Abstract: A method and system for monitoring and analyzing at least one signal are disclosed. An abstract of at least one reference signal is generated and stored in a reference database. An abstract of a query signal to be analyzed is then generated so that the abstract of the query signal can be compared to the abstracts stored in the reference database for a match. The method and system may optionally be used to record information about the query signals, the number of matches recorded, and other useful information about the query signals. Moreover, the method by which abstracts are generated can be programmable based upon selectable criteria. The system can also be programmed with error control software so as to avoid the re-occurrence of a query signal that matches more than one signal stored in the reference database.

Abstract: Embodiments of the present invention enable compression and decompression of data. Applications of the present invention are its use in embodiments of systems for compression and decompression of GPS long-term Ephemeris (LTE) data, although the present invention is not limited to such applications. In embodiments, the LTE data may be grouped into a set of data values associated with a parameter. In embodiments, a data set may be compressed by using a multi-order differencing scheme. In such a scheme, a set of the differences between values may be compressed because the differences have smaller magnitudes than the values. In embodiments, a multi-order differencing scheme determines how many levels (orders) of differencing may be applied to an original data set before it is compressed. In embodiments, the original data may be recovered from a compressed data set based on the type of multi-order differencing scheme used to generate the compressed data.

Abstract: Methods and systems for digital control utilizing oversampling.

Abstract: Embodiments of the present invention enable compression and decompression of data. Applications of the present invention are its use in embodiments of systems for compression and decompression of GPS long-term Ephemeris (LTE) data, although the present invention is not limited to such applications. In embodiments, the LTE data may be grouped into a set of data values associated with a parameter. In embodiments, a data set may be compressed by using a multi-order differencing scheme. In such a scheme, a set of the differences between values may be compressed because the differences have smaller magnitudes than the values. In embodiments, a multi-order differencing scheme determines how many levels (orders) of differencing may be applied to an original data set before it is compressed. In embodiments, the original data may be recovered from a compressed data set based on the type of multi-order differencing scheme used to generate the compressed data.

Abstract: A backward compression system and a backward compression method are provided. By using the system and the method, under limited memory space, a relationship between input data and previous data is identified in real time, the input data or previous data is encoded according to the relationship, and the order of data output is such that the encoded data is output first and the complete data is output second. When the output data is stored in circular memory and the memory gets full, the oldest encoded data is overwritten first, and the complete data is not overwritten until all the related encoded data is overwritten. Therefore, more original data can be preserved after decompression. Thus, system signals can be compressed and utilization of limited memory space can be improved.

Abstract: A delta-sigma analog-to-digital converter (ADC) having a serialized quantizer output has a data rate greater than a quantization rate of the delta-sigma modulator, but less than a bit rate determined by the product of the number of bits required to represent the input to a feedback digital-to-analog converter and the quantization rate. Additional information can be encoded in the serial bit stream by selection among redundant codes based on the value of the additional information. The serial bit stream may encode differences between successive quantizer output samples and the additional information may include the absolute value of the quantizer output, synchronization information and/or framing information for distinguishing data corresponding to multiple ADC input channels.

Abstract: Compression of signal samples output from a parallel, time-interleaved analog to digital converter (TIADC) for a baseband signal, includes calculating first or higher order differences of consecutive signal samples followed by lossless or lossy encoding of the difference samples to produce compressed samples. Compression of a TIADC output signal with a nonzero center frequency, includes calculating sums or differences of pairs of signal samples separated by an appropriate number of sampling intervals followed by lossless or lossy encoding. The sums or differences of the signal samples have lower magnitudes than the original samples, allowing more efficient compression. Lossy compression alternatives produce compressed data with a fixed bit rate or with a fixed quality in the decompressed samples.

Abstract: Methods and apparatus are provided for look-ahead block processing in predictive delta-sigma modulators. An input signal is quantized using a predictive delta-sigma modulator by generating error prediction values for a current block of input values based on a linear combination of error prediction values from one or more previous blocks, input values of one or more previous blocks, quantized values of one or more previous blocks and the current block of input values; computing speculative error prediction values for at least one input value in the current block, wherein the speculative error prediction values are computed for a plurality of possible quantizer output values; selecting one of the speculative error prediction values based on a quantized value from the current block; and subtracting the error prediction values for the current block from the corresponding current block of input values.

Abstract: A digital sigma-delta modulator (100) for modulating a digital input signal (x) is described. The digital sigma-delta modulator (100) comprises a quantizer (115) for quantizing an input signal (s) and producing a quantized output signal (y) at a first output (110) and an error output signal (?q) at a second output (165), at least one feedback loop (120, 125) connected to an input adder (140) and the first outputs (110) and the second output (165) of the quantizer (115) and a feedback filter (130, 135) in the at least one feedback loop (120, 125). The input adder (140) produces the sum signal (s) by adding the digital input signal (x) at an input (105) and output signals of the at least one feedback loop filters (130,135).

Abstract: An encoder encodes data into parallel codewords. Each codeword is expressed as a set of logic 0s and a set of logic 1s on two sets of output nodes. The encoder selects a current codeword which differs from the immediately preceding codeword by a fixed number of zero-to-one transitions on the first set of nodes and a fixed number of one-to-zero transitions on the second set of nodes. The current codeword is selected such that the first and second sets of nodes are different than additional nodes that contain transitions between the immediately preceding codeword and a bi-preceding codeword, and that logic values on additional nodes are unchanged between immediately preceding codeword and current codeword. A decoder decodes the codewords by comparing symbols on node pairs other than those for which transitions were expressed in the preceding code word, and decoding the results of those comparisons.

Abstract: An encoding method for dividing a bit string of an input signal at a position of x bits from a least significant bit into a high-order bit string and a low-order bit string, performing variable-length-encoding of the high-order bit string, and performing fixed-length-encoding of the low-order bit string includes deriving a reference integer I close to 2x (x=m/2, m is an integer of 0 or more); obtaining a quotient and a remainder that are determined by performing a dividing operation on numerical values represented respectively by the bit strings by using the reference integer I; and performing variable-length-encoding of each of quotients of two consecutive bit strings, combining remainders corresponding to the quotients and performing fixed-length-encoding of the result, and generating a codeword.

Abstract: A method and a device for decoding a signal transmitted via at least one transmission line of a data transmission system, in a user of the data transmission system receiving the signal. Instead of at discrete instants, as currently done, sampling at a specific sampling instant does not take place. To this end, a potential-edge position (PEP) for an imminent edge is estimated first. Then, given n-fold oversampling, maximally n sampling values before the PEP and maximally n sampling values after the PEP are determined and compared with previously recorded and stored sampling values. The stored sampling values are preferably stored in an edge-acceptance vector (EAV) and correspond to an edge change of the signal to be decoded at a particular point in time. Preferably not all detected 2n sampling values are compared to the content of the EAVs, but the comparison is limited to a portion, combined to a sensitivity range, of the 2n sampling values of each EAV.

Abstract: Embodiments of the present disclosure provide methods, systems, and apparatuses related to a time-interleaved delta-sigma modulator are described. Other embodiments may be described and claimed.

Abstract: In one embodiment, a mechanism for coding a non-increasing sequence of values is disclosed. In one embodiment, a method includes receiving a sequence of values to encode, the sequence of values being non-increasing, encoding a first value of the sequence using a number of bits that are required for fully representing the first value in an encoded format, and for each subsequent value in the sequence, encoding the subsequent value using a number of bits required for a minimal bit encoding of a previous value in the sequence.

Abstract: Embodiments of the present invention enable compression and decompression of data. Applications of the present invention are its use in embodiments of systems for compression and decompression of GPS long-term Ephemeris (LTE) data, although the present invention is not limited to such applications. In embodiments, the LTE data may be grouped into a set of data values associated with a parameter. In embodiments, a data set may be compressed by using a multi-order differencing scheme. In such a scheme, a set of the differences between values may be compressed because the differences have smaller magnitudes than the values. In embodiments, a multi-order differencing scheme determines how many levels (orders) of differencing may be applied to an original data set before it is compressed. In embodiments, the original data may be recovered from a compressed data set based on the type of multi-order differencing scheme used to generate the compressed data.

Abstract: An apparatus for processing a signal and method thereof are disclosed. Data coding and entropy coding are performed with interconnection, and grouping is used to enhance coding efficiency. The present invention includes the steps of obtaining a group reference value corresponding to a plurality of data included in one group through grouping including first grouping and second grouping and a first difference value corresponding to the group reference value and obtaining the data using the group reference value and the first difference value.

Abstract: A two stage compression sub-system for clear channel data. The front stage of the compressing sub-system is an octet based repeat compressor (for example a flag compressor). The second stage is dictionary based compressor (for example Lempel-Ziv (LZ) or Huffmann). Data is compressed using several different techniques, and the technique that provides the best compression is used for each particular packet. For example, each packet can be: a) compress through both compression stages. b) compress through front stage flag compressor only c) compress through back stage dictionary compressor only d) not compressed through either stage (for highly incompressible data) After compression, each packet is provided with a header which specifies the exact method used to compress that packet. At the decoder, the packet header is interrogated to determine how the packet should be de-compressed and the appropriate de-compression is then used.

Abstract: Data coding and entropy coding are performed with interconnection, and grouping is used to enhance coding efficiency. The present invention includes the steps of hierarchically extracting identification information indicating at least three or more data coding schemes. The identification information indicating two coding schemes having high frequencies of use for the identification information are extracted from different layers.

Abstract: An apparatus for processing a signal and method thereof are disclosed. Data coding and entropy coding are performed with interconnection, and grouping is used to enhance coding efficiency. The present invention includes the steps of obtaining data corresponding to a plurality of data coding schemes and deciding an entropy table for at least one of a pilot reference value and a pilot difference value included in the data using an entropy table identifier unique to the data coding scheme and entropy-decoding at least one of the pilot reference value and the pilot difference value using the entropy table.

Abstract: Compression of signal samples output from a parallel, time-interleaved analog to digital converter (TIADC) for a baseband signal, includes calculating first or higher order differences of consecutive signal samples followed by lossless or lossy encoding of the difference samples to produce compressed samples. Compression of a TIADC output signal with a nonzero center frequency, includes calculating sums or differences of pairs of signal samples separated by an appropriate number of sampling intervals followed by lossless or lossy encoding. The sums or differences of the signal samples have lower magnitudes than the original samples, allowing more efficient compression. Lossy compression alternatives produce compressed data with a fixed bit rate or with a fixed quality in the decompressed samples.

Abstract: Compression of signal samples output from a parallel, time-interleaved analog to digital converter (TIADC) for a baseband signal, includes calculating first or higher order differences of consecutive signal samples followed by lossless or lossy encoding of the difference samples to produce compressed samples. Compression of a TIADC output signal with a nonzero center frequency, includes calculating sums or differences of pairs of signal samples separated by an appropriate number of sampling intervals followed by lossless or lossy encoding. The sums or differences of the signal samples have lower magnitudes than the original samples, allowing more efficient compression. Lossy compression alternatives produce compressed data with a fixed bit rate or with a fixed quality in the decompressed samples.

Abstract: A performance monitor device includes an input unit to input both of address information and event occurrence information, an address mask unit to determine an address area to which each piece of the inputted address information belongs, an execution frequency counter to count a number of times of execution of programs in the address areas, an execution frequency holding unit to hold a counting result of the number of times of execution, an event occurrence information counter to count the event occurrence information corresponding to the address areas having the counting result of the number of times of execution included within a predetermined number of highest ranks, a holding unit to hold a counting results of the event occurrence information, and a storing unit to store the counting result of the event occurrence information corresponding to the address area having the highest number of times of execution in predetermined periods.

Abstract: A method and system of providing a recommendation measures a distance between a first document and group of clustered historic documents using a compression-based dissimilarity measurement (CDM). The CDM identifies the closest clustered historic documents and identifies a recommendation corresponding to the closest cluster.

Abstract: In a frequency analysis system, such as a signal detection system or a spectrum analyzer, the frequency domain resolution is enhanced by compression and decompression of the signal samples. The limited capacity of the data storage and/or data transfer resources limit the number of samples that can be stored or transferred. A compressor forms a compressed signal prior to data transfer or storage. A decompressor decompresses the compressed signal prior to transformation to the frequency domain, by a fast Fourier transform or other frequency domain transform. The frequency domain resolution is enhanced because more decompressed samples are available for the frequency domain transform. The compressor and decompressor apply computationally efficient algorithms that can be implemented to operate in real time.

Abstract: Compression of signal samples output from a parallel, time-interleaved analog to digital converter (TIADC) for a baseband signal, includes calculating first or higher order differences of consecutive signal samples followed by lossless or lossy encoding of the difference samples to produce compressed samples. Compression of a TIADC output signal with a nonzero center frequency, includes calculating sums or differences of pairs of signal samples separated by an appropriate number of sampling intervals followed by lossless or lossy encoding. The sums or differences of the signal samples have lower magnitudes than the original samples, allowing more efficient compression. Lossy compression alternatives produce compressed data with a fixed bit rate or with a fixed quality in the decompressed samples.

Abstract: It is an object to provide a method of coding the position information of a digital map in a small data volume by utilizing a compressing and coding technique. In a coding method of coding data indicative of a shape vector on a digital map, an arithmetic processing is carried out over position information about a node string and a shape which indicate the shape vector to be represented by data having a statistical deviation, and the data having the statistical deviation are coded to reduce a data volume. It is possible to considerably decrease a transmission data volume in the case in which the vector shape of the digital map is to be transferred.

Abstract: In a pulse width modulation method of the present invention, a digital signal is modulated and a pulse width modulation signal is generated in a pulse width modulator by using a digital signal output unit and the pulse width modulator The pulse width modulation method includes: outputting to the pulse width modulator a first value corresponding to the input signal as a first digital signal at a first timing by the digital signal output unit; determining a limited value range based on the first value by the digital signal output unit; determining a second value corresponding to a new input signal by the digital signal output unit; judging whether or not the second value is included in the limited value range, and when the second value being judged to be included, outputting the second value to the pulse width modulator as a second digital signal, and when the second value being judged not to be included, outputting a value included in the limited value range to the pulse width modulator as the second digital s

Abstract: In a coded data generation method of resampling a road shape for setting a plurality of nodes, arranging position information of each node represented by a deflection angle from the immediately preceding node to generate a data string of the deflection angles, converting the deflection angles into predicted difference values each indicating the difference from the predicted value, and variable-length coding the data string of the predicted difference values, the data string of the predicted difference values when the deflection angles are converted into the predicted difference values is evaluated and a prediction expression to calculate the predicted value is selected adaptively from among a plurality of prediction expressions ?=1, ?=2, ?=3, and ?=4 based on the evaluation result. The prediction expression to calculate the predicted value is selected adaptively in response to road shape A, B, C, D, so that the data compression effectiveness is enhanced.

Abstract: Method, system and computer program product for replacing a portion of a digital signal by applying a first difference correction that, after range limiting, converts the samples in the replacement portion to extremum values; then applying a second difference correction based on the difference between the extremum values and the desired replacement values. The first and second sets of correction values are thus independent of the original values in the first digital signal.

Abstract: The present invention significantly improves the performance of matching target file window partitions to source file window partitions in delta compression. In particular, the present invention enhances delta compression performance of delta compressors based on the idea of modeling a dataset with the frequencies of its n-grams and employs a method to compute good source and target window matching in linear time.

Abstract: A parallel precoder circuit executes a differential encoding operation on an n-row parallel input information series, and outputs an n-row parallel output information series, where 2?n. Output sets of differential encoding operation circuits each of which having a largest column number from among differential encoding operation circuits disposed in first row to (n?1)th row become first-row to (n?1)th-row parallel outputs information series, and an output set of an nth-row delay circuit becomes nth-row parallel output information series.

Abstract: Systems and methods of storing previously transmitted data and using it to reduce bandwidth usage and accelerate future communications are described. By using algorithms to identify long compression history matches, a network device may improve compression efficiently and speed. A network device may also use application specific parsing to improve the length and number of compression history matches. Further, by sharing compression histories, compression history indexes and caches across multiple devices, devices can utilize data previously transmitted to other devices to compress network traffic. Any combination of the systems and methods may be used to efficiently find long matches to stored data, synchronize the storage of previously sent data, and share previously sent data among one or more other devices.

Abstract: A noise shaping quantizer having a first noise shaping quantization unit for applying a first noise shaping operation on an input signal.

Abstract: A parallel precoder circuit executes an EXOR operation on an n-row parallel input, and outputs an n-row parallel output, where 2?n. Outputs of EXOR circuits each of which having a largest column number from among EXOR circuits disposed in first to (n?1)th rows become first-row to (n?1)th-row parallel outputs, respectively. A output of an nth-row delay circuit becomes an nth-row parallel output.

Abstract: A coding apparatus includes a predicting unit, an intermediate-code generating unit, a first coding unit and a second coding unit. The predicting unit generates a piece of prediction data based on each piece of pixel data constituting a color image. The intermediate-code generating unit compares each piece of prediction data with the corresponding piece of pixel data, to generate an intermediate code in accordance with whether or not a difference between each piece of prediction data and the corresponding piece of pixel data is in a predetermined range. The first coding unit performs entropy coding on the generated intermediate code. The second coding unit performs entropy coding on the generated intermediate code. The intermediate-code generating unit assigns each generated intermediate code to either of the first and second coding units according to whether or not the difference is in the predetermined range.

Abstract: A method and apparatus for stably encoding/decoding data, and a method and apparatus for recording/reproducing data are disclosed. The method inserts decoding information into a data section including several predetermined-bit data, determines encoding values of the data according to a transition state of the data and a value of corresponding data, and generates the decoding information and the determined encoding values in units of the data section.

Abstract: The invention relates to a method for synchronizing a plurality of digital input signals which are formed by sampling with the aid of a dedicated operating clock in each case. In order to be able to carry out such a method reliably with a relatively low outlay, according to the invention digital auxiliary signals (xd(nk+j), (yd(nk+j)) are formed by sampling the digital input signals (x(k)) with the aid of a common postprocessing clock, use being made of a postprocessing clock which is at least twice as fast as the fastest operating clock; synchronized digital output signals (x(m), y(m)) which correspond to the digital input signals (x(k)) are formed by means of interpolating each digital auxiliary signal (xd(nk+j), yd(nk+j)).

Abstract: A cascade-type variable-order delta-sigma modulator with low power consumption that can change the number of stages of the quantization loops, which are connected in a cascade configuration, to an optimum number depending on peripheral circuitries in a configuration as simple as possible. The present invention includes first to nth stages of delta-sigma modulating type quantization loops (n is an integer equal to or more than 2) connected in a cascade configuration, and a noise rejecting circuit. Each quantization loop quantizes an input signal, outputs the quantization result, and feeds back the quantization result to itself. The noise rejecting circuit rejects a quantization noise of the first stage of quantization loop, and comprises (n?1) selectors for activating and de-activating the respective output signals of the second and succeeding stages of the quantization loops in compliance with the control signal.

Abstract: Systems and methods implemented in a multi-bit digital noise shaper for reducing or eliminating undesirable transient response when the noise shaper exits a clipping state. In one embodiment, the noise shaper includes a quantizer, a filter, and a filter control unit that detects clipping in the quantizer and dynamically adjusts the allowable range of the internal state values of the filter. In one embodiment, a clipping mechanism is provided for each state value within the filter to clip the state value if it exceeds a corresponding clipping level. The clipping level for each state value is lower when the quantizer is clipping, and higher when the quantizer is not clipping. The clipping level for each state value may be transitioned either immediately or gradually from a current level to a target level (which is lower when the quantizer is clipping, and higher when the quantizer is not clipping.

Abstract: A noise shaper for shaping a power spectral density of an input signal which consists of signal intervals, wherein each signal interval has a corresponding signal amplitude being constant for a variable interval duration time of the signal interval, said noise shaper comprising a calculation unit having at least one serial connected integrator wherein each integrator calculates an integrated signal of different order from said input signal, and a weighting unit for weighting each integrated signal with a corresponding adjustable weighting coefficient according to a noise transfer function.

Abstract: A network device capable of transmitting data includes a processor, an encoder and a port. The encoder encodes the data using a known valid dictionary while constructing a new dictionary over an epoch of data. A network device capable of receiving encoded data is also disclosed. The network device includes a processor, a port and a decoder. The decoder is operable to decode the data using a known valid dictionary, while constructing a new dictionary over the epoch of data. When a valid dictionary has been constructed, the receiving device notifies the transmitting device.

Abstract: An enhancement that reduces the digital interface rate of analog-to-digital (A/D) and digital-to-analog (D/A) converters through the use of compression and decompression is described. Improved A/D converters compressing a sampled version of an A/D converter's analog input signal in real time, thereby significantly decreasing the required bit rate of the A/D converter's digital interface. Similarly, improved D/A converters decrease the required bit rate of the D/A converter's digital interface. D/A converters include a decompressor that decompresses the D/A converter's compressed digital input in real time, prior to conversion to an analog output signal.

Abstract: A sigma-delta converter has a signal input for receiving a data word. A clock signal input is designed to supply a clock signal. The sigma-delta converter includes a first clocked-operation accumulator stage whose input side is connected to the signal input, and at least one second clocked-operation accumulator stage connected in series with the first accumulator stage, with its input side coupled to an accumulator output of the first accumulator stage. The sigma-delta converter is configured to process the data word upon each clock signal only in one accumulator stage in the first and the at least one second accumulator stage, and output the processed data word at the accumulator output of the one accumulator stage. As a result, a time-critical response during signal processing is limited just to the accumulator stage which is currently processing the data word.

Abstract: In a coded data generation method of resampling a road shape for setting a plurality of nodes, arranging position information of each node represented by a deflection angle from the immediately preceding node to generate a data string of the deflection angles, converting the deflection angles into predicted difference values each indicating the difference from the predicted value, and variable-length coding the data string of the predicted difference values, the data string of the predicted difference values when the deflection angles are converted into the predicted difference values is evaluated and a prediction expression to calculate the predicted value is selected adaptively from among a plurality of prediction expressions ?=1, ?=2, ?=3, and ?=4 based on the evaluation result. The prediction expression to calculate the predicted value is selected adaptively in response to road shape A, B, C, D, so that the data compression effectiveness is enhanced.

Abstract: The present invention provides a digital signal processing apparatus which can perform batch processing of mixing and gain controlling, etc., one time while the frequency characteristics of different filters are being mixed to a plurality of input signals in case of the re-quantization only once.

Abstract: A Recursive bit-stream converter (Rebic) having digital low pass filter and multi-bit quantizer means in a feedback arrangement and means to serialize digital words obtain a non-integer Rebic factor via at least two quantizers that are successively operative to serialize their digital words to the output of the converter.

Abstract: A data compression apparatus includes: a difference creating section that determines a difference between adjacent numerical values on continuity of numerical values constituting the data to be compressed so as to create new data to be compressed; an offset section wherein numerical values constituting the new data to be compressed consisting of the continued numerical values, which is created by the difference creating section, is subjected to an offset by a predetermined value; a divisional section that divides every numerical value of the data to be compressed, which is subjected to the offset by the offset section, into an upper significant digit bit portion and a lower significant digit bit portion; an upper significant data compression section that applies reversal compression processing to the upper significant digit data; and a lower significant data compression section that applies reversal compression processing to the lower significant digit data.

Abstract: A sample sequence ?S similar to a first or last sample sequence of the current frame is extracted from its samples SFC and concatenated, as an alternative sample sequence AS, to each of the front and back of the current frame, and the current frame with the alternative sample sequence concatenated thereto is subjected to filtering or prediction coding to obtain processing result SOU of the current frame. In the case of prediction coding, auxiliary information, which indicates which part of the current frame was used as the alternative sample sequence, is also output. By this, filtering, autoregressive prediction coding and decoding, which require processing extending over preceding and succeeding frames as in an interpolation filter, can be concluded in the current frame with substantially no degradation of the continuity and coding efficient of the reconstructed signal.

Abstract: An efficient method for compressing sampled analog signals in real time, without loss, or at a user-specified rate or distortion level, is described. The present invention is particularly effective for compressing and decompressing high-speed, bandlimited analog signals that are not appropriately or effectively compressed by prior art speech, audio, image, and video compression algorithms due to various limitations of such prior art compression solutions. The present invention's preprocessor apparatus measures one or more signal parameters and, under program control, appropriately modifies the preprocessor input signal to create one or more preprocessor output signals that are more effectively compressed by a follow-on compressor. In many instances, the follow-on compressor operates most effectively when its input signal is at baseband. The compressor creates a stream of compressed data tokens and compression control parameters that represent the original sampled input signal using fewer bits.

Abstract: In an encoding apparatus, when difference value between adjacent quantization units of quantization accuracy information where, e.g., distribution range is 0˜7, e.g., if difference value is 3 or more, 8 is subtracted, and if difference value is less than ?4, 8 is added to thereby transform two difference values where difference therebetween is 8 into the same value. Thus, the distribution range of difference value becomes ?4˜3, and size of code book (table) can be held down to the same size in the case where difference is not taken. In addition, high order 1 bit of difference value may be masked to carry out replacement into value consisting of only low order 3 bits, thus also making it possible to prevent increase in size of code book (table).