates an example of reconstruction points for transformed gain parameters resulting from a speech codec. The transformation has been done to reduce the variance of the gain. This reduced variance makes it possible to construct a quantizer that introduces less distortion. As apparent from Fig. 1, the two different gains are strongly correlated. In accordance with the invention, the reconstruction points in Fig. 1 are sorted in advance by ordering them by their distance from a reference point in an N- dimensional space. In Fig. 1, that reference point is placed in the upper right-hand corner, and it is supposed that N = 2. Since the reconstruction points for correlated data are grouped around a line or curve in the N-dimensional space, it is possible to create a cross-reference list that makes it possible to access a set of reconstruction points surrounding an arbitrarily predicted reconstruction point. In case the reconstruction points are grouped around a line in the N-dimensional space as in Fig. 1, it is possible to create the cross- reference list by sorting the reconstruction points by their distance to the reference point at one end of the line. In Fig. 2, a transfer function for transforming the prediction value, in this example the "distance to reference point", into "sorted reconstruction point" is shown. The transfer function in Fig. 2 which is created in advance, is used to predict a reconstruction point, called "sorted VQ index" in Fig. 2, from the "distance to reference point" as will be described below. The transfer function is created by calculating the distance to the reference point, as described below, for each sorted reconstruction point. The transfer function in Fig. 2 can very well be represented by two or three linearized first degree equations, giving a low complexity transformation function from "distance to reference point" into "sorted reconstruction point" . In accordance with the invention, finding of an optimal reconstruction point for an N-dimensional point to be quantized, where the N-dimensional point corresponds to N parameters extracted from an input signal, is done in the following way: Use the unquantized values of the N-dimensional point to be quantized to calculate the distance from the reference point by means of the equation where N is the dimension of the space, X t is the unquantized value in the i:th dimension, and Refi is the reference point in the i:th dimension. Then, transform the calculated distance into "sorted reconstruction point" using the linearized version of the transfer function shown in Fig. 2. After that, among the reconstruction points as sorted, select a set of reconstruction points surrounding the predicted reconstruction point. The size of the selected set of reconstruction points should be chosen large enough so that the optimal reconstruction point always exists within the selected set. This can be checked during development by conducting a search for the optimal reconstruction point both in a conventional manner, i.e. over all reconstruction points, and in accordance with the invention, and verifying that the same optimal reconstruction point always is found. In the example in Fig. 1, it will only be necessary to include about 10 % of the total number of reconstruction points on each side of the predicted reconstruction point to ensure that the optimal reconstruction point is included in the selected set of reconstruction points. Thus, the size of the selected set of reconstruction points may in fact be predetermined. Thereafter, for each reconstruction point within the selected set of reconstruction points, a so called distortion value is calculated. The distortion value represents the difference between an original signal, e.g. a speech signal coming in to a speech encoder, and a reconstructed signal, e.g. an output speech signal from the speech encoder. Should the distortion value be more dependent upon one dimension than the other dimension(s), this can be taken into account in the above equation for distance calculation, e.g. by giving different weight to the different dimensions. Finally, as the optimal reconstruction point, choose the reconstruction point having the lowest calculated distortion value in said selected set of reconstruction points surrounding the predicted reconstruction point. In the above example, the search complexity will be reduced by approximately 80% since only a small part of the total number of reconstruction points has to be searched. The complexity can be further reduced if it can be accepted that the optimal reconstruction point is not always used. This further reduction of complexity can be achieved by reducing the selected set of reconstruction points. The only cost for the prediction is a small memory increase required for storing the cross reference list used to access the reconstruction points sorted according to the distance measure. When the reconstruction points are to be transmitted over a transmission channel with bit errors, the reconstruction points are often so ordered that a single bit error will give as small a distortion as possible. This method is called index assignment. If index assignment is unnecessary for the reconstruction points, the cross reference list is not needed since the reconstruction points can be ordered in this way from the beginning. Thus, no extra memory is required. In the example in Fig. 3, the reconstruction points are grouped almost evenly in a square in a two dimensional space. In this example, there is no correlation between the values in the different dimensions. The reference point is therefore placed in a smaller dimension where it is possible to find correlation. In this example, this is the first dimensional space. In Fig. 3, the reference point may be placed at the x-mark to the right, and only the distance in the horizontal plane would be used. This will lead to that the selected set of reconstruction points will be larger than it would have been, had there been a correlation between the values in the different dimensions. However, the saving in complexity will still be considerable. In Fig. 4, the reconstruction points are approximately placed along the border of a circle. In this case, the "distance" can be the angular distance, i.e. the angle, to the predicted reconstruction point. If the predicted reconstruction point in this case has an angle close to 0 or 2π radians, the selected set of reconstruction points must include reconstruction points that have an angle close to both 0 and 2π. This will lead to a low complexity search also when the reconstruction points are placed in this manner. As should be apparent from the above, the complexity of finding the optimal reconstruction point will be reduced by means of the invention. It should also be obvious to anyone skilled in the art that the method described above may be run on a processor.

Claims: CLAIMS 1. In an N-dimensional space, N>2, containing a predetermined number of predetermined reconstruction points to be used by a decoder to reconstruct an input signal coded by an encoder, a method of finding an optimal reconstruction point for an N-dimensional point to be quantized, said N-dimensional point corresponding to N parameters extracted from the input signal, characterized by - sorting, in advance, the predetermined reconstruction points with regard to their distance from a reference point, - creating, in advance, a function to transform a distance from the reference point into a sorted reconstruction point, - calculating the distance from the reference point to the N-dimensional point, - transforming, by means of the created function, the calculated distance into a predicted reconstruction point, the distance of which from the reference point being closest to the distance to be transformed, - selecting a set of reconstruction points surrounding, as sorted, the predicted reconstruction point, - calculating a distortion value for all reconstruction points in said selected set of reconstruction points, and - choosing the reconstruction point having the lowest calculated distortion value as the optimal reconstruction point in said selected set of reconstruction points. 2. The method as claimed in claim 1, characterized in that a predetermined set of reconstruction points surrounding, as sorted, the predicted reconstruction point, is selected. 3. An arrangement for finding, in an N-dimensional space, N>2, containing a predetermined number of predetermined reconstruction points to be used by a decoder to reconstruct an input signal coded by an encoder, an optimal reconstruction point for an N-dimensional point to be quantized, said N-dimensional point corresponding to N parameters extracted from the input signal, characterized by - means for sorting, in advance, the predetermined reconstruction points with regard to their distance from a reference point, - means for creating, in advance, a function to transform a distance from the reference point into a sorted reconstruction point, - means for calculating the distance from the reference point to the N-dimensional point, - means for fransforming, by means of the created function, the calculated distance into a predicted reconstruction point, the distance of which from the reference point being closest to the distance to be transformed, - means for selecting a set of reconstruction points surrounding, as sorted, the predicted reconstruction point, - means for calculating a distortion value for all reconstruction points in said selected set of reconstruction points, and - means for choosing the reconstruction point having the lowest calculated distortion value as the optimal reconstruction point in said selected set of reconstruction points. 4. The arrangement as claimed in claim 3, characterized in that said means for selecting are adapted to select a predetermined set of reconstruction points surrounding, as sorted, the predicted reconstruction point.

Inventors: LINDQVIST MORGAN, LINDQVIST, MORGAN
Applicants: ERICSSON TELEFON AB L M, TELEFONAKTIEBOLAGET LM ERICSSON (PUBL)
Application year: 1999
Main classification: G10L19
IPC codes: G10L11, G10L19, H03M7, H04N7