Method and apparatus for quantization and inverse-quantization of picture data

Abstract: The quantization information (Q3 Q4 Q5) entered to a shifter 110 is shifted using the quantization quantity (Q1 Q2) as an amount of shifting. The upper three bits of the shifted quantization information are added in an addition unit 112 to a value S1 resulting from conversion by a table 111 of the quantization information (Q1 Q2). The four bits from the addition unit 112 are appended to the lower three bits of the shifted quantization information to reproduce 7-bit quantization characteristics. The picture data may be quantized or inverse-quantized using the quantization characteristics having a wide range and appropriate precision.

Description: This invention relates to methods and apparatus for quantization and inverse quantization of picture data. Embodiments of the invention relate to: such methods and apparatus using a recording medium for storage, such as an optical disc or a magnetic tape; an apparatus for recording/reproducing the information using the recording medium for storage, such as an optical disc or a magnetic tape; and an apparatus for transmitting/receiving the information which may be suitably applied to a so-called teleconferencing system; a moving-picture telephone system; or a broadcasting system US-A-4 791 483 discloses an adaptive DPCM video encoder which compresses a digitised video signal. The signal is quantised using a non-linear quantization function. A plurality of quantization transfer functions are stored and are selected according to an evaluation of the size of step transitions as determined from a quantized difference signal produced by a recursive filter. The quantization transfer functions are stored in a plurality of ROMs. The plurality of transfer functions results in the storage of a large amount of data in the ROMs. Recently, in a so-called signal transmission system for transmitting video and voice signals to a remote place, such as a teleconferencing system or a television telephone system, it has been a customary practice to make efficient use of the transmission channel by encoding the video or voice signal for improving the information transmission efficiency. For moving picture data, having an extremely large quantity of the information, above all, there must be provided means for recording picture signals with high efficiency encoding and for decoding the recorded signals with high efficiency when reading out the recorded signals. As such means, a number of high efficiency encoding systems have been proposed which take advantage of the correlation of picture signals. Among these high efficiency encoding systems, there is the MPEG (Moving Picture Experts Group) system. With the MPEG system, the difference between picture frames of picture signals is taken for reducing the redundancy along the time scale by taking advantage of the correlation between frames, and subsequently the processing by discrete cosine transform (DCT) is performed for reducing the redundancy along the spatial scale by taking advantage of line correlation for achieving high efficiency encoding of the picture signals. In utilizing the correlation between frames, if frame pictures PC1, PC2 and PC3 are generated at timings t = t 1 , t 2 and t 3 , respectively, as shown at (A) in Fig.9, a picture PC12 may be generated by taking the difference between the picture signals of the frame pictures PC1 and PC2, as shown at (B) in Fig.9, while a picture PC23 may be generated by taking the difference between the picture signals of the frame pictures PC2 and PC3, as shown at (B) in Fig.9. Since the frame pictures temporally adjacent to each other usually are not changed significantly from each other, the difference between these two frame pictures is of a smaller value. That is, with the picture PC12, shown at (B) in Fig.9, difference signals representing the hatched portion of the picture PC12 shown at (B) in Fig.9 are produced as the difference between the picture signal of the frame pictures PC1 and PC2, shown at (A) in Fig.9, while difference signals representing the hatched portion of the picture PC23 shown at (B) in Fig.9 are produced as the difference between the picture signal of the frame pictures PC2 and PC3, shown at (A) in Fig.9. The encoding volume may be compressed by encoding these difference signals. However, the original picture cannot be restored by transmitting only the difference signals. Consequently, in compression encoding the picture signals, the frame pictures are classed into intra-coded pictures or I-pictures, predictive-coded pictures or P-pictures and bidirectionally predictive-coded pictures or B-pictures. That is, as shown for example at (A) and (B) in Fig.10, 17 frame picture signals of from a frame F1 to a frame F17 are grouped together as a group of pictures, which is a processing unit. The leading frame F1 is encoded as the I-picture, while the second frame F2 and the third frame F3 are processed as the B-picture and the P-picture, respectively. The fourth frames ff., that is the frames F4 up to F17, are processed alternately as the B-pictures and as the P-pictures. As for the picture signals of the I-picture, the one-frame picture signals are transmitted in their entirety. On the other hand, as for the picture signals for the B-picture, a difference between means values of the picture signals of a temporally preceding frame and means values of the picture signals of a temporally succeeding frame is found and encoded for transmission, as shown at (B) in Fig.10. Figs.11 (A) and (B) illustrate the principle of the method for encoding the moving picture signals as described above. Thus, Figs.11(A) and (B) illustrate frame data of the moving picture signals and the transmission frame data, respectively. Referring to Fig.11, since the first frame F1 is processed as the I-picture, that is as the non-interpolated frame, this frame F1 is directly transmitted on the transmission channel as transmission data FIX (non-interpolated transmission data). On the other hand, since the second frame F2 is processed a the B-picture, that is as an interpolated frame, the difference between mean values of the temporally succeeding frame F3 (inter-frame encoded non-interpolated frame) and the temporally preceding frame F1 is taken and transmitted as the transmission data (interpolated transmission frame data). Specifically, the B-picture is processed in four different modes. The first processing mode consists in directly transmitting the data of the original frame F2 as the transmission data F2X, as shown by a broken-line arrow SP1 (intra-coding). The processing mode is similar to that for the I-picture. The second processing mode consists in taking a difference between the frame F2 and the temporally succeeding frame F3 and transmitting the difference as indicated by a broken-line arrow SP2 in Fig.11 (backward predictive coding). The third processing mode consists in taking a difference between the frame F2 and the temporally preceding frame F1 and transmitting the difference as indicated by a broken-line arrow SP3 in Fig.11 (forward predictive coding). The fourth processing mode consists in taking a difference between the temporally preceding frame F1 and the temporally succeeding frame F3 and transmitting the difference as transmission data F2X as indicated by a broken-line arrow SP4 in Fig.11 (bidirectionally predictive coding). Of these four methods, the method which will give the least amount of transmission data is employed. It is noted that, when transmitting the difference data, a motion vector x1 between the frame reference (frame under consideration) and a prediction picture (picture of the frame the difference from reference the frame of which is calculated), that is a motion vector x1 between the frames F1 and F2 for forward prediction coding, a motion vector x2, that is a motion vector between the frames F2 and F3 for backward prediction coding, or both the motion vectors x1 and x2 for bidirectionally predictive-coding, are transmitted along with the difference data. As for the frame F3 of the P-picture (inter-frame coded non-interpolated frame), difference signals between the frame F3 and the temporally preceding frame F1 as the prediction picture as indicated by a broken-line arrow SP3 and a motion vector x3 are calculated and transmitted as transmission data F3X (forward prediction-coding). Alternatively, data of the original frame F3 are directly transmitted as transmission data F3X, as indicated by a broken-line arrow SP1 (intra-coding). One of these two P-pictures which will give the smaller amount of transmission data is selected a in the case of the B-picture mentioned above. Meanwhile, the frame F4 of the B-picture and the frame F5 of the P-picture are processed in the same manner as above for producing transmission data F4X, F5X and motion vectors x4, x5 and x6. Fig.12 illustrates another example of inter-frame encoding and intra-frame encoding of a picture sequence. In this figure, a cycle of 15 frames represents an encoding unit. It is noted that a frame 2 is an I-picture, while frames 5, 8, 11 and 14 are P-pictures coded by inter-frame coding, with the prediction being made only from the forward direction, and frames 0, 1, 3, 4, 6, 7, 9, 10, 12 and 13 are B-pictures coded by inter-frame coding, with prediction being made from both the backward and forward directions. The inputting, encoding, decoding and outputting (display) sequences for the above-described intra-frame/ inter-frame encoding are shown in Fig.13. Fig.14 illustrates an example of the construction of an apparatus for encoding, transmitting and decoding the moving picture signals based on the above-described principle. The encoding apparatus 1 encodes the input picture signals and transmits the encoded signals to a recording medium 3 for recording thereon. A decoding apparatus 2 reproduces, decodes and outputs signals recorded on the recording medium 3. In the encoding device 1, video signals VD are entered via an input terminal 10 to a pre-processing circuit 11 and separated into luminance signals and color signals, herein chrominance difference signals. The luminance signals and the chrominance signals are separately analog-to-digital converted by analog-to-digital (A/D) converters 12, 13. The digitized picture signals from the A/D converters 12, 13 are transmitted to and stored in a frame memory 14. In the frame memory 14, the luminance signals and the chrominance signals are stored in a luminance signal frame memory 15 and chrominance frame memory 16, respectively. A format converting circuit 17 translates frame format signals stored in the frame memory 14 into block format signals. The video signals stored in the frame memory 14 are frame format data consisting of V lines each consisting of H dots, as shown at (A) in Fig.15. The format converting circuit 17 divides the one-frame signals into N slices each consisting of 16 lines. Each slice is divided into M macroblocks, as shown at B in Fig.15. Each macroblock is made up of luminance signals corresponding to 16×16 pixels or dots, which are further divided into blocks Y[1] to Y[4], each consisting of 8×8 dots, as shown at (C) in Fig.15. The 16×16 dot luminance signals are associated with 8×8 dot Cb signals and 8×8 dot Cr signals. The moving picture signals within the slices shown at (A) in Fig.15 are arrayed so that moving picture signals represent continuous signals on the basis of the macroblocks shown at (C) in Fig.15 and the moving picture signals within each of the macroblocks also represent continuous block-based signals in the raster scanning sequence. The data thus converted into block format data are supplied from the format converting circuit 17 to an encoder 18 and encoded in a manner which will be explained in more detail by referring to Fig.16. The signals encoded by the encoder 18 are outputted as a bit stream to the transmission channel so as to be recorded on for example, the recording medium 3. The data reproduced from the recording medium 3 are supplied to a decoder 31 of the decoding device 2 so as to be decoded in a manner which will be explained in more detail by referring to Fig.19. The data decoded by the decoder 31 are entered to a format converting circuit 32 and thereby converted from the block format data into the the above-mentioned frame format data. The luminance signals of the frame format are transmitted to and stored in a luminance signal frame memory 34 of a frame memory 33 and the chrominance signals are transmitted to and stored in a chrominance signal frame memory 35. The luminance signals and the color difference signals read out from the luminance signal frame memory 34 and from the chrominance signal frame memory 35 are digital-to-analog converted by the digital-to-analog converters (D/A converters) 36, 37. The resulting analog signals are transmitted to a post-processing circuit 38 so as to be synthesized into output picture signals which are outputted at an output terminal 30 for display on a display device, such as CRT. Referring to Fig.16, the construction of the encoder 18 is explained. The picture data supplied via an input terminal 49 are entered on the macroblock basis to a motion vector detecting circuit 50 which is adapted for processing the picture data of the respective frames as the I-picture, P-pictures or B-pictures, in accordance with a pre-set sequence. The respective input frame pictures are processed as the I-picture, P-picture or as the B-picture in the pre-set manner. For example, the group of pictures constituted by the frames F1 to F17 shown in Fig.10 is processed in the sequence of I, B, P, B, P, ··· B, P, as shown therein. The picture data of the frame to be processed as the I-picture, for example, the frame F1, is transmitted from the motion vector detection circuit 50 to a forward original picture section 51a of a frame memory 51 for storage therein, while the picture data of the frame to be processed as the B-picture, for example, the frame F2, is transmitted to and stored in a reference original picture section 51a of the frame memory 51 and the picture data of the frame to be processed as the P-picture, for example, the frame F3, is transmitted to and stored in a backward original picture section 51c of the frame memory 51. At the next timing when the picture of a frame to be processed as the B-picture such as the frame F4 or the picture of a frame to be processed as P-picture such as the frame F5 is entered, the picture data of the first P-picture, so far stored in the backward original picture section 51c, that is the frame F4, is transferred to the forward original picture section 51a, and the picture of the next B-picture, that is the frame F4, is stored (or overwritten) in the original picture section 51b, while the picture data of the next P-picture, that is the frame F5, is stored (or overwritten) in the backward original picture section 51c. The sequence of the operations is repeated sequentially. The signals of the respective pictures, stored in the frame memory 51, are read out and transmitted to a prediction mode changeover circuit 52 in which the frame prediction mode operation or the field prediction mode operation is carried out. Besides, in a processing section 53, the intra-coding, forward predictive coding, backward predictive coding or bidirectional predictive coding operations are carried out under control of a prediction decision circuit 54. The decision as to which of these operations is to be carried out is made depending on prediction error signals, that is the difference between the reference picture (picture under consideration), and the prediction picture therefor. Consequently, the motion vector detection circuit 50 generates the sum of absolute or squared values of the prediction error signals employed for the decision. The frame prediction mode and the field prediction mode in the prediction mode switching circuit 52 is explained. If the frame prediction mode is set in the prediction mode changeover circuit 52, the prediction mode switching circuit 52 directly outputs the four luminance blocks Y[1] to Y[4] supplied from the motion vector detection circuit 50 to a downstream side processing unit 53. In such case, as shown at (A) in Fig.17, the odd-field line data and the even-field line data co-exist in each luminance block. In Fig.17, solid lines and broken lines in each macroblock represent odd-field line data (first field line data) and even-field line data (second field line data), respectively, while a and b represent units of the motion compensation. In the frame prediction mode, prediction is performed based on the four luminance blocks (macroblocks) and a motion vector is associated with the four luminance blocks. Conversely, if the field prediction mode is set in the prediction mode changeover circuit 52, the signals entered in the array shown at (A) in Fig.17 from the motion vector detection circuit 50 are constructed so that the luminance blocks Y[1] and Y[2] are composed only of odd-field line data while the remaining two luminance blocks Y[3] and Y[4] are composed only of even-field line data, as shown at (B) in Fig.17. These luminance blocks Y[1] to Y[4] are outputted to the processing section 53. In such case, a motion vector is associated with the two luminance blocks Y[1] and Y[2], while another motion vector is associated with the other two luminance blocks Y[3] and Y[4]. Referring further to Fig.16, the motion vector detection circuit 50 outputs the sum of absolute values of the prediction errors for the frame prediction mode and the sum of absolute values of the prediction errors for the field prediction mode to the prediction mode changeover circuit 52. The changeover circuit 52 compares these sums of the absolute values of the prediction errors for the frame prediction mode and the field prediction mode to each other to cause the above-described operations for the prediction mode having the lesser value of the sum to be performed to output the resulting data to the processing section 53. In effect, the corresponding operations are carried out by the motion vector detection circuit 50. That is, the motion vector detection circuit 50 outputs the signals having the configuration for the selected mode to the prediction mode changeover circuit 52. The prediction mode changeover circuit 52 directly outputs the signals to the downstream processing section 53. Meanwhile, for the frame prediction mode, the chrominance signals are supplied to the processing unit 53 in a state in which the odd-line field data co-exist with the even-line field data, as shown at (A) in Fig.17. For the field prediction mode, the upper half (four lines) of the chrominance blocks Cb[5] and Cr[6] are the odd-field chrominance signals associated with the luminance blocks Y[1] and Y[2], respectively, while the lower half (four lines) of the chrominance blocks Cb[5] and Cr[6] are the even-field chrominance signals associated with the luminance blocks Y[3] and Y[4], respectively, as shown at (B) in Fig.17. The manner in which the motion vector detection circuit 50 generates the sum of the absolute values of the prediction errors is useful for determining which of the intra-coding, forward predictive coding, backward predictive coding or the bidirectional predictive coding is to be performed in the prediction decision circuit 54. That is, as a sum of the absolute values of the prediction errors for the intra-coding, a difference between an absolute value |ΣAij| of the sum ΣAij of the signals Aij of the macroblock of a reference picture and an absolute value Σ|Aij| of the absolute values |Aij| of the signals Aij of the macroblock is found. Besides, as a sum of the absolute values of the prediction errors for the forward prediction, a sum Σ|Aij - Bij| of absolute values |Aij - Bij| of the differences (Aij - Bij) between the signals Aij of the macroblock of the reference picture and the signals Bij of the macroblock of the prediction picture is found. The sum of absolute values of the prediction errors for the backward prediction and that for the bidirectional predictive coding are also found similarly to the sum of absolute values of the prediction errors for the forward prediction. In these cases, it is of course necessary to use the prediction pictures which are different from that used for the forward prediction. These sum values are supplied to the prediction decision circuit 54 which then selects the least one of the sums of the absolute values of the prediction errors of the forward predictive coding, backward predictive coding and the bidirectional predictive coding, as the sum of the absolute values of the prediction errors of the inter-prediction. Besides, the prediction decision circuit 54 selects, by comparison, the smaller one of the sum of the absolute values of the prediction errors for the inter-prediction and the sum of the absolute values of the prediction errors for the intra-coding and selects the mode corresponding to the selected sum of the absolute values as the prediction mode. That is, if the sum of the absolute values of the prediction errors for the intra-coding has the smaller value, the intra-picture prediction mode is set. If the sum of the absolute values of the prediction errors for the inter-coding has the smaller value, one of the forward predictive mode, the backward predictive mode and the bidirectional predictive mode having the smallest value is set. Thus the motion vector detection circuit 50 supplies the signals of the macroblock of the reference picture to the processing section 53 via the prediction mode changeover circuit 52, in the configuration corresponding to the frame prediction mode or the field prediction mode as selected by the prediction mode changeover circuit 52 as shown in Fig.17. Besides, the motion vector detection circuit 50 detects the motion vector between the prediction picture and the reference picture associated with the prediction mode of the four prediction modes as selected by the prediction decision circuit 52 to output the detected motion vector to the variable length coding circuit 58 and the motion compensation circuit 64 as later explained. Meanwhile, the motion vector is selected which will give the smallest value of the sum of the absolute values of the corresponding prediction errors. When the motion vector detection circuit 50 reads out the picture data of the I-picture from the forward original picture section 51a, the prediction decision circuit 54 sets the intra-frame (intra-picture) prediction mode, that is the mode in which the motion compensation is not carried out, as the predictive mode, and causes a switch of the processing section 53 be set to a fixed contact a . Thus the picture data of the I-picture are entered to a DCT changeover circuit 55. The CDT mode changeover circuit 55 sets the data of the four luminance blocks to the state in which the odd-field line data co-exist with the even-field line data (frame DCT mode) or to the state in which the odd-field line data are separated from the even-field line data (field DCT mode), as shown at (A) or (B) in Fig.18, and outputs the data in one of these states to a DCT circuit 56. That is, the DCT mode changeover circuit 55 compares the coding efficiency which is achieved when the DCT operation is performed on the odd-field data co-existing with the even-field data to the coding efficiency which is achieved when the DCT operation is performed on the odd-field data and the even-field data separated from each other to select the mode having the higher coding efficiency. The input signals are set to a configuration in which the odd-field line data co-exist with the even-field line data, as shown at (A) in Fig.18. The differences between the odd-field line signals and the even-field line signals vertically adjacent to one another are calculated, and the sum of the absolute values or the squared values of the differences is found. On the other hand, the input signals are set to a configuration in which the odd-field line data are separated from the even-field line data, as shown at (B) in Fig.18. The differences between the vertically adjacent odd-field line data and the differences between the vertically adjacent even-field line data are calculated and the sum of the absolute values or squared values is found. These sums are compared to each other and a DCT mode is set to the mode for the smaller sum value. That is, the DCT mode switching circuit 55 sets the frame DCT mode or the field DCT mode if the former sum value or the latter sum value is smaller, respectively. The data having the configuration associated with the selected DCT mode is outputted to the DCT circuit 56, while a DCT flag indicating the selected DCT mode is outputted to a VCL circuit 58 and to a motion compensation circuit 64. The comparison between the predictive mode shown in Fig. 17 in the predictive mode changeover circuit 52 and the DCT mode shown in Fig. 18 in the DCT mode changeover circuit 55 reveals that the data structures are the same in the respective modes as long as the luminance blocks are concerned. If the frame prediction mode, that is the mode in which the odd lines co-exist with the even lines, is selected in the prediction mode changeover circuit 52, the probability is high that the frame DCT mode (the mode in which the odd lines co-exist with the even lines) is also selected in the DCT mode changeover circuit 55, whereas, if the field prediction mode, that is the mode in which the odd lines are separated from the even lines, is selected in the prediction mode changeover circuit 52, the probability is high that the field DCT mode (the mode in which the odd line data are separated from the even line data) is also selected in the DCT mode changeover circuit 55. However, this is not necessarily the case, and the prediction mode is set in the prediction mode changeover circuit 52 so that the sum of the absolute values of the differences will become smaller, while the DCT mode is set in the DCT mode changeover circuit 55 so that the coding efficiency will become more favorable. The I-picture picture data outputted from the DCT mode changeover circuit 55 is entered to the DCT circuit 56 where it is processed with discrete cosine transform (DCT) so a to be transformed into DCT coefficients. These DCT coefficients are entered to a quantizing circuit 57 so as to be quantized at the quantization steps corresponding to the amount of data storage in a downstream side buffer 59 before being entered to a variable length coding circuit 58. The variable length coding circuit (VLC circuit) 58 translates the picture data, herein the I-picture data, supplied from the quantizing circuit 57, into data of the variable length codes, such as the Huffman code, in association with the quantization step (quantization scale) supplied from the quantizing circuit 57, to transmit the variable length code data to a transmission buffer 59. To the variable length coding circuit 58, there are also supplied the quantization step (quantization scale) from the quantization circuit 57, the prediction mode from the prediction decision circuit 54, that is the mode indicating which of the intra-picture coding, forward predictive coding, backward predictive coding or the bidirectional predictive coding has been set, the motion vector from the motion vector detection circuit 50, the prediction flag from the prediction mode changeover circuit 52, that is a flag indicating which of the frame prediction mode or the field prediction mode has been set, and a DCT flag, that is a flag indicating which of the frame DCT mode and the field DCT mode has been set, these data or flags being also converted into corresponding variable length coded data. The transmission buffer 59 transiently stores the input data to output the data corresponding to the stored data amount to the quantizing circuit 57. When the residual data amount in the transmission buffer 59 is increased up to an allowable upper limit, the transmission buffer 59 increments the quantization step in the quantizing circuit 57 by the quantization control signal to decrease the amount of the quantization data. Conversely, if the residual data quantity in the transmission buffer buffer 59 is decreased up to an allowable lower limit, the transmission buffer 59 decrements the quantization step in the quantizing circuit 57 by the quantization control signal to increase the amount of the quantized data. In this manner, the data overflow or underflow may be prevented from being incurred in the transmission buffer 59. The data stored in the transmission buffer 59 is read out at a pre-set timing and outputted on the transmission channel via an output terminal 69 so as to be recorded on, for example, the recording medium 3. On the other hand, data of the I-picture outputted from the quantization circuit 57 is entered at the inverse quantization circuit 60 so as to be inverse quantized with the quantization step data supplied from the quantization circuit 57. An output of the inverse quantization circuit 60 is entered at an inverse DCT (IDCT) circuit 61 where inverse DCT is performed on the output data. It is noted that the prediction flag from the prediction mode changeover circuit 52 and the DCT flag from the DCT mode changeover circuit 55 are entered to a converting circuit 66. The estimation flag from the estimation mode changeover circuit 52 is also entered to a converting circuit 65. The estimation play from the estimation mode changeover circuit 52 is entered to a converting circuit 65. The data processed with inverse DCT by the IDCT circuit 61 are transmitted via the converting circuit 66, 65 and a processor 62 for data matching and subsequently transmitted to and stored in a forward prediction picture section 63a of a frame memory 63. Meanwhile, when processing the frame picture data sequentially entered thereto as, for example, the pictures I, B, P, B, P, B, ···, the motion vector detection circuit 50 first processes the initially entered frame picture data as the I-picture and, before processing the subsequently entered second frame picture as the B-picture, processes the third frame picture data entered thereto next to the second picture data as the P-picture. It is because the B-picture is based on backward prediction and hence cannot be decoded unless the P-picture as the backward predicted picture is not available for prediction. Thus the motion vector detection circuit 50 starts processing picture data of the P-picture stored in the backward original picture section 51c next to the processing of the I-picture. The sum values of the absolute values of the macroblock based inter-frame differences (prediction errors) are transmitted from the motion vector detection circuit 50 to the prediction mode changeover circuit 52 and to the predictor decision circuit 54. Responsive to the sums of the absolute values of the prediction errors of the macroblocks of the P-picture, the prediction mode changeover circuit 52 and the prediction decision circuit 54 set the prediction mode to one of the frame/field prediction mode, intra-picture prediction, forward prediction, backward prediction or bidirectional prediction. If the prediction mode is set to the intra-picture prediction mode, the switch in the processing section 53 is changed over to the fixed terminal a , as mentioned above. Thus the picture data of the P-picture are transmitted to the transmission channel via the DCT mode changeover circuit 55, DCT circuit 56, quantization circuit 57, variable length coding circuit 58 and a transmission buffer 59, similarly to the picture data of the I-picture. Besides, the picture data are also supplied to and stored in a backward prediction picture section 63b of the frame memory 63 via the inverse quantization circuit 60, IDCT circuit 61, converting circuit 66, processor 62 and the converting circuit 65. If the prediction mode is the forward prediction mode, the switch in the processing section 53 is changed over to the terminal b , at the same time that the picture data stored in the forward prediction picture section 63a in the frame memory 63, herein the picture data of the I-picture, are read out and motion-compensated by a motion compensation circuit 64 responsive to the motion vector outputted by the motion vector detection circuit 50. That is, when commanded by the prediction decision circuit 54 to set the forward prediction mode, the motion compensation circuit 64 read out the data after shifting the readout address of the forward prediction picture section 63a from a position corresponding to the macroblock position currently outputted by the motion vector detection circuit 50 by an amount corresponding to the motion vector for generating prediction picture data. The prediction data outputted by the motion compensation circuit 64 is supplied to a processor 53a which then subtracts the macroblock based prediction picture data supplied from the motion compensation circuit 64 from data of the macroblock of the reference picture supplied from the prediction mode changeover circuit 52 to output the difference which is the prediction error. The difference data is supplied via the DCT mode changeover circuit 55, DCT circuit 56, quantization circuit 57, variable length coding circuit 58 and transmission buffer 59 to the transmission channel via the output terminal 69. The difference data is also locally decoded by the inverse quantization circuit 60 and the IDCT circuit 61 so as to be entered via the converting circuit 66 to the processor 62. The prediction flag from the prediction mode changeover circuit 52 and the DCT flag from the DCT mode changeover circuit 55 are supplied to the converting circuit 66 for matching an output of the IDCT circuit 61. The processor 62 is also supplied with data which is the same as the prediction picture data supplied to the processor 53a. The processor 62 adds the output prediction picture data of the motion compensation circuit 64 to the output difference data of the IDCT circuit 61. In this manner, the picture data of the original I-picture is produced. The picture data of the P-picture are supplied to and stored in the backward prediction picture section 63b via the converting circuit 65. After the data of the I-picture and the data of the P-picture are stored in the forward predictive-coded picture section 63a and the backward predictive-coded picture section 63b, respectively, the motion vector detection circuit 50 executes the processing of the B-picture. Responsive to the magnitude of the sum of the absolute values of the inter-frame difference on the macroblock basis, the prediction mode changeover circuit 52 sets the frame mode or the field mode, while the prediction decision circuit 54 sets the prediction mode to one of the intra-picture prediction mode, forward prediction mode, backward prediction mode or the bidirectional prediction mode. If the prediction mode is the intra-frame prediction mode or the forward prediction mode, the switch in the processing section 53 is changed over to the fixed contact a or b , respectively. At this time, the processing similar to that for the P-picture is performed for transmitting the data. On the other hand, if the backward prediction mode or the bidirectional prediction mode is set, the switch in the processing section 533 is set to the fixed terminal c or d , respectively. For the backward prediction mode, for which the switch in the processing section 53 is set to the fixed terminal c , picture data stored in the backward predictive-coded picture section 63b, herein the picture data for the P-picture, is read out and motion-compensated by the motion compensation circuit 64 responsive to the motion vector outputted by the motion vector detection circuit 50. That is, when commanded by the prediction decision circuit 54 to set the backward prediction mode, the motion compensation circuit 64 reads out the data after shifting the readout address of the backward predictive-coded picture section 63b from a position corresponding to the macroblock position currently outputted by the motion vector detection circuit 50 by an amount corresponding to the motion vector for generating predictive-coded picture data. The predictive-coded picture data outputted by the motion compensation circuit 64 is supplied to a processor 53b which then subtracts the predictive-coded picture data supplied from the motion compensation circuit 64 from data of the macroblock of the reference picture supplied from the prediction mode changeover circuit 52 to output the difference data which is supplied via the DCT mode changeover circuit 55, DCT circuit 56, quantization circuit 57, variable length coding circuit 58 and transmission buffer 59 to the transmission channel via the output terminal 69. For the bidirectional prediction mode, for which the switch in the processing section 53 is set to the fixed terminal d , picture data stored in the forward predictive-coded picture section 63a, herein the picture data for the I-picture, and picture data stored in the backward predictive-coded picture section 63b, herein the picture data for the P-picture, are read out and motion-compensated by the motion compensation circuit 64 responsive to the motion vector outputted by the motion vector detection circuit 50. That is, when commanded by the prediction decision circuit 54 to set the bidirectional prediction mode, the motion compensation circuit 64 reads out the data after shifting the readout addresses of the forward predictive-coded picture section 63a and the backward predictive-coded picture section 63b from a position corresponding to the macroblock position currently outputted by the motion vector detection circuit 50 by amounts corresponding to the motion vectors for the forward and backward predictive-coded pictures for generating predictive-coded picture data. The predictive-coded picture data outputted by the motion compensation circuit 64 is supplied to a processor 53c which then subtracts the mean value of the predictive-coded picture data supplied from the motion compensation circuit 64 from data of the macroblock of the reference picture supplied from the motion vector detection circuit 50 to output the difference data which is supplied via the DCT mode changeover circuit 55, DCT circuit 56, quantization circuit 57, variable length coding circuit 58 and transmission buffer 59 to the transmission channel via the output terminal 69. Since the picture of the B-picture is not used as a prediction picture for other pictures, it is not stored in the frame memory 63. Meanwhile, the frame memory 63 may be so constructed that the forward predictive-coded picture section 63a and the backward predictive-coded picture section 63b may be bank-exchanged so that the picture stored in one or the other of the sections 63a, 63b is outputted as the forward predictive-coded picture or the backward predictive-coded picture for a given reference picture. Although the foregoing description has been made mainly of the luminance blocks, the chrominance blocks are also processed on the basis of the macro-blocks shown in Figs.17 and 18 prior to transmission. Meanwhile, the motion vector employed in processing the chrominance blocks is the motion vector of the associated luminance block reduced by 1/2 in the vertical and horizontal directions. Fig.19 shows, in a block diagram, a typical construction of the decoder 31 shown in Fig.14. Picture data transmitted over the transmission channel, that is the recording medium 3, is received by a reception circuit, not shown, or reproduced by a reproducing circuit, also not shown, so as to be subsequently transiently stored via an input terminal 80 in a reception buffer 81. The picture data thus stored transiently is supplied to a variable length decoding circuit 82 of a decoding circuit 90. The variable length decoding circuit 82 then decodes the data supplied from the reception buffer 81 by variable length decoding and outputs the motion vector, prediction mode, prediction flag and the DCT flag to a motion compensation circuit 87, while outputting the quantization step data and decoded picture data to the inverse quantization circuit 83. The inverse quantization circuit 83 inverse-quantizes the picture data supplied from the variable length decoding circuit 82 depending on the quantization step data supplied thereto to output the inverse-quantized data to an IDCT circuit 84. Output data from the inverse quantization circuit 83, that is the DCT coefficients, are processed with inverse DCT by the IDCT circuit 84 so as to be supplied via a converting circuit 88 to a processor 85. Picture data supplied from the IDCT circuit 84 are matched by the converting circuit 88 based on the prediction flags and the DCT flags supplied to the converging circuit 88. If the picture data supplied to the processor 85 are the data of the I-picture, the data are outputted by the processor 85 so as to be supplied to and stored in the forward predictive-coded picture section 86a in the frame memory 86 via the converting circuit 89 for generating predictive-coded picture data for the picture data (data of the P- or B-picture) subsequently entered to the processor 85. The data are also outputted by a converting circuit 89 to the format converting circuit 32 shown in Fig.14 via an output terminal 91. If the picture data supplied to the processor 5 is the data of the forward prediction mode, and is the data of the P-picture having the picture data of an immediately previous frame as the predictive-coded picture data, the picture data (I-picture data) of the immediately previous frame, stored in a forward predictive-coded picture section 86a of a frame memory 86, is read out and motion-compensated by the motion compensation circuit 87 depending on the motion vector outputted from the variable length decoding circuit 82. The motion-compensated data is summed in the processor 85 to the picture data supplied from the IDCT circuit 84 (the difference data) and the resulting sum data is outputted. The sum data, that is the data of the decoded P-picture, is supplied to and stored in a backward predictive-coded picture section 86b within the frame memory 86 via the converting circuit 89 for generating the prediction picture data for the picture data subsequently entered to the processor 85, that is the B- or P-picture data. If the data is the P-picture data and is intra-picture prediction mode data, the data is not processed in the processor 85, as is the I-picture data, and is directly transmitted to and stored as it is in the backward predictive-coded picture section 86b via the converting circuit 89. Since the P-picture is the picture to be displayed next to the following B-picture, it is not as yet outputted to the format converting circuit 32 at this time point. That is, as mentioned previously, the P-picture entered after the B-picture is processed and transmitted prior to the B-picture. If the picture data supplied from the IDCT circuit 84 is the B-picture data, the picture data of the I-picture stored in the forward predictive-coded picture section 86a, the picture data of the P-picture stored in the backward predictive-coded picture section 86b, or both of these picture data are read out responsive to the predictive mode supplied from the variable length coding circuit 82, that is to the forward prediction mode, backward prediction mode or to the bidirectional prediction mode, respectively, and motion-compensated by the motion compensation circuit 87 depending on the motion vector outputted by the variable length decoding circuit 82 for generating the predictive-coded picture. Such predictive-coded picture is not generated if no motion compensation is required, that is if the prediction mode is the intra-picture prediction mode. The data motion-compensated in this manner by the motion compensation circuit 87 is summed in the processor 85 to an output of the converting circuit 88. This sum output is transmitted via the converting circuit 89 and the output 91 to the format converting circuit 32 shown in Fig.14. Since the sum output is the B-picture data which is not utilized for generating a prediction picture for other pictures, it is not stored in the frame memory 86. After the outputting of the B-picture, picture data of the P-picture stored in the backward prediction picture section 86b is read out and transmitted via the motion compensation circuit 87 to the processor 85. The motion compensation is not performed at this time. In the present decoder 31, the circuits corresponding to the prediction mode changeover circuit 52 and the DCT mode changeover circuit 55 in the encoder shown in Fig.16 are not shown. The processing operation performed by these circuits, that is the operations of reverting the configuration having odd field line signals and even field line signals separated from one another to the original configuration having these signals mixed with one another, is executed by the motion compensation circuit 87. Although the processing of luminance signals has been explained in the foregoing, processing of the chrominance signals is executed in a similar manner, except that the motion vector employed for the luminance signals, which is reduced by one half in each of the vertical and horizontal directions, is employed for the chrominance signals. Meanwhile, in executing quantization and inverse quantization in the encoding of picture signals, it is a routine practice to employ a value indicating the fineness of quantization, that is the width of quantization, or the quantization stepsize. Even numbers of from 2 to 62 are employed as the width of quantization. The width of quantization is expressed by the quantization characteristics (QUANT). Integers of from 1 to 31 are employed for expressing the quantization characteristics which indicate the stepsize descriptions. The width of quantization is a value twice the value of the quantization characteristic. The width of quantization is required for compressing a picture in general to a target data volume. It is however extremely difficult to compress a picture having statistic properties deviated significantly from those of a general picture using the above-mentioned width of quantization, for example, to compress a picture exhibiting extremely low pixel correlation or a picture approximated to a white noise by DCT encoding which takes advantage of coefficient concentration in the frequency domain. That is, in such case, a picture cannot be compressed to a target size even if the maximum value 31 of the quantization characteristics is employed. On the other hand, if it is desired to obtain a picture of extremely high picture quality, such a picture substantially free from distortion, known as loss-less picture, even the minimum value 1 of the quantization characteristics is too large to perform quantization so as to restore the picture accurately. Besides, in the encoding of picture signals, the compressed bit stream is frequently controlled by the target transmission rate. At this time, in a usual linear quantizer, the above-mentioned quantization characteristics are inversely proportionate to or, more accurately, logarithmically related with the number of generated bits of the picture data quantized on the basis of the above-mentioned quantization characteristics. Consequently, if, with the quantization characteristics remaining within a small range of values, the quantization characteristics are changed by one, the amount of the generated bits is changed significantly. If, for example, the quantization characteristics are changed from 1 to 2, the amount of the generated bits is reduced substantially by one half. This indicates that, if the quantization characteristics are within a small range, the interval between neighboring values of the quantization characteristics is so broad as to render it difficult to finely control the amount of the generated bits. Conversely, if the quantization characteristics are in a broader range, the amount of the generated bits is scarcely changed even if the quantization characteristics are changed by one. If, for example, the quantization characteristics are changed from 30 to 31, the amount of bit generation for the quantization characteristics of 31 is not changed by more than 5% from that for the quantization characteristics of 30. This indicates that the interval between neighboring values of the quantization characteristics is unnecessarily narrow for the larger range of values of the quantization characteristics. For overcoming the above-mentioned difficulties, there is known a method of mapping the quantization characteristics to a non-linear sequence of numbers instead of directly employing a sequence of numbers increased monotonously from 1 to 31. The relation between the quantization information for finding quantization characteristic mapped to such non-linear sequence of numbers and quantization characteristics is shown in Table 7. Meanwhile, the quantization information is termed an index number and incidentally expressed by numerical figures. index number quantization information quantization characteristics (QUANT) decimal expression binary expression 0 00000 1.0 0000001.0 1 00001 1.5 0000001.1 2 00010 2.0 0000010.0 3 00011 2.5 0000010.1 4 00100 3.0 0000011.0 5 00101 3.5 0000011.1 6 00110 4.0 0000100 7 00111 5.0 0000101 8 01000 6.0 0000110 9 01001 7.0 0000111 10 01010 8.0 0001000 11 01011 9.0 0001001 12 01100 11.0 0001011 13 01101 13.0 0001101 14 01110 15.0 0001111 15 01111 17.0 0010001 16 10000 19.0 0010011 17 10001 21.0 0010101 18 10010 23.0 0010111 19 10011 27.0 0011011 20 10100 31.0 0011111 21 10101 35.0 0100011 22 10110 39.0 0100111 23 10111 43.0 0101011 24 11000 47.0 0101111 25 11001 51.0 0110011 26 11010 55.0 0110111 27 11011 59.0 0111011 28 11100 67.0 1000011 29 11101 75.0 1001011 30 11110 83.0 1010011 31 11111 91.0 1011011 Although the above-mentioned problem due to the ranges of values of quantization characteristic may be overcome by employing quantization characteristics mapped to the non-linear sequence, quantization characteristics are given as table values mapped to the non-linear sequence of numbers, so that it becomes necessary to provide a arrangement for storing table values in the encoding/decoding apparatus. As a result thereof, the size of the hardware of the encoding/decoding apparatus is increased. The construction of a conventional inverse quantizer making use of quantization characteristics of the non-linear sequence of numerals is shown schematically in Fig.20. The quantization characteristics of the non-linear sequence of numbers are stored in a table 200 constituted by a ROM, and 8-bit data of the quantization characteristics are read out from the table 200. The quantization characteristics are multiplied in a multiplier 201 by an n-bit conversion coefficient for the quantized picture data for inverse-quantizing the quantized data. A large-size circuit is required for both the table 200 and the multiplier 201 in the inverse quantizer. That is, with the conventional picture signal encoding/decoding apparatus, since numbers of 1 to 31, or the values of the sequence of numbers shown in Fig.7 are employed, it becomes necessary to provide a multiplier for the inverse quantizer and in the inverse quantizer in the picture signal encoding/decoding apparatus. The multiplier has an increased circuit size and unnecessarily increases the size of the picture signal encoding/decoding apparatus. In view of the above-depicted state of the art, it is an object of the present invention to provide a picture signal encoding method and apparatus and a picture signal decoding method and apparatus in which suitable quantization characteristics may be employed for quantization and inverse quantization of picture signals without increasing the circuit scale. Aspects of the invention are specified in the claims to which attention is directed. According to one aspect of the present invention, there is provided a quantization method for quantizing picture signals in which input picture signals to be encoded are quantized comprising setting a digital signal value k, k being a positive integer as a first quantization information, setting a digital signal value i/2 + j representing a second quantization information, j being a positive integer and i being 0 or 1, and quantizing the picture signals according to non-linear quantization characteristic signal steps, wherein said non-linear quantization characteristic signal steps are represented by the equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4. The said one aspect also provides a corresponding quantization apparatus. According to another aspect of the present invention there is provided a quantization method for quantizing picture signals in which input picture signals to be encoded are quantized comprising setting a digital signal value m where m is an integer representing first quantization information, setting a digital signal value a i , a being 0 or 1 and i being an integer representing a second quantization information, and quantizing the picture signals based on non-linear quantization characteristic signal steps wherein the non-linear quantization characteristic signal steps are represented by the equation: QUANT = 2 (m-1) + α i x 2 (m-2) + α 2 x 2 (m-3) + ... + α n x 2 (m-n-1) where n is a preset integer indicating a fineness of quantization. The said another aspect also provides a corresponding quantization apparatus. According to a further aspect of the present invention, there is provided a quantization method for quantizing picture signals in which input picture signals to be encoded are quantized, comprising setting a digital signal value k, k being a positive integer as a first quantization information j being a positive integer, and i being 0 or 1, and quantizing the picture signals according to non-linear quantization characteristic steps as specified in Table 2 of the ANNEX to the claims. The further aspect also provides a corresponding quantization apparatus. According to a yet further aspect of the invention, there is provided a picture signal encoding method in which a picture signal is encoded and subsequently undergoes quantization and variable length coding, wherein an evaluation of the number of bits generated by linear quantization is made, a linear/non-linear quantization changeover signal, indicating a method of quantization, is generated as a function of said evaluation, and if said linear/non-linear quantization changeover signal indicates non-linear quantization, quantization is performed based on non-linear quantization characteristic signal steps represented by powers of 2 and a coefficient multiplied by the powers of 2, with a value for expressing an index of the powers of 2 as a first quantization information among a set of quantization information and a value corresponding to said coefficient as a second quantization information. The yet further aspect also provides a corresponding encoding apparatus. Other aspects of the invention provide decoding methods and apparatus in which quantised signals are dequantised in a manner complementary to the manner in which they were quantised. The invention, by defining the quantization steps (QUANT) as powers of two and a coefficient multiplied by powers of 2 with a first quantization information (e.g. k expressing the index of the power of 2) and a second quantisation information (e.g. i/2+j corresponding to the coefficient) at least reduces the need to store large quantization tables. Furthermore quantization and dequantization can be performed, simply, by shifting and adding operations. Examplary embodiments of the invention are described hereinafter, by way of example only, with reference to the accompanying drawings in which: Fig.1 illustrates a schematic arrangement of a circuit for reproducing quantization characteristics within an encoding apparatus and a decoding apparatus for picture signals according to the present invention. Fig.2 shows a schematic arrangement of a shifter 110 in Fig.1. Fig.3 shows a schematic arrangement of an inverse quantization circuit in the encoding apparatus and decoding apparatus for picture signals according to the present invention. Fig.4 illustrates a schematic arrangement of a circuit for reproducing quantization characteristics within an encoding apparatus and a decoding apparatus for picture signals according to a third embodiment of the present invention. Fig.5 shows a schematic arrangement of a shifter 110 in Fig.1. Fig.6 shows a schematic arrangement of an inverse quantization circuit in the encoding apparatus and decoding apparatus for picture signals according to the third embodiment of the present invention. Fig.7 shows a schematic arrangement of an inverse quantization circuit in the encoding apparatus and decoding apparatus for picture signals according to a fourth embodiment of the present invention. Fig.8 illustrates a schematic arrangement of a quantization circuit within an encoding apparatus for picture signals according to the present invention. Fig.9 illustrates the principle of high efficiency encoding. Fig.10 illustrates picture type in compressing picture data. Fig.11 illustrates the principle of encoding moving picture signals. Fig.12 illustrates a GOP structure for moving picture signals. Fig.13 illustrates the sequence of unpitying, encoding, decoding and outputting picture signals. Fig.14 is a block circuit diagram showing a typical structure of a conventional encoding/decoding apparatus. Fig.15 illustrates the operation of format conversion in the format converting circuit 17 shown in Fig.14. Fig.16 is a block circuit diagram showing a typical structure of the encoder 18 shown in Fig.14. Fig.17 illustrates the operation of the prediction mode changeover circuit 52 shown in Fig.16. Fig.18 illustrates the operation of the DCT mode changeover circuit 52 shown in Fig.16. Fig.19 is a block circuit diagram showing a typical structure of the decoder 31 shown in Fig.14. Fig.20 illustrates a schematic arrangement of a conventional non-linear quantization circuit. With the first embodiment of the present invention, the binary numbers for expressing indices or exponents of powers of 2 in the quantization information represent the first quantization information, while the binary numbers corresponding to the coefficients to be multiplied by the values of the powers of 2 represent the second quantization information, and quantization or inverse quantization is carried out based on the quantization characteristics (QUANT) represented by the non-linear sequence of numbers expressed by products of the values of the powers of 2 and the above-mentioned coefficients. If the first quantization information is expressed as k and the second quantization information is expressed' as (i/2 + j), the quantization characteristics (QUANT) may be found by the equation (1) QUANT = (i/2 + j) × 2 k + α (α = 2 (k+2) - 4) where j and j are positive integers and i is 0 or 1. Using the quantization characteristic (QUANT), encoding or decoding of picture signals is performed by an encoder or a decoder, respectively. It is noted that variable length coded data are contained in the bit stream encoded by the MPEG system. Therefore, a special code is required which enables monistical decoding even if a variety of possible variable length coded data should have occurred during decoding from an arbitrary point. In the above bit stream, the special code is a code consisting of 23 or more consecutive 0's. In this consideration, the quantization characteristics (QUANT) in which the totality of bits in the quantization information is 0 is inhibited to limit the variable length code data other than the above special code data lest 23 or more 0s should occur for any combinations of the other variable length code data. The sequence represented by the equation (1) is an arithmetic progression having a constant difference between two adjacent terms equal to a power of 2, if the quantization information is thought to be constant. If the number expressed by the quantization information j is p , the constant difference is changed over at an interval of 2 × p. The quantization characteristics (QUANT) which may be expressed by the equation (1) is given in Table 8. In table 8, k , j and i of the quantization information are 2 bits, 2 bits and 1 bit, respectively, totalled at 5 bits, and the quantization characteristics (QUANT) associated therewith, inclusive of the binary representation, are also shown. The five bits of the quantization information are expressed as (Q1 Q2 Q3 Q4 Q5), beginning from the MSB. The first two bits of the quantization information k(Q1 Q2) represent the first quantization information for expressing the indices for the powers of 2. Of the remaining three bits of the quantization information, two bits j (Q3 Q4) and one bit i (Q5) represent the second quantization information which is a value corresponding to the coefficient to be multiplied by the powers of 2 of the equation (1). A group of eight values of the quantization characteristics represented by X (= 1/2 + j) constitutes an arithmetic progression which has its constant difference changed at a changeover point from one group to the next group. If the non-linear sequence of numbers shown in Table 8 is employed, the conversion of the quantization information may be grasped monistically. Consequently, if the width of quantization is expressed by the value which may be represented by the equation (1), the necessity of providing a memory for storage of the corresponding conversion table may be eliminated. Since the five bits represented by the quantization information k , j and i represent the number of bits required for transmitting the values of the quantization characteristics of from 1 to 31, the method and apparatus for encoding/decoding of picture signals employing the method for finding the quantization characteristics (QUANT) according to an embodiment of the present invention may be rendered interchangeable with the method and apparatus for encoding/decoding of picture signals employing the conventional method for finding the quantization characteristics. In the above Table 8, the groups of the quantization characteristics (QUANT) are indicated at 0+X, 4+2X, 12+4X and 28+8X, or in general terms α + X2 k where k is an integer, α = (2 k+2 - 4) and X = (i/2 + j). α represents the initial value of each group. X represents the quantization stepsize in each group. The circuit provided within the picture signal decoding apparatus for reproducing quantization characteristics by the conversion into the non-linear sequence of numbers shown in Table 8 is shown schematically in Fig.1. The sequence of numbers of each group X may be expressed by X × 2 n , n being a natural number, if the quantization information (Q3 Q4 Q5) is entered into a shifter 110 and shifted using the values of the quantization information (Q1 Q2). That is, if the quantization information (Q1 Q2) is (0 0), (0 1), (1 0) or (1 1), the quantization information (Q3 Q4 Q5) is shifted by 0, 1, 2 or 3 bits, respectively. Table 9 shows the values of the quantization information (Q1 Q2), entered to a table 111 in Figure 1, a value of an output S1, issued after conversion by the table 111 and a value S2 sequentially read out in the table 111, as mentioned above. Table 111 has the form shown in the lefthand and middle columns of Table 9 below:- Q1 Q2 S1 S2 0 0 000 0 0 1 001 4 1 0 011 12 1 1 111 28 The construction of the shifter 110 shown in Fig.1 is shown schematically in Fig.2. The quantization information (Q3 Q4 Q5), entered at AND gates 121 to 132, is changed over depending on the shift amount generated on the basis of quantization information (Q1 Q2) by a shift amount generator 120 and is transmitted through OR gates 133, 136 and ExOR gates 134, 135. The resulting quantization information is outputted at bit 0 output terminal b[0] to bit 5 output terminal [5]. The values of 0, 4, 12 and 28, which are sequentially read out in accordance with the quantization information (Q1 Q2), are stored in the table 111. The upper three bits of the read out values and upper three bits of X × 2 n , n being a natural number, are summed in an additive node 112. The four bits of the resulting sum signal and the lower three bits of the value X × 2 n appended thereto give the 7-bit quantization characteristics (QUANT) as reproduced values. The circuit arrangement for finding the above-described nonlinear quantization characteristics is smaller in size than the circuit arrangement for finding the conventional non-linear quantization characteristics shown in Fig.7. The reason is that the conventional non-linear quantization characteristics are destitute of periodicity and reference must be had incidentally to the table so that a large number of gates is required. The quantization characteristics thus produced are multiplied by the conversion coefficient for the quantized picture data (the quantization data) by way of inverse quantization. Since the four of the seven bits are effective bits, as may be seen from Table 8, a three-stage multiplier may be used for multiplying the quantization characteristics by the conversion coefficient as the quantized data (the quantization data) of the picture signals. The arrangement of the inverse quantization circuit within the picture signal encoding and decoding apparatus is shown schematically in Fig.3. The quantization information (Q1 Q2) entered to a table 141 is supplied to an addition unit 140 after conversion into a value S3 indicated in Table 10. Q1 Q2 S3 0 0 000 0 1 100 1 0 110 1 1 111 In the addition unit 140, the value S3 and the quantization information (Q3 Q4 Q5) are summed together and the resulting sum is transmitted to a signal switching unit 144. To the signal switching unit are also entered the quantization information (Q3 Q4 Q5) for carrying out the linear quantization and MSB equal to 0 of the quantization information for carrying out the non-linear quantization. To the signal switching unit are additionally entered a linear/non-linear quantization signal for selecting which of the linear and non-linear quantization is to be carried out. The linear quantization herein means that the values of the quantization information expressed as the binary values are related linearly with the values of the widths of quantization, that is the quantization step sizes. Conversely, the non-linear quantization means that the values of the quantization information expressed as the binary values are related non-linearly with the values of the widths of quantization. If linear quantization is selected in the signal switching unit 144 by the linear quantization /non-linear quantization switching signal, the quantization information (Q1 Q2 Q3 Q4 Q5) for linear quantization is selected and transmitted to a multiplier 142. Conversely, if non-linear quantization is selected by the linear/non-linear quantization switching signal, the 4-bit quantization signal from the addition unit 140 and 0 as the MSB of the quantization information are selected and transmitted to the multiplier 142. The multiplier 142 multiplies the input quantization information with the n-bit conversion coefficient to give a product which is outputted to a shifter 143. The quantization information (Q1 Q2) and the above-mentioned linear quantization /non-linear quantization switching signal are entered to the shifter 143. If the linear quantization has been selected by the linear quantization /non-linear quantization switching signal, the shifter 143 directly transmits the output of the multiplier 142 as the playback output. Conversely, if the non-linear quantization has been selected by the linear quantization /non-linear quantization switching signal, the shifter 143 shifts the output of the multiplier 142 with the amount of shift produced on the basis of the input quantization information (Q1 Q2), as shown in Table 11, to output the shifted data as the playback data. linear/non-linear quantization changeover signal Q1 Q2 shift amount linear quantization × × 0 bit non-linear quantization 0 0 0 bit non-linear quantization 0 1 1 bit non-linear quantization 1 0 2 bits non-linear quantization 1 1 3 bits In the above Table, marks × for (Q1 Q2) for the linear quantization, as selected by the linear quantization /non-linear quantization switching signal, indicate that the amount of shift is not affected by any possible combinations of the values of the quantization information (Q1 Q2). If the reproduced value of the data on inverse quantization of the quantized data is A, the conversion coefficient as the quantization data is Coeff and the width of quantization is SP, the playback value A may be represented by A = Coeff × SP = Coeff × (2 × QUANT) If the non-linear quantization has been selected, the equation (2) employed for finding the quantization characteristics (QUANT) is modified to QUANT = ((i/2 + j) + (4 - 4/2 k )) × 2 k In the above equation, the term (i/2 + j) corresponds to the second quantization information (Q3 Q4 Q5) entered to the addition unit 140, the term (4 - 4/2 k )) corresponds the an output of the table 141 and the term 2 k corresponds to the amount of shift in the shifter 143. Thus the playback value A is given by A = Coeff ((i/2 + j) + (4 - 4/2 k )) × 2 (k+1) The shifter 143 employed for finding the playback value A is simpler in construction. The multiplier 142 of a smaller number of stages may also be employed, which is capable of multiplying n bits of the conversion coefficient, 4 bits of the output data of the switching unit 144 and the MSB. In the above-described first embodiment, the maximum value that can be assumed by the quantization characteristics is 56.0, with the quantization width being 112. However, if the white noise, for example, is entered in actual pictures, larger values of quantization characteristics are required. For coping with this, the following two methods may be employed. The first method is to allocate larger values of the quantization characteristics, such as 64, 96 or 128, for the quantization information of "00000" binary, which is currently not employed. If 64 or 128 is allocated as the values of the quantization characteristics, processing may be facilitated because shifting by a shifter suffices for multiplication in inverse quantization. If 96 is allocated as the value of the quantization characteristics, processing may similarly be facilitated because a single-stage addition unit suffices. The second method is to allocate the values of the quantization characteristics of 64, 96 or 128 for the quantization information of "11111" binary, in consideration that a long sequence of "0" is likely to be produced if the quantization information "00000" binary is employed. The quantization characteristics for the case in which the amount of shift of the fourth group represented by 28 × 8X is changed significantly is shown in Table 12 by way of a third embodiment. The quantization information of the fourth group, represented by 28 + 16X in Table 12, is found by intentionally setting the maximum value of the shift amount indicated by the quantization information k so as to be larger to disregard the continuity of the quantization information k . Thus the maximum possible value of the quantization characteristics is 84.0 which is large enough to accommodate special inputs such as the white noise. This method is desirable in controlling the coding because it renders it possible to provide continuous quantization characteristics up to the maximum value. In the present third embodiment, the quantization information "00000" is inhibited, as in the above-described first embodiment. The circuit for reproducing the quantization characteristics, provided within the picture signal decoding apparatus for reproducing the quantization characteristics by conversion into a non-linear sequence of numbers shown in Table 12, is shown schematically in Fig.4. The values of X × 2 n , n being a natural number, may be expressed by entering the quantization information (Q3 Q4 Q5) to a shifter 150 and by shifting the quantization information (Q3 Q4 Q5) using the values of the quantization information (Q1 Q2). That is, the quantization information (Q3 Q4 Q5) is shifted by 0. 1, 2 or 4 bits if the quantization information (Q1 Q2) is (0 0), (0 1), (1 0) or (1 1), respectively. Fig.5 shows a schematic construction of the shifter 150 shown in Fig.4. The quantization information (Q3 Q4 Q5) entered to AND gates 161 to 172 is changed over responsive to the shift amount produced in a shift amount generator 160 based on the quantization information (Q1 Q2), and is transmitted via OR gates 173, 175 and an ExOr gate 174 so that the quantization information is outputted at a bit 0 output terminal b[0] to bit 6 output terminal [6]. The values of 0, 4, 12 and 28, which are read out sequentially in accordance with the quantization information (Q1 Q2), are stored in a table 151, and upper four bits of the readout values and upper four bits of the value X × 2 n , n being a natural number, are summed together in an additive node 152. The five-bit sum value is appended to lower three bits of the value X × 2 n to reproduce the 8-bit quantization characteristics (QUANT). The values sequentially read out from the table 151 are those shown in Table 9, as in the above-described first embodiment. The inverse quantization circuit in the encoding /decoding apparatus for picture signals is shown schematically in Fig.6. The quantization information (Q1 Q2) entered to a table 181 is converted into the values S4 shown in Fig.13 so as to be supplied to an addition unit 180. Q1 Q2 S4 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 In the addition unit 180, the value S4 from the table 181 and the quantization information (Q3 Q4 Q5) are summed together and the resulting sum is multiplied in a multiplier 182 with an n-bit conversion coefficient. The resulting product is sh-ifted in a shifter 183 based on the quantization information (Q1 Q2) for reproducing picture data. Meanwhile, the number of bits from the multiplier 182 of the inverse quantization circuit in the present third embodiment differs from the number of bits from the multiplier 142 of the inverse quantization circuit in the above-described first embodiment. That is, if the quantization information k in the third embodiment has the values of 0, 1 or 2, the playback value A of the picture data may be found from the equation (4). On the other hand, if the quantization information k has a value of 3, the playback value A of the picture data may be found from A = Coeff × ((i/2 + j) + 1.75) × 2 5 The shifter 183 employed for finding the playback value A is simpler in construction. The multiplier 182 of a smaller number of stages may also be employed, which is capable of multiplying n bits of the conversion coefficient and 5 bits of the output data of the multiplier 180. A fourth embodiment of the present invention is hereinafter explained. With the encoding method for picture signals according to the embodiment of the present invention, the picture signals are quantized in accordance with the quantization characteristics (QUANT) represented by QUANT = 2 (m-1) + α 1 × 2 (m-2) + α 2 × 2 (m-3) + ··· + α n × 2 (m-n-1) where m is an integer index of a power necessary for representing the quantization characteristics, and α i , i being 1 ~ n, is a pre-set integer for representing the fineness of the quantization characteristics. In the present fourth embodiment, the signals are quantized with values of the index m being integers of from 0 to 7 and the fineness n of the quantization characteristics of 2, as a typical example for the equation (6). Although the value (m - 1) is employed in the equation (6) in place of m as the index of the power, there is no essential difference whether the index m or (m - 1) is employed. The quantization characteristics which may be represented by the above equation (6) are shown in Table 14. index number quantization information (QUANT) decimal expression binary expression 0 0.5 0000000.1 1 0.625 0000000.101 2 0.75 0000000.11 3 0.875 0000000.111 4 1.0 0000001 5 1.25 0000001.01 6 1.5 0000001.1 7 1.75 0000001.11 8 2.0 0000010 9 2.5 0000010.1 10 3.0 0000011 11 3.5 0000011.1 12 4.0 0000100 13 5.0 0000101 14 6.0 0000110 15 7.0 0000111 16 8.0 0001000 17 10.0 0001010 18 12.0 0001100 19 14.0 0001110 20 16.0 0010000 21 20.0 0010100 22 24.0 0011000 23 28.0 0011100 24 32.0 0100000 25 40.0 0101000 26 48.0 0110000 27 56.0 0111000 28 64.0 1000000 29 80.0 1010000 30 96.0 1100000 31 112.0 1110000 If the non-linear sequence shown in Fig.14 is employed, the mapping may be determined monistically by the equation (6), so that there is no necessity of providing a memory for storing the mapping data. If the mapping to the non-linear sequence shown in Table 14 is employed, the following code data is transmitted for transmitting the quantization information according to the equation (6). First, for transmitting the quantization information m , it is necessary to transmit integers of from 0 to 7, so that three bits are required. Besides, for transmitting the quantization information α 1 and α 2 , each one bit is required, so that a total of five bits are required. The number of bits of five is precisely that required for transmitting the figures of from 1 to 31, so that compatibility of the system operating under the conventional quantization characteristics with the system operating under the quantization characteristics according to the present invention may be maintained. A typical construction of the 5-bit quantization information (Q1 Q2 Q3 Q4 Q5) is given hereinbelow. The quantization information m is represented by the first three bits (Q1 Q2 Q3) binary, and the quantization information α 1 and the quantization information α 2 are represented each by one bit (Q4 Q5). Q1 Q2 Q3 Q4 Q5 5 bits Q1 Q2 Q3 000 to 111 quantization information m Q4 0 or 1 quantization information α 1 Q5 0 or 1 quantization information α 2 The inverse quantization when employing the mapping to the non-linear sequence shown in Table 14 is now considered. If the non-linear sequence shown in Table 14 is represented by binary numbers, only three bits become "1" simultaneously in any of the binary numbers. Consequently, addition is performed twice at the maximum and two adders suffice. Besides, the bits "1" occur consecutively without occurring at random, so that it suffices to shift data to a desired place by a shifter placed downstream of two-stage adders. The inverse quantization circuit according to the present invention, which is based on the above-described principle, is shown in Fig.7. The inverse quantization device according to the present invention is made up of two full adders 190, 191 and a shifter 192. The shifter shifts data left by a number of bits shown in Table 15 depending on the value of (Q1 Q2 Q3). At this time, the LSB is padded with 0. By way of a concrete example, the case in which a DCT coefficient, which is equal to 100, is quantized with a quantization width of 20, is explained. The quantization characteristic is equal to 5, which value is transmitted after coding to "000000101" if nine bits are employed for coding. If encoded with five bits by the method of the present invention, the width of quantization of 20, encoded in five bits, becomes "10101" because 20 = 16 + 4, 16 = 2 4 and 4 = 2 2 , so that m = 5, α 1 = 0 and α 2 = 1. On reception of the quantization value (quantization data) of "000000101" and the width of quantization of "10101", the decoder enters the data to the inverse quantization circuit. That is, in Fig.7, a0 ··· a8 = "000000101" and Q1 Q2 Q3 = "101" : quantization information m Q4 = "0" Q5 = "1" In the inverse quantization circuit, shown in Fig.7, since Q5 = "1", a0 to a8 in the upper most row are directly entered to an adder 190. However, since Q4 = "0", an output of a0 to a8 of the next row become "0" without being entered to the adder 190. A0 to a8 in the third row are added to the result of addition, so that the new sum result is "000000011001". This value is entered to the shifter 192 and shifted by two bits in accordance with Q1 Q2 Q3 = "101" so that an output of the shifter 192 becomes "000001100100" and hence the quantization value of "100" digital is produced. The amounts of shift in the shifter 192 and the method of computing the amounts of shift in the present concrete example are shown in Tables 15 and 16, respectively. Q3 Q2 Q1 amount of left shift (0 pad) 0 right shift : 3 or shift binary point left : 3 1 right shift : 2 or shift binary point left : 2 2 right shift : 1 or shift binary point left : 1 3 0 4 1 5 2 6 3 7 4 A fifth embodiment of the present invention is explained. In the fourth embodiment, the fineness of quantization characteristics up to the third place below the binary point in binary representation is defined, as shown in Table 14. However, the fineness of quantization characteristics accepted by the quantization circuit is determined independently. For example, if the fineness of quantization characteristics accepted by the quantization circuit is up to the first place below the binary point in binary representation, the quantization information shown in Table 14, having the excessive fineness of quantization characteristics are inhibited. The quantization characteristics limited is this manner are shown in Table 17. In the fifth embodiment, the inhibited quantization information cannot be employed. quantization information quantization characteristics (QUANT) m α1 α2 decimal expression binary expression 000 0 0 0.5 0000000.1 000 0 1 inhibit inhibit 000 1 0 inhibit inhibit 000 1 1 inhibit inhibit 001 0 0 1.0 0000001 001 0 1 inhibit inhibit 001 1 0 1.5 0000001.1 001 1 1 inhibit inhibit 010 0 0 2.0 0000010 010 0 1 2.5 0000010.1 010 1 0 3.0 0000011 010 1 1 3.5 0000011.1 011 0 0 4.0 0000100 011 0 1 5.0 0000101 011 1 0 6.0 0000110 011 1 1 7.0 0000111 100 0 0 8.0 0001000 100 0 1 10.0 0001010 100 1 0 12.0 0001100 100 1 1 14.0 0001110 101 0 0 16.0 0010000 101 0 1 20.0 0010100 101 1 0 24.0 0011000 101 1 1 28.0 0011100 110 0 0 32.0 0100000 110 0 1 40.0 0101000 110 1 0 48.0 0110000 110 1 1 56.0 0111000 111 0 0 64.0 1000000 111 0 1 80.0 1010000 111 1 0 96.0 1100000 111 1 1 112.0 1110000 In a sixth embodiment, the quantization information having the excessive fineness of quantization characteristics is changed as to the manner of allocation thereof so as to represent the near-by quantization characteristics having acceptable fineness, instead of inhibiting the quantization information having the excessive fineness of quantization characteristics. This embodiment is shown in Table 18, in which the quantization information representing quantization characteristics of, for example, 0.5, is "000xx", x indicating "don't care' thus showing that the bit in these positions may be 0 or 1. In the present sixth embodiment, there is no inhibited quantization information, as in the fifth embodiment. quantization information quantization characteristics (QUANT) m α1 α2 decimal expression binary expression 000 × × 000 0 0 000 0 1 0.5 0000000.1 000 1 0 000 1 1 001 0 × 001 0 0 1.0 0000001 001 0 1 001 1 × 001 1 0 1.5 0000001.1 001 1 1 010 0 0 2.0 0000010 010 0 1 2.5 0000010.1 010 1 0 3.0 0000011 010 1 1 3.5 0000011.1 011 0 0 4.0 0000100 011 0 1 5.0 0000101 011 1 0 6.0 0000110 011 1 1 7.0 0000111 100 0 0 8.0 0001000 100 0 1 10.0 0001010 100 1 0 12.0 0001100 100 1 1 14.0 0001110 101 0 0 16.0 0010000 101 0 1 20.0 0010100 101 1 0 24.0 0011000 101 1 1 28.0 0011100 110 0 0 32.0 0100000 110 0 1 40.0 0101000 110 1 0 48.0 0110000 110 1 1 56.0 0111000 111 0 0 64.0 1000000 111 0 1 80.0 1010000 111 1 0 96.0 1100000 111 1 1 112.0 1110000 It is noted that variable length coded data are contained in the bit stream encoded by the MPEG system. Therefore, a special code is required which enables monistical decoding if, when decoding is made from an arbitrary point, a variety of possible variable length coded data should have occurred. In the encoded bit stream according to the MPEG system, the special code is a code consisting of 23 or more consecutive 0's. In this consideration, limitations are imposed on the variable length code data other than the above special code data lest 23 or more 0s should occur for any combinations of the other variable length code data. Consequently, the quantization information constituted only by 0s is not used as far as is possible. Thus, in Tables 14, 17 and 18, the quantization information "00000" presents problems. For overcoming the problems, "0" and "1" are inverted between each other in e.g. Table 14 for inhibiting the large quantization characteristics "112" which is thought to be used only on rare occasions. Such example is shown in Table 19. Table 20 shows an example in which the fineness of Table 18 is doubled for inverting the quantization information. quantization information quantization characteristics (QUANT) m α1 α2 decimal expression binary expression 111 1 1 0.5 0000000.1 111 1 0 0.625 0000000.101 111 0 1 0.75 0000000.11 111 0 0 0.875 0000000.111 110 1 1 1.0 0000001 110 1 0 1.25 0000001.01 110 0 1 1.5 0000001.1 110 0 0 1.75 0000001.11 101 1 1 2.0 0000010 101 1 0 2.5 0000010.1 101 0 1 3.0 0000011 101 0 0 3.5 0000011.1 100 1 1 4.0 0000100 100 1 0 5.0 0000101 100 0 1 6.0 0000110 100 0 0 7.0 0000111 011 1 1 8.0 0001000 011 1 0 10.0 0001010 011 0 1 12.0 0001100 011 0 0 14.0 0001110 010 1 1 16.0 0010000 010 1 0 20.0 0010100 010 0 1 24.0 0011000 010 0 0 28.0 0011100 001 1 1 32.0 0100000 001 1 0 40.0 0101000 001 0 1 48.0 0110000 001 0 0 56.0 0111000 000 1 1 64.0 1000000 000 1 0 80.0 1010000 000 0 1 96.0 1100000 000 0 0 inhibit inhibit quantization information quantization characteristics (QUANT) m α1 α2 decimal expression binary expression 111 × × 111 1 1 111 1 0 1.0 0000000.1 111 0 1 111 0 0 110 1 × 110 1 1 2.0 0000001 110 1 0 110 0 × 110 0 1 3.0 0000001.1 110 0 0 101 1 1 4.0 0000010 101 1 0 5.0 0000010.1 101 0 1 6.0 0000011 101 0 0 7.0 0000011.1 100 1 1 8.0 0000100 100 1 0 10.0 0000101 100 0 1 12.0 0000110 100 0 0 14.0 0000111 011 1 1 16.0 0001000 011 1 0 20.0 0001010 011 0 1 24.0 0001100 011 0 0 28.0 0001110 010 1 1 32.0 0010000 010 1 0 40.0 0010100 010 0 1 48.0 0011000 010 0 0 56.0 0011100 001 1 1 64.0 0100000 001 1 0 80.0 0101000 001 0 1 96.0 0110000 001 0 0 112.0 0111000 000 1 1 128.0 1000000 000 1 0 160.0 1010000 000 0 1 192.0 1100000 000 0 0 inhibit inhibit An encoding/decoding apparatus for picture signals in which linear quantization is changed over to non-linear quantization and vice versa when employing the quantization information is hereinafter explained. The schematic arrangement of the encoding apparatus for picture signals according to the present invention is similar to the conventional encoding apparatus shown in Fig.16. However, the inverse quantization circuit 60 has one of the schematic arrangements shown in Figs.3, 6 and 7, while the quantization circuit 57 has a schematic arrangement shown in Fig.8. The signals from the DCT circuit 56 shown in Fig.16 are transmitted to the quantization circuit 57 shown in Fig.8 and thence to a maximum coefficient selecting circuit 210. In the maximum coefficient selecting circuit 210 a value obtained on dividing the maximum transform coefficient by the maximum quantization width 62 (62 results from multiplying the maximum index number 31 by 2) employed for linear quantization is compared to a maximum value of 256 of the quantization level. If the value is equal to or larger than the maximum quantization width, a quantization characteristic selecting circuit 211 selects the quantization characteristics for linear quantization. At this time, the quantization characteristic selecting circuit 211 outputs a quantization selecting signal indicating that the linear quantization has been selected to a signal changeover switch 212 and to the variable length coding circuit 58 shown in Fig.16. Consequently, the signal changeover switch 212 is set to a fixed terminal a so that the output of the quantization characteristic selecting circuit 211 is transmitted via the terminal a of the signal changeover switch 212 to a linear quantization circuit 213. In the linear quantization circuit 213, linear quantization is performed on the data with the linear quantization characteristics and the resulting linear-quantized data is outputted to the variable length coding circuit 58 and to the inverse quantization circuit 60. Since not only the quantization characteristic selecting signal but also the quantization width (quantization scale) is supplied to the variable length coding circuit 58, the variable length coding circuit 58 performs variable length coding using the quantization width. On the other hand, if the value obtained at the maximum coefficient selecting circuit 210 and compared to the quantization level is found to be smaller than the maximum quantization width, the quantization characteristic selecting circuit 211 selects the quantization characteristics for non-linear quantization. Thus a quantization selecting signal from the quantization characteristic selecting circuit 211 indicating that the non-linear quantization has been selected is outputted to the signal selecting switch 212 which is changed over to a fixed terminal b . An output of the quantization characteristic selecting circuit 211 is transmitted via the terminal b of the signal changeover switch 212 to a non-linear quantization circuit 214 via the terminal b of the signal changeover switch 212 so that non-linear quantization is performed in accordance with non-linear quantization characteristics. The non-linear quantized data are outputted to the variable length coding circuit 58 and to the inverse quantization circuit 60. Since not only the quantization characteristic selecting signal but also the quantization width (quantization scale) is supplied to the variable length coding circuit 58, as in the case of the linear quantization, the variable length coding circuit 58 performs variable length coding using the quantization width. Since the linear quantization /non-linear quantization switching signal is changed over on the frame basis, the linear quantization is changed over to the non-linear quantization or vice versa on the frame basis. It is also possible for the maximum coefficient selecting circuit 210 to check the flag indicating the quantization characteristics, prescribed in the MPEG system, to decide which of the linear quantization or the non-linear quantization is to be performed. It is also possible for the maximum coefficient selecting circuit 210 to check the dynamic range to decide which of the linear quantization or the non-linear quantization is to be performed. The schematic arrangement of the decoding apparatus for picture signals according to the present invention is similar to that of the conventional decoding apparatus shown in Fig.19. However, the inverse quantization circuit 83 may have any one of the schematic arrangements shown in Figs.3, 6 and 7. In embodiments of the invention, larger quantization characteristics may be employed for encoding a picture in need of large quantization characteristics, while smaller quantization characteristics may be employed for decoding a high quality picture. On the other hand, the quantization characteristics may be obtained which may be suitable in controlling the number of bits generated by encoding with high accuracy. Besides, since there is no necessity of storing the non-linear sequence of numbers for quantization characteristics, the circuit arrangement is not increased in size and quantization and inverse quantization my be achieved using shifting operations and a multiplier having a reduced number of stages, the multiplier scale may be halved as compared with that in the conventional encoding /decoding method and encoding/decoding apparatus.

Claims: A quantization method for quantizing picture signals in which input picture signals to be encoded are quantized comprising setting a digital signal value k (bits Q1, Q2), k being a positive integer (0, 1, 2, 3, ...) as a first quantization information, setting a digital signal value i/2 + j (bits Q3-Q5) representing a second quantization information, j being a positive integer (0, 1, 2, 3, ...) and i being 0 or 1, and quantizing the picture signals according to non-linear quantization characteristic signal steps (QUANT), wherein said non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4. A quantization apparatus for quantizing picture signals in which input picture signals to be encoded are quantized, comprising: means for setting a digital signal value k (bits Q1, Q2) representing first quantization information, k being a positive integer (0, 1, 2, 3...), means for setting a digital signal value i/2+j (bits Q3 to Q5) representing a second quantization information, j being a positive integer (0, 1, 2, 3...), and i being 0 or 1, and means for quantizing the picture signals according to non-linear quantization characteristic signal steps (QUANT) wherein said non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4. The method or apparatus as claimed in claim 1 or 2 wherein the non-linear quantization characteristic signal steps (QUANT) are multiplied by a constant and used as a width of quantization. The method or apparatus as claimed in claim 1, 2 or 3 wherein said first quantization information and said second quantization information are together represented by five bits (bits Q1 to Q5). The method or apparatus as claimed in claim 1, 2, 3 or 4 wherein the relation between said quantization information k, i or j and the non-linear quantization characteristic signal steps (QUANT) are as specified in Table 1 of the ANNEX to the claims. A quantization method for quantizing picture signals in which input picture signals to be encoded are quantized, comprising setting a digital signal value k (bits Q1, Q2) k being a positive integer (0, 1, 2, 3) as a first quantization information, setting a digital signal value i/2+j (bits Q3 to Q5) representing a second quantization information, j being a positive integer (0, 1, 2, 3), and i being 0 or 1, and quantizing the picture signals according to non-linear quantization characteristic signal steps (QUANT)wherein said non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4 for k=0,1,and 2; and by the equation QUANT = (i/2 + j) x 2 k+1 + 2 (k+2) - 4 for k=3. The method or apparatus of claim 5, wherein each of the quantization characteristic signal steps (QUANT) is expressed by a binary expression so that within each binary expression there is a sequence of four consecutive bits each of which may be zero or one depending on the values of i, j and k, the sequence being spaced from the least significant bit by a number of bits equal to k, the other bits of the binary expression being zero. (TABLE 1) The method of claim 6, wherein each of the quantization characteristic signal steps (QUANT) is expressed by a binary expression so that for k=0, 1 and 2 within each binary expression there is a sequence of four consecutive bits each of which may be zero or one depending on the values of i, j and k, the sequence being spaced from the least significant bit by a number of bits equal to k, the other bits of the binary expression being zero, whereas for k=3 within each binary expression there is a sequence of five consecutive bits each of which may be zero or one depending on the values of i, j and k, the sequence being spaced from the least significant bit by a number of bits equal to k, the other bits of the binary expression being zero. (TABLE 2) A quantization apparatus for quantizing picture signals in which input picture signals to be encoded are quantized, comprising: means for setting a digital signal value k (bits Q1, Q2) representing first quantization information, k being a positive integer (0, 1, 2, 3), means for setting a digital signal value i/2+j (bits Q3 to Q5) representing a second quantization information, j being a positive integer (0, 1, 2, 3), and i being 0 or 1, and means for quantizing the picture signals according to non-linear quantization characteristic signal steps (QUANT) wherein said non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4 for k=0,1,and 2; and by the equation QUANT = (i/2 + j) x 2 k+1 + 2 (k+2) - 4 for k=3. The method or apparatus as claimed in claim 6, 7, 8 or 9, wherein the non-linear quantization characteristic signal steps (QUANT) are multiplied by a constant and used as a width of quantization. The method or apparatus as claimed in claim 6, 7, 8, 9 or 10, wherein said first quantization information and said second quantization information are together represented by five bits (bits Q1 to Q5). A quantization method for quantizing picture signals in which input picture signals to be encoded are quantized comprising setting a digital signal value m (bits Q1, Q2, Q3) where m is a positive integer as a first quantization information, setting a digital signal value a i , a being 0 or 1 representing a second quantization information, and quantizing the picture signals according to non-linear quantization characteristic signal steps (QUANT) wherein the non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = 2 (m-1) + a 1 x 2 (m-2) + a 2 x 2 (m-3) + ... + a n x 2 (m-n-1) where i is an integer (1, 2, ... n) indicating a fineness of quantization. A quantization apparatus for quantizing picture signals in which input picture signals to be encoded are quantized comprising: means for setting a digital signal value m , (bits Q1, Q2, Q3) where m is an integer, representing first quantization information, means for setting a digital signal value a i , a being 0 or 1 representing second quantization information, and means for quantizing the picture signals according to non-linear quantization characteristics signal steps (QUANT) wherein the non-linear quantization characteristic signal steps (QUANT) are represented by the equation QUANT = 2 (m-1) + a 1 x 2 (m-2) + a2 x 2 (m-3) + ... +an x 2 (m-n-1) where i is an integer (1, 2...n) indicating a fineness of quantization. The method or apparatus as claimed in claim 12 or 13 wherein L bits represent said first quantization information m, and n bits represent said second quantization information a i , where i is said integer (1, 2, .....n) The method or apparatus as claimed in claim 14 wherein L is 3 and n is 2. The method or apparatus as claimed in claim 15, wherein the relation between m, a i and the non-linear quantization characteristic signal steps (QUANT) is as shown in Table 3 of the ANNEX to the claims. A picture signal dequantization method in which transmitted data which have been quantized according to the method of claim 1, 3, 4, 5 or 7 are inverse-quantized for restoring a picture from the quantized data, comprising the steps of reproducing said non-linear quantization characteristic signal steps (QUANT) at the time of inverse quantization using said digital signal value k (bits Q1, Q2), k being said positive integer (0, 1, 2, 3, ...) as said first quantization information and said digital signal value i/2 + j (bits Q3 to Q5) representing said second quantization information, j being said positive integer (0, 1, 2, 3, ...) and i being 0 or 1, wherein said non-linear quantization characteristic signal steps (QUANT) are represented by said equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4. A picture signal dequantization apparatus in which transmitted data which have been quantized according to the apparatus of claim 1, 3, 4, 5 or 7 are inverse-quantized for restoring a picture from the quantized data, comprising: means for reproducing said non-linear quantization characteristic signal steps (QUANT) at the time of inverse quantization using said digital signal value k, (bits Q1, Q2) k being said positive integer (0, 1, 2, 3,...) as said first quantization information and said digital signal value i/2+j (bits Q3 to Q5) representing said second quantization information, j being said positive integer (0, 1, 2, 3, ...) and i being 0 or 1, and means for inverse quantizing the data according to the reproduced non-linear quantization characteristic signal steps (QUANT) wherein said non-linear quantization characteristic signal steps (QUANT) are represented by said equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4. The dequantizing method or apparatus as claimed in claim 17 or 18, wherein the obtained non-linear quantization characteristic signal steps (QUANT) are multiplied by a constant and the result used as a quantization width. The dequantizing method or apparatus as claimed in claim 17 or 18, wherein said first quantization information and said second quantization information are together represented by five bits (bits Q1 to Q5). The dequantization method or apparatus as claimed in claim 20, wherein shifting and adding of said first and second quantization information is performed for calculating said equation (QUANT). The dequantization apparatus as claimed in claim 21, wherein a dequantization means comprises a converting means (151) for converting said first quantization information k into the expression 2 (k+2) - 4, shifting means (150) for shifting said second quantization information (i/2 +j) based on said first quantization information k, and addition means (152) for adding the converted first information to said shifted second information. The dequantization apparatus as claimed in claim 21 wherein a dequantization means comprises a converting means (141, 181) for converting said first quantization information k into the expression 4-4/2 k , addition means (140, 180) for summing the converted first information and said second quantization information (i/2 +j), multiplication means (142, 182) for multiplying the result of said addition by a conversion coefficient (coeff) for restoring the original picture signals, and shifting means (143, 183) for shifting the result of said multiplication by a number of bits as set by said first quantization information k. The dequantization method or apparatus as claimed in claim 19 or 20. wherein the relation between said quantization information k, i and j and the non-linear quantization characteristic signal steps (QUANT) is as shown in Table 1 of the ANNEX to the claims. A picture signal dequantization method in which transmitted data which have been quantized according to the method of claim 6 or 8 are inverse-quantized for restoring a picture from the quantized data, comprising the steps of reproducing said non-linear quantization characteristic signal steps (QUANT) at the time of inverse quantization using said digital signal value k (bits Q1, Q2), k being said positive integer (0, 1, 2, 3, ...) as said first quantization information and said digital signal value i/2 + j (bits Q3 to Q5) representing said second quantization information, j being said positive integer (0, 1, 2, 3, ...) and i being 0 or 1, wherein said non-linear quantization characteristic signal steps (QUANT) are represented by said equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4 for k=0,1,and 2; and by the equation QUANT = (i/2 + j) x 2 k+1 + 2 (k+2) - 4 for k=3. A picture signal dequantization apparatus in which transmitted data which have been quantized according to the apparatus of claim 9 or of claim 10 or 11 when dependent on claim 9 are inverse-quantized for restoring a picture from the quantized data, comprising: means for reproducing said non-linear quantization characteristic signal steps (QUANT) at the time of inverse quantization using said digital signal value k, (bits Q1, Q2) k being said positive integer (0, 1, 2, 3,...) as said first quantization information and said digital signal value i/2+j (bits Q3 to Q5) representing said second quantization information, j being said positive integer (0, 1, 2, 3, ...) and i being 0 or 1, and means for inverse quantizing the data according to the reproduced non-linear quantization characteristic signal steps (QUANT) wherein said non-linear quantization characteristic signal steps (QUANT) are represented by said equation: QUANT = (i/2 + j) x 2 k + 2 (k+2) - 4 for k=0,1,and 2; and by the equation QUANT = (i/2 + j) x 2 k+1 + 2 (k+2) - 4 for k=3.. The dequantization method or apparatus as claimed in claim 25 or 26 wherein the obtained non-linear quantization characteristic signal steps (QUANT) are multiplied by a constant and the result used as a quantization width. The dequantization method or apparatus as claimed in claim 25 or 26 wherein said first quantization information and said second quantization information are together represented by five bits (bits Q1 to Q5). The dequantization method or apparatus as claimed in claim 28 wherein, shifting and adding of said first and second quantization information is performed for calculating said equation (QUANT). A picture signal dequantizing method in which transmitted data which have been quantized according to the method of claim 12, 14, 15 or 16 is inverse-quantized for restoring a picture from the quantized data, comprising the steps of reproducing said non-linear quantization characteristic signal steps (QUANT) at the time of inverse quantization using said digital signal value m (bits Q1, Q2, Q3) m being said positive integer as said first quantization information and said digital signal value a i , a being 0 or 1 representing said second quantization information wherein the non-linear quantization characteristic signal steps (QUANT) are represented by the equation: QUANT = 2 (m-1) + a 1 x 2 (m-2) + a 2 x 2 (m-3) + ... + a n x 2 (m-n-1) where i is an integer (1, 2, ... n) which indicates a fineness of quantization. A picture signal dequantizing apparatus in which transmitted data which have been quantized according to the apparatus of claim 13, 14, 15, or 16 is inverse-quantized for restoring a picture from the quantized data, comprising: means for reproducing said non-linear quantization characteristic signal steps (QUANT) using said digital signal value m, (bits Q1, Q2, Q3) m being said positive integer as said first quantization information and said digital signal value a i , a being 0 or 1 representing said second quantization information; and means for inverse quantizing said data according to non-linear quantization characteristic signals (QUANT) represented by the equation: QUANT = 2 (m-1) + a 1 x 2 (m-2) + a 2 x 2 (m-3) + ... + a n x 2 (m-n-1) where i is an integer (1, 2...n) which indicates a fineness of quantization. The method or apparatus as claimed in claim 28 or 29 wherein L bits represent said first quantization information m, and n bits represent said second quantization information a i , where i is said integer (1, 2, .....n) The method or apparatus as claimed in claim 30 or 31 wherein the relation between m, a i and the non-linear quantization characteristic signal steps (QUANT) are as shown in Table 3 of the ANNEX to the claims. A picture signal encoding and quantization method in which a picture signal is encoded and subsequently undergoes quantization and variable length coding, and wherein a decision is made for a linear/non-linear quantization according to a linear/non-linear quantization changeover signal, indicating the method of quantization, and if said linear/non-linear quantization changeover signal indicates a non-linear quantization, quantization is performed according to non-linear quantization characteristic signal steps (QUANT) as claimed in claim 1, 6 or 12. A picture signal encoding and quantization apparatus for encoding and quantizing a picture signal, comprising means for encoding and subsequently quantizing and variable length coding the picture signal, and including selecting means (212) for making a decision for a linear/non-linear quantization according to a linear/non-linear quantization changeover signal, indicating the method of quantization, and means which, if said linear/non-linear quantization changeover signal indicates a non-linear quantization, quantizes according to non-linear quantization characteristic signal steps (QUANT) as claimed in claim 2, 9 or 13. The method or apparatus as claimed in claim 34 or 35, wherein said decision is made on a frame basis. A picture signal decoding and dequantization method for decoding and dequantizing a picture signal encoded and quantized in accordance with claim 34 comprising the steps of: detecting whether said changeover signal indicates linear or non-linear quantization was used to quantize the picture signals, and if non-linear quantization was used, reproducing said non-linear quantization characteristic signal steps (QUANT) in accordance with claim 17, 25 or 30 for restoring the original picture signals. A picture signal decoding and dequantization apparatus for decoding and dequantizing a picture signal encoded and quantized in accordance with claim 35 comprising: means for detecting whether said changeover signal indicates linear or non-linear quantization was used to quantize the picture signals, and reproducing means which, if non-linear quantization was used, reproduces said non-linear quantization characteristic signal steps (QUANT) in accordance with claim 18, 26 or 31 for restoring the original picture signals. The method or apparatus as claimed in claim 37 or 38, wherein said linear/non-linear quantization changeover signal indicates a changeover between linear and non-linear quantization on a frame basis. The apparatus as claimed in claim 38, wherein the reproducing means comprising a converting means (141, 181) for converting said first quantization information k into the expression 4-4/2 k , addition means (140, 180) for summing the converted first information and said second quantization information i/2+j, multiplication means (142, 182) for multiplying the result of said addition by a conversion coefficient (coeff) for restoring the original picture signals, and shifting means (143, 183) for shifting the result of said multiplication by a number of bits as set by said first quantization information k and wherein means (144) for selecting linear or non- linear quantization is provided between said addition means (140) and the said multiplication means (142). The method as claimed in claim 37 wherein said reproducing step comprises converting (151) said first quantization information k into the expression 2 (k+2) - 4, shifting (50) said second quantization information i/2+j based on said first quantization information k, and adding (52) the converted first information to said shifted second information. The method as claimed in claim 37 wherein said reproducing step comprises converting (141, 181) said first quantization information k into the expression 4-4/2 k , summing (140, 180) the converted first information and said second quantization information i/2 +j, multiplying (142, 182) the result of said addition by a conversion coefficient (coeff) for restoring the original picture signals, and shifting (143, 153) the result of said multiplication by a number of bits as set by said first quantization information k. The method as claimed in claim 37 wherein the said reproducing step comprises the steps of converting (141, 181) said first quantization information k into the expression 4-4/2 k , summing (140, 180) the converted first information and said second quantization information i/2 +j, selecting said linear or non-linear dequantization according to the changeover signal, and, if non-linear quantization is selected, multiplying (142, 182) the result of said addition by a conversion coefficient (coeff) for restoring the original picture signals, and shifting (143, 183) the result of said multiplication by a number of bits as set by said first quantization information k. ANNEX TO CLAIMS: index number quantization quantization information characteristics k j i decimal expression binary expression 0 00 00 0 inhibit inhibit 1 00 00 1 0.5 00000.1 2 00 01 0 1.0 00001.0 3 00 01 1 1.5 00001.1 4 00 10 0 2.0 00010.0 5 00 10 1 2.5 00010.1 6 00 11 0 3.0 00011.0 7 00 11 1 3.5 00011.1 8 01 00 0 4.0 000100. 9 01 00 1 5.0 000101. 10 01 01 0 6.0 000110. 11 01 01 1 7.0 000111. 12 01 10 0 8.0 001000. 13 01 10 1 9.0 001001. 14 01 11 0 10.0 001010. 15 01 11 1 11.0 001011. 16 10 00 0 12.0 001100. 17 10 00 1 14.0 001110. 18 10 01 0 16.0 010000. 19 10 01 1 18.0 010010. 20 10 10 0 20.0 010100. 21 10 10 1 22.0 010110. 22 10 11 0 24.0 011000. 23 10 11 1 26.0 011010. 24 11 00 0 28.0 011100. 25 11 00 1 32.0 100000. 26 11 01 0 36.0 100100. 27 11 01 1 40.0 101000. 28 11 10 0 44.0 101100. 29 11 10 1 48.0 110000. 30 11 11 0 52.0 110100. 31 11 11 1 56.0 111000. ANNEX TO CLAIMS: index number quantization information quantization characteristics k j i decimal expression binary expression 0 00 00 0 inhibit inhibit 1 00 00 1 0.5 00000.1 2 00 01 0 1.0 00001.0 3 00 01 1 1.5 00001.1 4 00 10 0 2.0 00010.0 5 00 10 1 2.5 00010.1 6 00 11 0 3.0 00011.0 7 00 11 1 3.5 00011.1 8 01 00 0 4.0 000100. 9 01 00 1 5.0 000101. 10 01 01 0 6.0 000110. 11 01 01 1 7.0 000111. 12 01 10 0 8.0 001000. 13 01 10 1 9.0 001001. 14 01 11 0 10.0 001010. 15 01 11 1 11.0 001011. 16 10 00 0 12.0 001100. 17 10 00 1 14.0 001110. 18 10 01 0 16.0 010000. 19 10 01 1 18.0 010010. 20 10 10 0 20.0 010100. 21 10 10 1 22.0 010110. 22 10 11 0 24.0 011000. 23 10 11 1 26.0 011010. 24 11 00 0 28.0 011100. 25 11 00 1 36.0 100100. 26 11 01 0 44.0 101100. 27 11 01 1 52.0 110100. 28 11 10 0 60.0 111100. 29 11 10 1 68.0 1000100. 30 11 11 0 76.0 1001100. 31 11 11 1 84.0 1010100. ANNEX TO CLAIMS: index number quantization information quantization characteristics (QUANT) m a1 a2 decimal expression binary expression 0 000 0 0 0.5 0000000.1 1 000 0 1 0.625 0000000.101 2 000 1 0 0.75 0000000.11 3 000 1 1 0.875 0000000.111 4 001 0 0 1.0 0000001 5 001 0 1 1.25 0000001.01 6 001 1 0 1.5 0000001.1 7 001 1 1 1.75 0000001.11 8 010 0 0 2.0 0000010 9 010 0 1 2.5 0000010.1 10 010 1 0 3.0 0000011 11 010 1 1 3.5 0000011.1 12 011 0 0 4.0 0000100 13 011 0 1 5.0 0000101 14 011 1 0 6.0 0000110 15 011 1 1 7.0 0000111 16 100 0 0 8.0 0001000 17 100 0 1 10.0 0001010 18 100 1 0 12.0 0001100 19 100 1 1 14.0 0001110 20 101 0 0 16.0 0010000 21 101 0 1 20.0 0010100 22 101 1 0 24.0 0011000 23 101 1 1 28.0 0011100 24 110 0 0 32.0 0100000 25 110 0 1 40.0 0101000 26 110 1 0 48.0 0110000 27 110 1 0 56.0 0111000 28 111 0 0 64.0 1000000 29 111 0 1 80.0 1010000 3.0 111 1 0 96.0 1100000 31 111 1 1 112.0 1110000

Inventors: TAHARA KATSUMI, WADA TOHRU, YAGASAKI YOICHI, TAHARA, KATSUMI, WADA, TOHRU, YAGASAKI, YOICHI, TAHARA, KATSUMI, C/O INTELLECTUAL PROPERTY DIV., Wada, Tohru, c/o Intellectual Property Division, YAGASAKI, YOICHI, C/O INTELLECTUAL PROPERTY DIV.
Applicants: SONY CORP, SONY CORPORATION
Application year: 1993
Main classification: H04N7
IPC codes: H04N7