WO2017109865A1 - Data compression apparatus, data decompression apparatus, data compression program, data decompression program, data compression method, and data decompression method - Google Patents

Abstract

A data compression apparatus (10) predicts, using an external value e[i - m] at a position shifted by a position difference m from an external value e[i] at a target position i in an external data string e, a predicted value p[i] of an input value d[i] at the target position i in an input data string d. The data compression apparatus (10) calculates, as a residual r[i], the difference from the predicted value p[i] that has been predicted. The data compression apparatus (10) then codes the calculated residual r[i], and generates a code c[i] relating to the input value d[i].

Description

Data compression apparatus, data expansion apparatus, data compression program, data expansion program, data compression method, and data expansion method

This invention relates to a technique for reversibly compressing an integer string.

One method for reversibly compressing an integer string is a method for encoding a residual between an input value and a predicted value. In the method of encoding the residual, first, a predicted value is calculated for each input value of the input data string to be encoded. Next, a residual with the predicted value is calculated for each input value. The residual is then encoded.
As a specific method of encoding the residual, the previous value, which is the previous value of the input data string, is used as the predicted value, the previous value is subtracted from the input value, and the residual is calculated by gamma. There is a method of encoding by encoding or delta encoding.

The closer the value to be compressed is to 0, the higher the compression rate.
In the method of encoding the residual, the closer the predicted value and the input value are, the closer the residual is to 0. Therefore, it is highly possible that the compression rate can be increased by improving the accuracy of predicting the predicted value.

A method of using external data is known as a technique for improving the accuracy of predicting predicted values. Patent Document 1 describes a technique for compressing and recording stereoscopic video data composed of two channel data. Patent Document 1 describes that, for one channel data, a residual with the other channel data is encoded. In this example, the other channel data corresponds to external data.

JP-A-6-302103

When one integer row of two integer sequences is shifted, as in the case where two integer sequences are two waveform data having a constant phase difference, a behavior similar to that of the other integer sequence may be exhibited. is there. In this case, in the technique described in Patent Document 1, there is a high possibility that the residual does not become a value close to zero.
An object of the present invention is to improve the accuracy of predicting a predicted value when the position of one integer sequence is shifted and the behavior is similar to that of the other integer sequence.

The data compression apparatus according to the present invention is
The input value d [i] of the target position i in the input data string d is used by using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. ] For predicting the predicted value p [i] of
A residual calculator that calculates a difference between the input value d [i] and the predicted value p [i] predicted by the predictor as a residual r [i];
An encoding unit that encodes the residual r [i] calculated by the residual calculation unit and generates a code c [i] for the input value d [i].

In the present invention, the input of the target position i in the input data string d is performed using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. Predict the predicted value p [i] of the value d [i]. Thereby, when the position of the external data string e is shifted, the accuracy of predicting the predicted value can be improved when the behavior similar to that of the input data string d is exhibited.

1 is a configuration diagram of a data compression system 1 according to Embodiment 1. FIG. FIG. 4 is a diagram illustrating an example of an input data string d and an external data string e according to the first embodiment. 1 is a configuration diagram of a data compression apparatus 10 according to Embodiment 1. FIG. 1 is a configuration diagram of a data decompression device 20 according to Embodiment 1. FIG. 3 is a flowchart showing the operation of the data compression apparatus 10 according to the first embodiment. 5 is a flowchart showing the operation of the data decompression apparatus 20 according to the first embodiment. The block diagram of the data compression apparatus 10 which concerns on the modification 1. FIG. The block diagram of the data expansion | deployment apparatus 20 which concerns on the modification 1. FIG. The block diagram of the data compression apparatus 10 in case the function of each part is implement | achieved by hardware. The block diagram of the data expansion | deployment apparatus 20 in case the function of each part is implement | achieved by hardware. FIG. 4 is a configuration diagram of a data compression apparatus 10 according to a second embodiment. FIG. 4 is a configuration diagram of a data decompression apparatus 20 according to a second embodiment. 9 is a flowchart showing the operation of the data compression apparatus 10 according to the second embodiment. 14 is a flowchart showing the operation of the position difference determination unit 116 in step S303 in FIG. 9 is a flowchart showing the operation of the data decompression apparatus 20 according to the second embodiment. 14 is a flowchart showing the operation of the position difference determination unit 116 according to Modification 4 in step S302 of FIG. FIG. 6 is a configuration diagram of a data compression apparatus 10 according to a third embodiment. FIG. 6 is a configuration diagram of a data decompression device 20 according to a third embodiment. 10 is a flowchart showing the operation of the data compression apparatus 10 according to the third embodiment. 10 is a flowchart showing the operation of the data decompression apparatus 20 according to the third embodiment.

Embodiment 1 FIG.
*** Explanation of configuration ***
With reference to FIG. 1, the structure of the data compression system 1 which concerns on Embodiment 1 is demonstrated.
The data compression system 1 includes a data compression device 10 and a data decompression device 20. The data compression device 10 and the data decompression device 20 are connected via a network 30.
The data compression apparatus 10 is an apparatus that receives an input data string d and an external data string e as input and generates a code data string c obtained by encoding the input data string d. The data decompression device 20 is a device that generates the output data sequence o obtained by decoding the code data sequence c, using the code data sequence c generated by the data compression device 10 and the external data sequence e as inputs.

The input data string d is an ordered integer string, and an integer value included in the input data string d is referred to as an input value. The external data string e is an ordered integer string different from the input data string d, and an integer value included in the external data string e is referred to as an external value. The i-th input value in the input data string d is written as an input value d [i], and the i-th external value in the external data string e is written as an external value e [i].
In the data compression system according to the first embodiment, the input value d [i] at the target position i in the input data string d is the external value e [at a position shifted by m from the target position i in the external data string e. When the value is close to (im), the compression rate can be increased. Specifically, as shown in FIG. 2, a sequence of values sampled at a certain time from one of two waveform data having a certain phase difference is an input data string d, and sampled at a certain time from the other. A case is assumed where the column of the obtained values is the external data column e. In FIG. 2, the values sampled from one of the two waveform data at regular time intervals are the input values d [0],. . . , D [X], and values sampled from the other at fixed time intervals are external values e [0],. . . , E [X]. In FIG. 2, the phase difference is the position difference m. In FIG. 2, the positional difference m is a positive value, but the positional difference m may be a negative value.
The number of input values included in the input data string d and the number of external values included in the external data string e are arbitrary. In the first embodiment, description will be made assuming that the number of external values included in the external data string e is equal to or greater than the number of input values included in the input data string d. If the number of external values is less than the number of input values, an arbitrary integer value such as 0 may be added to the external data string e by the number of differences between the number of input values and the number of external values.

With reference to FIG. 3, the configuration of the data compression apparatus 10 according to the first embodiment will be described.
The data compression apparatus 10 is a computer.
The data compression device 10 includes a processor 11, a storage device 12, and a communication device 13. The processor 11 is connected to other hardware via the signal line 14 and controls these other hardware.

The data compression apparatus 10 includes an input unit 111, a prediction unit 112, a residual calculation unit 113, an encoding unit 114, and an output unit 115 as functional configurations. The functions of the input unit 111, the prediction unit 112, the residual calculation unit 113, the encoding unit 114, and the output unit 115 are realized by software.
The storage device 12 stores a program that realizes the functions of the respective units of the data compression device 10. This program is read into the processor 11 and executed by the processor 11. Thereby, the function of each part of the data compression apparatus 10 is implement | achieved.

With reference to FIG. 4, the configuration of the data decompression apparatus 20 according to the first embodiment will be described.
The data decompression device 20 is a computer.
The data decompression device 20 includes a processor 21, a storage device 22, and a communication device 23. The processor 21 is connected to other hardware via the signal line 24 and controls these other hardware.

The data decompression device 20 includes an input unit 211, a prediction unit 212, a decoding unit 213, an output value calculation unit 214, and an output unit 215 as functional configurations. The functions of the input unit 211, the prediction unit 212, the decoding unit 213, the output value calculation unit 214, and the output unit 215 are realized by software.
The storage device 22 stores a program that realizes the functions of the respective units of the data decompression device 20. This program is read into the processor 21 and executed by the processor 21. Thereby, the function of each part of data decompression device 20 is realized.

The processors 11 and 21 are ICs that perform processing. IC is an abbreviation for Integrated Circuit. Specifically, the processors 11 and 21 are a CPU, a DSP, and a GPU. CPU is an abbreviation for Central Processing Unit. DSP is an abbreviation for Digital Signal Processor. GPU is an abbreviation for Graphics Processing Unit.
Specifically, the storage devices 12 and 22 are a RAM and an HDD. RAM is an abbreviation for Random Access Memory. HDD is an abbreviation for Hard Disk Drive. The storage device may be configured by other hardware such as a ROM and a flash memory. ROM is an abbreviation for Read Only Memory.
The communication devices 13 and 23 are devices including a receiver that receives data and a transmitter that transmits data. The communication devices 13 and 23 are specifically communication chips or NICs. NIC is an abbreviation for Network Interface Card.

Information, data, signal values, and variable values indicating the processing results of the functions of the respective units realized by the processor 11 are stored in the storage device 12 or in a register or cache memory in the processor 11. In the following description, it is assumed that information, data, signal values, and variable values indicating the processing results of the functions of the respective units realized by the processor 11 are stored in the storage device 12.
Similarly, information, data, signal values, and variable values indicating the processing results of the functions of the respective units realized by the processor 21 are stored in the storage device 22, a register in the processor 21, or a cache memory. In the following description, it is assumed that information, data, signal values, and variable values indicating the processing results of the functions of the respective units realized by the processor 21 are stored in the storage device 22.

It is assumed that programs for realizing the functions of the respective units realized by the processors 11 and 21 are stored in the storage devices 12 and 22. However, this program may be stored in a portable storage medium such as a magnetic disk, a flexible disk, an optical disk, a compact disk, a Blu-ray (registered trademark) disk, or a DVD.

In FIG. 3, only one processor 11 is shown. However, there may be a plurality of processors 11, and the plurality of processors 11 may execute programs that realize the functions of the respective units in cooperation. Similarly, in FIG. 4, only one processor 21 is shown. However, there may be a plurality of processors 21, and the plurality of processors 21 may execute programs that realize the functions of the respective units in cooperation.

*** Explanation of operation ***
The operation of the data compression apparatus 10 according to the first embodiment will be described with reference to FIGS. 3 and 5.
The operation of the data compression apparatus 10 according to the first embodiment corresponds to the data compression method according to the first embodiment. The operation of the data compression apparatus 10 according to the first embodiment corresponds to the processing of the data compression program according to the first embodiment.

As a premise of the processing illustrated in FIG. 5, the input unit 111 receives the input data string d and the external data string e via the communication device 13, and writes the input data string d, the external data string e, and the storage device 12. It shall be.

5 is set to the variable i, and the process shown in FIG. 5 is started.

In the completion determination process in step S101, the input unit 111 determines whether or not encoding for all input values of the input data string d has been completed. Specifically, the input unit 111 counts the number of input values of the input data string d, and when the variable i is the number of input values, the encoding for all the input values is completed. judge.
If the input unit 111 determines that the encoding is complete (YES in step S101), the input unit 111 ends the process. If the input unit 111 determines that the encoding has not been completed (NO in step S101), the process proceeds to step S102.

In the prediction process of step S102, the prediction unit 112 uses the external value e [i−m] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data sequence e. The predicted value p [i] of the input value d [i] of the target position i at d is predicted.
Specifically, the prediction unit 112 reads the position difference m from the storage device 12, and reads the external value e [im] at the position shifted by the position difference m from the target position i from the storage device 12. In the first embodiment, it is assumed that the position difference m is stored in the storage device 12 in advance. Then, the prediction unit 112 calculates the predicted value p [i] according to the equation p [i] = e [im]. The prediction unit 112 writes the calculated predicted value p [i] in the storage device 12.
If there is no external value to be used for prediction, such as when the number of external values is less than the number of input values, the external value may be regarded as an arbitrary integer value such as 0.

Here, under the assumption that the input value d [i] is close to the external value e [im], the predicted value p [i] is calculated according to the equation p [i] = e [im]. It was done. However, the formula used for calculating the predicted value p [i] is determined based on the relationship between the input value d [i] and the external value e [im]. Specifically, when the input value d [i] is a value close to twice the external value e [im], the predicted value according to the equation p [i] = e [im] × 2. p [i] is calculated. When the input value d [i] is close to the value obtained by adding 3 to the external value e [im], the predicted value p [i] is calculated according to the equation p [i] = e [im] +3. i] is calculated.

In the residual calculation process in step S103, the residual calculation unit 113 calculates the difference between the input value d [i] and the predicted value p [i] predicted by the prediction unit 112 in step S102 as the residual r [i]. Calculate as
Specifically, the residual calculation unit 113 reads the input value d [i] written in advance and the predicted value p [i] written in step S102 from the storage device 12. Then, the residual calculation unit 113 calculates the residual r [i] by subtracting the predicted value p [i] from the input value d [i]. The residual calculation unit 113 writes the calculated residual r [i] in the storage device 12.

In the encoding process in step S104, the encoding unit 114 encodes the residual r [i] calculated by the residual calculation unit 113 in step S103, and the code c [i] for the input value d [i]. Is generated.
Specifically, the encoding unit 114 reads the residual r [i] written in step S103 from the storage device 12. The encoding unit 114 converts the residual r [i] by an integer encoding method such as a gamma code, a delta code, or a Golomb-Rice code, and generates a code c [i] for the input value d [i]. The encoding unit 114 writes the generated code c [i] in the storage device 12.

In the output process of step S105, the output unit 115 outputs the code c [i] generated by the encoding unit 114 in step S104 as the value of the target position i of the code data string c.

In the increment process of step S106, the input unit 111 adds 1 to the value of the variable i, and returns the process to step S101.

With reference to FIGS. 4 and 6, the operation of the data decompression apparatus 20 according to the first embodiment will be described.
The operation of the data decompression apparatus 20 according to the first embodiment corresponds to the data decompression method according to the first embodiment. The operation of the data decompression apparatus 20 according to the first embodiment corresponds to the processing of the data decompression program according to the first embodiment.

As a premise of the processing illustrated in FIG. 6, the input unit 211 receives the code data sequence c and the external data sequence e via the communication device 23, and writes the code data sequence c, the external data sequence e, and the storage device 22. It shall be.

The variable i is set to 0, and the process shown in FIG. 6 is started.

In the completion determination process of step S201, the input unit 211 determines whether or not decoding has been completed for all codes of the code data string c. Specifically, the input unit 211 counts the number of codes in the code data string c, and determines that the decoding for all codes is completed when the variable i is the number of codes.
If the input unit 211 determines that the decoding is complete (YES in step S201), the process ends. If the input unit 211 determines that the decoding has not been completed (NO in step S201), the process proceeds to step S202.

In the prediction process in step S202, the prediction unit 212 uses the external value e [i−m] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. The predicted value p [i] of the output value o [i] of the target position i at o is predicted.
Specifically, the prediction unit 212 reads the position difference m from the storage device 22, and reads the external value e [im] at a position shifted by the position difference m from the target position i from the storage device 22. In the first embodiment, it is assumed that the position difference m is stored in the storage device 22 in advance. Then, the prediction unit 212 calculates the predicted value p [i] according to the same formula as that used in step S102 of FIG. The prediction unit 212 writes the calculated predicted value p [i] in the storage device 22.

In the decoding process of step S203, the decoding unit 213 generates the residual r [i] by decoding the code c [i].
Specifically, the decoding unit 213 reads the code c [i] from the storage device 22. Then, the decoding unit 213 converts the code c [i] by a decoding method corresponding to the integer coding method used by the coding unit 114 in step S104 of FIG. 5 and calculates a residual r [i]. The decoding unit 213 writes the calculated residual r [i] in the storage device 22.

In the output value calculation process of step S204, the output value calculation unit 214 uses the prediction value p [i] predicted by the prediction unit 212 in step S202 and the residual r [i] generated by the decoding unit 213 in step S203. Is calculated as an output value o [i].
Specifically, the output value calculation unit 214 stores the prediction value p [i] predicted by the prediction unit 212 in step S202 and the residual r [i] generated by the decoding unit 213 in step S203. 22 is read out. Then, the output value calculation unit 214 calculates the output value o [i] by adding the predicted value p [i] to the residual r [i]. The output value calculation unit 214 writes the calculated output value o [i] in the storage device 22.

In the output process of step S205, the output unit 215 outputs the output value o [i] calculated by the output value calculation unit 214 in step S204 as the value of the target position i of the output data string o.

In the increment process of step S206, the input unit 211 adds 1 to the value of the variable i, and returns the process to step S201.

*** Effects of Embodiment 1 ***
As described above, in the data compression system 1 according to the first embodiment, the external value e [i−m] at a position shifted by the positional difference m from the target position i in the external data string e is used to input the input data string d. A predicted value p [i] of the input value d [i] is predicted. Thereby, if the position of one external data string e is shifted, the accuracy of predicting the predicted value can be improved when the behavior similar to that of the input data string d is exhibited.

*** Other configurations ***
<Modification 1>
In Embodiment 1, the predicted value p [i] is predicted using the external value e [im]. However, as a first modification, not only the external value e [i−m] but also other external values and at least one of input values whose codes have already been generated in the input data string d are used to predict the predicted value p. [I] may be predicted. The first modification will be described with respect to differences from the first embodiment.

With reference to FIG. 7, the structure of the data compression apparatus 10 which concerns on the modification 1 is demonstrated.
7 is different from FIG. 3 in that the prediction unit 112 receives the input value d [j] of the input data string d and the external data string e. The variable j is an integer value from 0 to i-1.

In the first modification, in step S102 of FIG. 5, the prediction unit 112 determines not only the external value e [im] but also other external values and the input value d [0] whose code has already been generated in the input data string d. ],. . . , The predicted value p [i] is predicted using at least one of the input value d [i−1]. In this case, the necessary external value and input value are read from the storage device 12, and the predicted value p [i] is calculated according to an equation using the read external value and input value.
As a specific example, the prediction unit 112 uses the external value e [im−1], the external value e [im], and the input value d [i−1], and p [i] = d It is conceivable to calculate the predicted value p [i] according to the equation [i-1] + (e [im] -e [im-1]).

With reference to FIG. 8, the structure of the data decompression | decompression apparatus 20 which concerns on the modification 1 is demonstrated.
8 is different from FIG. 4 in that the prediction unit 212 receives the output value o [j] of the output data string o and the external data string e. The variable j is an integer value from 0 to i-1.

In the first modification, in step S202 in FIG. 6, the prediction unit 212 determines not only the external value e [im] but also other external values and an output value o [0] whose code has already been generated in the output data sequence o. ],. . . , The predicted value p [i] is predicted using at least one of the output value o [i-1].
Specifically, the prediction unit 212 calculates the prediction value p [i] by the same method as the method by which the prediction unit 112 calculates the prediction value p [i] in step S102 of the first modification. However, when the prediction unit 112 uses the input value d [j] in S102, the output value o [j] corresponding to the input value d [j] is used instead of the input value d [j].

In the first modification, the prediction unit 112 of the data compression device 10 cannot use the input value for which the code has not yet been generated for the input data string d to predict the predicted value p [i]. This is necessary so that the data decompression device 20 can correctly decode the code data string c.
That is, the prediction unit 212 of the data decompression device 20 needs to predict the prediction value p [i] by the same method as the prediction unit 112 of the data compression device 10. However, when the prediction unit 212 of the data decompression apparatus 20 predicts the predicted value p [i], the output value o [0],. . . , Only the output value o [i−1] is obtained. Therefore, when the prediction unit 112 of the data compression apparatus 10 predicts the predicted value p [i], if the input value for which a code has not yet been generated is used, the data decompression apparatus 20 correctly sets the code data string c. It becomes impossible to decrypt.

<Modification 2>
In the first embodiment, the functions of the respective units of the data compression device 10 and the data decompression device 20 are realized by software. However, as a second modification, the functions of the respective units of the data compression device 10 and the data decompression device 20 may be realized by hardware. The second modification will be described with respect to differences from the first embodiment.

With reference to FIG. 9, the structure of the data compression apparatus 10 which concerns on the modification 2 is demonstrated.
When the function of each unit is realized by hardware, the data compression device 10 includes a communication device 13 and a processing circuit 15. The processing circuit 15 is a dedicated electronic circuit that realizes the functions of the respective units of the data compression device 10 and the functions of the storage device 12.

With reference to FIG. 10, the structure of the data decompression | decompression apparatus 20 which concerns on the modification 2 is demonstrated.
When the function of each unit is realized by hardware, the data decompression device 20 includes a communication device 23 and a processing circuit 25. The processing circuit 25 is a dedicated electronic circuit that implements the functions of each unit of the data decompression device 20 and the function of the storage device 22.

As the processing circuits 15 and 25, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, a logic IC, a GA, an ASIC, and an FPGA are assumed. GA is an abbreviation for Gate Array. ASIC is an abbreviation for Application Specific Integrated Circuit. FPGA is an abbreviation for Field-Programmable Gate Array.
The function of each part may be realized by one processing circuit 15 or 25, or the function of each part may be distributed to a plurality of processing circuits 15 and 25.

<Modification 3>
As a third modification, some functions may be realized by hardware, and other functions may be realized by software. That is, some of the functions of the data compression apparatus 10 may be realized by hardware, and other functions may be realized by software. Also for the data decompression device 20, some functions may be realized by hardware, and other functions may be realized by software.

The processors 11 and 21, the storage devices 12 and 22, and the processing circuits 15 and 25 are collectively referred to as “processing circuitry”. That is, the function of each part is realized by a processing circuit.

Embodiment 2. FIG.
The second embodiment is different from the first embodiment in that the position difference m is appropriately determined and the predicted value p [i] is predicted. In the second embodiment, this different point will be described.

*** Explanation of configuration ***
With reference to FIG. 11, the structure of the data compression apparatus 10 which concerns on Embodiment 2 is demonstrated.
The data compression apparatus 10 includes a position difference determination unit 116 in addition to the functional configuration shown in FIG. The function of the position difference determination unit 116 is realized by software.
The storage device 12 stores a program that realizes the function of the position difference determination unit 116. This program is read into the processor 11 and executed by the processor 11. Thereby, the function of the position difference determination unit 116 is realized.

With reference to FIG. 12, the configuration of the data decompression apparatus 20 according to the second embodiment will be described.
The data decompression device 20 includes a position difference determination unit 216 in addition to the functional configuration shown in FIG. The function of the position difference determination unit 216 is realized by software.
The storage device 22 stores a program that realizes the function of the position difference determination unit 216. This program is read into the processor 21 and executed by the processor 21. Thereby, the function of the position difference determination unit 216 is realized.

*** Explanation of operation ***
The operation of the data compression apparatus 10 according to the second embodiment will be described with reference to FIGS. 11 and 13.
The operation of the data compression apparatus 10 according to the second embodiment corresponds to the data compression method according to the second embodiment. The operation of the data compression apparatus 10 according to the second embodiment corresponds to the processing of the data compression program according to the second embodiment.

The processing in step S301 is the same as the processing in step S101 in FIG. The processing from step S304 to step S308 is the same as the processing from step S102 to step S106 in FIG.

In the determination determination process in step S302, the position difference determination unit 116 determines whether or not to newly determine the position difference m. The reason why the position difference is updated is that the position difference m may also change due to changes in the characteristics of the input data string d and the external data string e.
If the position difference determination unit 116 determines to determine the position difference m (YES in step S302), the process proceeds to step S303. On the other hand, if the position difference determination unit 116 determines not to determine the position difference m (NO in step S302), the process proceeds to step S304.

Specifically, the position difference determination unit 116 determines to determine the position difference m every time the reference input value is encoded.
The reference piece is an integer of 1 or more. The smaller the reference piece, the higher the frequency of updating the position difference m and the higher the processing load. However, it is expected that the smaller the reference piece is, the higher the ratio at which the position difference m is appropriately set, and the higher the prediction accuracy. Therefore, the reference piece is determined in advance in consideration of both the processing load and the prediction accuracy.
If the input data string d is data having periodicity, the position difference m may be determined again for each period of the input data string d. Therefore, in this case, the position difference determination unit 116 receives the input values d [0],. . . , The input value d [i−1] is read from the storage device 12. Then, the position difference determination unit 116 receives the input values d [0],. . . , The period is specified from the input value d [i−1], and the number of input values included in the specified one period is set as a reference value. In this case, the position difference determination unit 116 also specifies the period when determining the position difference m. As a result, even for an input data string d whose cycle varies, the positional difference m can be determined at an appropriate timing following the variation of the cycle.

In the position difference determination process in step S303, the position difference determination unit 116 shifts the position of the external value of the external data string e corresponding to the input value of the input data string d, thereby changing the input data string d and the external data string e. Is determined as the positional difference m.
In FIG. 2, the input value d [n] and the external value e [n] at the same position originally sampled at the same time correspond to each other. In this state, the input data string d and the external data string e are not correlated. However, if the position of the external value of the external data string e corresponding to the input value of the input data string d is shifted by the phase difference, the input data string d and the external data string e are correlated.
Specifically, the position difference determination unit 116 specifies the shift amount at which the peak, that is, the position of the extreme value approaches the input value for which the code has already been generated in the input data sequence d and the external data sequence e, The specified shift amount is determined as the position difference m. The position difference determination unit 116 overwrites the position difference m stored in the storage device 12 with the determined position difference m.

Processing for determining the position difference m will be described with reference to FIG.
In the data reading process in step S3031, the position difference determination unit 116 receives the input values d [0],. . . , The input value d [i−1] is read from the storage device 12. In addition, the position difference determination unit 116 outputs the external values e [0],. . . , The external value e [i−1] is read from the storage device 12.
In order to reduce the processing load for determining the position difference m, only the most recent input values and external values may be used. If only the most recent k input values and external values are used, the position difference determination unit 116 receives the input values d [i−k],. . . , Input value d [i−1] and external value e [ik],. . . , The external value e [i−1] is read from the storage device 12.
In the following, a case where only the latest k input values and external values are used will be described.

In the peak specifying process in step S3032, the position difference determination unit 116 receives the input values d [i−k],. . . , The position of the extreme value is specified from the input value d [i−1], and the data string of the specified extreme value is set to the extreme value a [0],. . . , Extreme value a [p−1]. Here, p is the number of specified extreme values. In addition, the position difference determining unit 116 outputs the external values e [ik],. . . , The position of the extreme value from the external value e [i-1], and the data string of the specified extreme value is converted to the extreme value b [0],. . . , Extreme value b [q-1]. Here, q is the number of specified extreme values.
When all the extreme values are selected when handling a data string in which fine fluctuations due to noise are mixed, there is a possibility that many unnecessary extreme values are included due to the influence of noise. Therefore, in order to reduce the influence of noise, only the maximum value within a certain fixed width may be extracted as an extreme value. The input values d [i−k],. . . , The extreme value whose difference from the maximum value of the input value d [i−1] is less than a certain value is extracted as the extreme value of the input value, and the external values e [i−k],. . . , Only extreme values whose difference from the maximum value of the external value e [i−1] is less than a certain value may be extracted as extreme values of the external value. This method is particularly effective when it is desired to focus only on the frequency component having the maximum amplitude of the data string.

In the position difference specifying process in step S3033, the position difference determining unit 116 sets j = 0,. . . , P−1 in ascending order, the extremum b [j] closest to the position before the extremum a [j] is selected, and the extremum a [i] and the extremum b [j] Calculate the difference in position. Then, the position difference determination unit 116 determines the position difference m based on the difference between the p positions. In the second embodiment, the position difference determining unit 116 determines the position difference having the largest position among the p position differences as the position difference m. The position difference determination unit 116 determines the intermediate value of the p position differences as the position difference m, or determines the integer closest to the average value of the p position differences as the position difference m. The position difference m may be determined by this method.

With reference to FIG. 12 and FIG. 15, the operation of the data decompression apparatus 20 according to the second embodiment will be described.
The operation of the data decompression apparatus 20 according to the second embodiment corresponds to the data decompression method according to the second embodiment. The operation of the data decompression device 20 according to the second embodiment corresponds to the processing of the data decompression program according to the second embodiment.

The process in step S401 is the same as the process in step S201 in FIG. The processing from step S404 to step S408 is the same as the processing from step S202 to step S206 in FIG.

In the determination determination process of step S402, the position difference determination unit 216 determines whether or not to newly determine the position difference m by the same determination method used by the position difference determination unit 116 in step S302 of FIG. To do.
If the position difference determination unit 216 determines to determine the position difference m (YES in step S402), the process proceeds to step S403. On the other hand, if the position difference determination unit 216 determines that the position difference m is not determined again (NO in step S402), the process proceeds to step S404.

Specifically, when the position difference determination unit 116 determines that the position difference m is determined every time the reference number of input values is encoded, the position difference determination unit 216 calculates the reference number of output values. Each time the position difference m is determined.
When the position difference determination unit 116 re-determines the position difference m for each cycle of the input data string d, the position difference determination unit 216 re-determines the position difference m for each cycle of the output data string o. . In this case, the position difference determination unit 216 outputs the output values o [0],. . . , The output value o [i−1] is read from the storage device 22. Then, the position difference determination unit 216 outputs the output values o [0],. . . , The cycle is specified from the output value o [i−1], and the number of output values included in the specified cycle is set as a reference value. In this case, the position difference determination unit 216 also specifies the cycle when determining the position difference m.

In the position difference determination process in step S403, the position difference determination unit 216 determines the position difference m by the same determination method used by the position difference determination unit 116 in step S303 in FIG.
That is, the position difference determining unit 216 shifts the position of the external value of the external data string e corresponding to the output value of the output data string o, thereby determining the shift amount where the output data string o and the external data string e are correlated. Determined as difference m. Specifically, the position difference determination unit 216 specifies and specifies the shift amount at which the peak, that is, the position of the extreme value is close, for the output data string o including the already calculated output values and the external data string e. The shifted amount is determined as the position difference m. The position difference determination unit 216 overwrites the position difference m stored in the storage device 22 with the determined position difference m. The process for determining the position difference m is the same as the process of the position difference determination unit 116 described with reference to FIG. However, when the input value d [v] for the integer v with the position difference determination unit 116 is used, the position difference determination unit 216 uses the output value o [v] instead of the input value d [v].

*** Effects of Embodiment 2 ***
As described above, in the data compression system 1 according to the second embodiment, the position difference m is appropriately determined, and the predicted value p [i] is predicted. Thereby, even when the characteristics of the input data string d vary, the accuracy of predicting the predicted value can be improved.

*** Other configurations ***
<Modification 4>
In the second embodiment, in step S302, the position difference determination unit 116 determines that the position difference m is newly determined every time the reference input value is encoded. However, as a fourth modification, the position difference determination unit 116 may determine that the position difference m is newly determined when the accuracy of predicting the predicted value p [i] continuously falls below the reference accuracy. The fourth modification will be described with respect to differences from the second embodiment.

The data compression apparatus 10 will be described.
The position difference determination unit 116 uses the accuracy when the input value d [i−1] is predicted without using the external data string e as the reference accuracy. Specifically, the position difference determining unit 116, the predicted value of the input value d which is predicted without using external data sequence ^{e [i-1] p *} [i-1] as an input value d [i-1] The absolute value of the residual r ^* [i−1] is used as the reference accuracy.
When the reference accuracy is smaller than the absolute value of the residual r [i-1] between the input value d [i-1] and the predicted value p [i-1], the accuracy of the predicted value p [i-1] is It will be below the standard accuracy. Therefore, the position difference determination unit 116 determines that the reference accuracy is smaller than the absolute value of the residual r [i−1] between the input value d [i−1] and the predicted value p [i−1]. When it is continuous, it is determined that the position difference m is newly determined.

With reference to FIG. 16, the operation of the position difference determination unit 116 according to the modified example 4 in step S302 of FIG. 13 will be described.
In the number determination process in step S3021, the position difference determination unit 116 determines whether or not the variable L is equal to or greater than the reference number. If the variable L is greater than or equal to the reference time (YES in step S3021), the position difference determination unit 116 advances the process to step S3022. On the other hand, if the variable L is not greater than or equal to the reference number (NO in step S3021), the position difference determination unit 116 advances the process to step S3023.

In the update determination process in step S3022, the position difference determination unit 116 determines to newly determine the position difference m. At this time, the position difference determination unit 116 sets 0 to the variable L.

In the non-update determination process in step S3023, the position difference determination unit 116 determines that the position difference m is not newly determined.

In the prediction process of step S3024, the position difference determination unit 116 causes the prediction unit 112 to predict the predicted value p [i-1] of the input value d [i-1] using the external data string e. Further, the position difference determination unit 116 causes the prediction unit 112 to predict the predicted value p ^* [i−1] of the input value d [i−1] without using the external data string e.
Here, the prediction unit 112 predicts the predicted value p [i−1] as in step S102 of FIG. In addition, the prediction unit 112 inputs the input values d [0],. . . , The predicted value p ^* [i-1] of the input value d [i-1] is predicted using the input value d [i-2]. As a specific example, the prediction unit 112 sets the input value d [i-2] as the predicted value p ^* [i-1].

In the residual calculation process of step S3025, the position difference determination unit 116 causes the residual calculation unit 113 to send a residual r [i-1] between the predicted value p [i-1] and the input value d [i-1]. Let's calculate. Further, the position difference determination unit 116 causes the residual calculation unit 113 to calculate the residual r ^* [i−1] between the predicted value p ^* [i−1] and the input value d [i−1].
Here, the residual calculation unit 113 calculates the residual r [i−1] by subtracting the predicted value p [i−1] from the input value d [i−1] as in step S103 of FIG. To do. The residual calculation unit 113 subtracts the predicted value p ^* [i-1] from the input value d [i-1] to calculate a residual r ^* [i-1].

In the absolute value determination processing in step S3026, the position difference determination unit 116 determines whether or not the absolute value of the residual r ^* [i−1] is smaller than the absolute value of the residual r [i−1]. If the absolute value of the residual r ^* [i−1] is smaller than the absolute value of the residual r [i−1], the position difference determination unit 116 proceeds with the process to step S3027. On the other hand, if the absolute value of the residual r ^* [i−1] is greater than or equal to the absolute value of the residual r [i−1], the position difference determination unit 116 advances the process to step S3028.

In the variable addition process of step S3027, the position difference determination unit 116 adds 1 to the variable L. On the other hand, in the variable initialization process of step S3028, the position difference determination unit 116 sets 0 to the variable L.

The data decompression device 20 will be described.
In step S402 in FIG. 15, the position difference determination unit 216 determines whether or not to determine the position difference m by the same determination method used by the position difference determination unit 116 in step S302 in FIG. 13. Therefore, if the position difference determination unit 116 determines whether to determine the position difference m by the determination method described based on FIG. 16, the position difference determination unit 216 also determines the position difference by the determination method described based on FIG. It is determined whether or not m is determined.
That is, the position difference determination unit 216 uses the accuracy when the output value o [i−1] is predicted without using the external data string e as the reference accuracy. Specifically, the position difference determination unit 216 predicts the predicted value p ^* [i−1] and the output value o [i−1] of the output value o [i−1] predicted without using the external data string e. The absolute value of the residual r ^* [i−1] is used as the reference accuracy.
When the reference accuracy is smaller than the absolute value of the residual r [i-1] between the output value o [i-1] and the predicted value p [i-1], the accuracy of the predicted value p [i-1] is It will be below the standard accuracy. Therefore, the position difference determination unit 216 determines that the reference accuracy is smaller than the absolute value of the residual r [i−1] between the output value o [i−1] and the predicted value p [i−1]. When it is continuous, it is determined that the position difference m is newly determined.
The operation of the position difference determination unit 216 according to the modification 4 in step S402 in FIG. 15 is the same as the operation of the position difference determination unit 116 described based on FIG. However, when the input value d [v] for the integer v with the position difference determination unit 116 is used, the position difference determination unit 216 uses the output value o [v] instead of the input value d [v].

In the fourth modification, the position difference determination unit 116 of the data compression apparatus 10 cannot use the input value for which the code has not yet been generated for the input data string d to determine the position difference m. This is for the same reason that the prediction unit 112 has not been able to use an input value for which a code has not yet been generated in the description of the first modification.

<Modification 5>
In the second embodiment, as in the first embodiment, the functions of the respective units of the data compression device 10 and the data decompression device 20 are realized by software. However, as in the second modification of the first embodiment, the functions of the respective units of the data compression device 10 and the data decompression device 20 may be realized by hardware. Further, as in the third modification of the first embodiment, the data compression device 10 and the data decompression device 20 may have some functions realized by hardware and other functions realized by software.

Embodiment 3 FIG.
The third embodiment is different from the second embodiment in that when the positional difference m is determined, the determined positional difference m is verified and appropriately determined again. In the third embodiment, this different point will be described.

*** Explanation of configuration ***
With reference to FIG. 17, the structure of the data compression apparatus 10 which concerns on Embodiment 3 is demonstrated.
The data compression apparatus 10 includes a verification unit 117 in addition to the functional configuration shown in FIG. The function of the verification unit 117 is realized by software.
The storage device 12 stores a program that realizes the function of the verification unit 117. This program is read into the processor 11 and executed by the processor 11. Thereby, the function of the verification unit 117 is realized.

With reference to FIG. 18, the structure of the data decompression | decompression apparatus 20 which concerns on Embodiment 3 is demonstrated.
The data decompression device 20 includes a verification unit 217 in addition to the functional configuration shown in FIG. The function of the verification unit 217 is realized by software.
The storage device 22 stores a program that realizes the function of the verification unit 217. This program is read into the processor 21 and executed by the processor 21. Thereby, the function of the verification unit 217 is realized.

*** Explanation of operation ***
The operation of the data compression apparatus 10 according to the third embodiment will be described with reference to FIGS. 17 and 19.
The operation of the data compression apparatus 10 according to the third embodiment corresponds to the data compression method according to the third embodiment. The operation of the data compression apparatus 10 according to the third embodiment corresponds to the processing of the data compression program according to the third embodiment.

The processing from step S501 to step S503 is the same as the processing from step S301 to step S303 in FIG. The processing from step S506 to step S510 is the same as the processing from step S304 to step S308 in FIG.

In the validity verification process in step S504, the verification unit 117 determines whether or not the position difference m determined by the position difference determination unit 116 in step S503 is valid.
If the verification unit 117 determines that the positional difference m is not valid (NO in step S504), the verification unit 117 advances the process to step S505. On the other hand, when the verification unit 117 determines that the position difference m is appropriate (YES in step S504), the verification unit 117 advances the process to step S506.

In Embodiment 3, the verification unit 117 predicts a certain input value d [j] for which a code has already been generated in the input data string d, using the position difference m determined by the position difference determination unit 116. When the absolute value of the residual r [j] between the value p [j] and the input value d [j] is greater than or equal to the reference value, it is determined that the position difference m is not valid. On the other hand, the verification unit 117 determines that the position difference m is appropriate when the residual r [j] is less than the reference value.
Specifically, the verification unit 117 reads the position difference m from the storage device 12. Then, the verification unit 117 causes the prediction unit 112 to predict the predicted value p [j] of the input value d [j] using the position difference m. Here, the variable j is an integer of 0 or more and less than the variable i. Next, the verification unit 117 causes the residual calculation unit 113 to calculate the residual r [j] between the predicted value p [j] and the input value d [j]. Then, the verification unit 117 determines whether or not the absolute value of the residual r [j] is less than the reference value.
The verification unit 117 may determine whether the positional difference m is valid or not, but the input value that can be used for the determination is the input value d for which a code has already been generated. [0],. . . , The input value d [i−1].

In the re-determination determination process in step S505, the verification unit 117 determines whether or not to cause the position difference determination unit 116 to re-determine the position difference m. Specifically, the verification unit 117 determines that the position difference m is not re-determined when it is determined that the position difference m is not valid continuously for a predetermined number of times in step S504, and otherwise, the position difference m is determined. It is determined that the difference m is determined again.

When it is determined that the position difference m is determined again (YES in step S505), the verification unit 117 returns the process to step S503. At this time, the verification unit 117 excludes the position difference m determined to be invalid once, so that the position difference determination unit 116 does not select it again. When the process returns to step S503, in step S503, the position difference determination unit 116 determines the largest position difference among the position differences that are not selected as the position difference m.

On the other hand, when it is determined that the position difference m is not determined again (NO in step S505), the verification unit 117 advances the process to step S506. At this time, the verification unit 117 sets the positional difference m to unusable. In this case, in step S506, the prediction unit 112 predicts the predicted value p [i] of the input value d [i] without using the position difference m. Specifically, the input values d [0],. . . , The predicted value p [i] of the input value d [i] is predicted using the input value d [i-1].

With reference to FIGS. 18 and 20, the operation of the data decompression apparatus 20 according to the third embodiment will be described.
The operation of the data decompression apparatus 20 according to the third embodiment corresponds to the data decompression method according to the third embodiment. The operation of the data decompression device 20 according to the third embodiment corresponds to the processing of the data decompression program according to the third embodiment.

The processing from step S601 to step S603 is the same as the processing from step S401 to step S403 in FIG. Also, the processing from step S606 to step S610 is the same as the processing from step S404 to step S408 in FIG.

In the validity verification process in step S604, the verification unit 217 uses the same determination method as the determination method used by the verification unit 117 in step S504 of FIG. 19 to determine the positional difference m determined by the positional difference determination unit 216 in step S603. It is determined whether it is appropriate.
In other words, in the third embodiment, the verification unit 217 predicts the predicted value p [j] predicted using the position difference m determined by the position difference determination unit 216 for a certain output value o [j] that has already been calculated. When the absolute value of the residual r [j] with respect to the output value o [j] is greater than or equal to the reference value, it is determined that the position difference m is not valid. On the other hand, the verification unit 217 determines that the positional difference m is appropriate when the residual r [j] is less than the reference value.
Specifically, the verification unit 217 reads the position difference m from the storage device 22. Then, the verification unit 217 causes the prediction unit 212 to predict the predicted value p [j] of the output value o [j] using the position difference m. Here, the variable j is an integer of 0 or more and less than the variable i. Next, the verification unit 217 causes the residual calculation unit 213 to calculate the residual r [j] between the predicted value p [j] and the output value o [j]. Then, the verification unit 217 determines whether or not the absolute value of the residual r [j] is less than the reference value.
If the verification unit 217 determines that the position difference m is not valid (NO in step S604), the verification unit 217 advances the process to step S605. On the other hand, if the verification unit 217 determines that the positional difference m is appropriate (YES in step S604), the verification unit 217 advances the process to step S606.

In the redetermination determination process in step S605, the verification unit 217 causes the position difference determination unit 216 to re-determine the position difference m using the same determination method as that used by the verification unit 117 in step S505 of FIG. Determine whether or not.
That is, the verification unit 217 determines that the position difference m is not re-determined when it is determined in step S604 that the position difference m is not valid continuously for a certain number of times, and otherwise the position difference m is determined. It is determined to be determined again.

When it is determined that the position difference m is to be determined again (YES in step S605), the verification unit 217 returns the process to step S603. At this time, the verification unit 217 excludes the position difference m determined to be invalid once from the selection target so that the position difference determination unit 216 does not select it again.

On the other hand, if the verification unit 217 determines that the position difference m is not determined again (NO in step S605), the verification unit 217 advances the process to step S606. At this time, the verification unit 217 sets the positional difference m to unusable. In this case, in step S606, the prediction unit 212 predicts the predicted value p [i] of the output value o [i] without using the position difference m. Specifically, the output values o [0],. . . , The predicted value p [i] of the output value o [i] is predicted using the output value o [i-1].

*** Effects of Embodiment 3 ***
As described above, in the data compression system 1 according to the third embodiment, when the position difference m is determined, the determined position difference m is verified and appropriately determined again. Thereby, when the determined position difference m is not appropriate, it is possible to prevent the accuracy of predicting the predicted value from being lowered.

*** Other configurations ***
<Modification 6>
In the third embodiment, as in the first and second embodiments, the functions of the respective units of the data compression device 10 and the data decompression device 20 are realized by software. However, as in the second modification of the first embodiment, the functions of the respective units of the data compression device 10 and the data decompression device 20 may be realized by hardware. Further, as in the third modification of the first embodiment, the data compression device 10 and the data decompression device 20 may have some functions realized by hardware and other functions realized by software.

1 data compression system, 10 data compression device, 11 processor, 12 storage device, 13 communication device, 14 signal line, 15 processing circuit, 111 input unit, 112 prediction unit, 113 residual calculation unit, 114 encoding unit, 115 output Unit, 116 position difference determination unit, 117 verification unit, 20 data decompression device, 21 processor, 22 storage device, 23 communication device, 24 signal line, 25 processing circuit, 211 input unit, 212 prediction unit, 213 decoding unit, 214 output Value calculation part, 215 output part, 216 position difference determination part, 217 verification part, d input data string, e external data string, c code data string, o output data string.

Claims (18)

1. The input value d [i] of the target position i in the input data string d is used by using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. ] For predicting the predicted value p [i] of
   A residual calculator that calculates a difference between the input value d [i] and the predicted value p [i] predicted by the predictor as a residual r [i];
   A data compression apparatus comprising: an encoding unit that encodes the residual r [i] calculated by the residual calculation unit and generates a code c [i] for the input value d [i].
2. 2. The data compression apparatus according to claim 1, wherein the prediction unit further predicts the predicted value p [i] using an input value for which a code has already been generated in the input data string d.
3. The data compression device further includes:
   By shifting the position of the external value of the external data string e corresponding to the input value of the input data string d, a shift amount that correlates the input data string d and the external data string e is determined as the positional difference m. The data compression apparatus according to claim 1, further comprising a position difference determination unit that performs the operation.
4. The position difference determination unit determines, as the position difference m, the shift amount at which the position of an extreme value is close for an input value for which a code has already been generated in the input data string d and the external data string e. Item 4. The data compression device according to Item 3.
5. The data compression apparatus according to claim 3 or 4, wherein the position difference determination unit newly determines the position difference m every time a reference input value is encoded.
6. The position difference determination unit calculates a predicted value p ^* [i−1] of the input value d [i−1] predicted without using the external data string e and the input value d [i−1]. The absolute value of the residual r ^* [i-1] is smaller than the absolute value of the residual r [i-1] between the input value d [i-1] and the predicted value p [i-1]. 5. The data compression device according to claim 3, wherein the position difference m is newly determined when the reference number of times continues for a reference time.
7. The data compression device further includes:
   For a certain input value d [j] for which a code has already been generated in the input data string d, a predicted value p [j] predicted using the position difference m determined by the position difference determination unit, and the input value The verification unit according to claim 3, further comprising: a verification unit that causes the positional difference determination unit to re-determine the positional difference m when the absolute value of the residual r [j] with respect to d [j] is greater than or equal to a reference value. The data compression device according to any one of claims.
8. The output value o [i] of the target position i in the output data string o is used by using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. ] For predicting the predicted value p [i] of
   A decoding unit that decodes the code c [i] to generate a residual r [i];
   Data including an output value calculation unit that calculates a sum of the prediction value p [i] predicted by the prediction unit and the residual r [i] generated by the decoding unit as the output value o [i]. Stretching device.
9. The data expansion device according to claim 8, wherein the prediction unit further predicts the prediction value p [i] using the output value calculated by the output value calculation unit.
10. The data decompression device further includes:
    By shifting the position of the external value of the external data string e corresponding to the output value of the output data string o, the shift amount that correlates the output data string o and the external data string e is determined as the positional difference m. The data decompression device according to claim 8 or 9, further comprising a position difference determination unit.
11. 11. The data decompression device according to claim 10, wherein the position difference determination unit determines the shift amount at which extreme positions are close to the output data string o and the external data string e as the position difference m.
12. The data expansion device according to claim 10 or 11, wherein the position difference determination unit newly determines the position difference m each time a reference output value is calculated.
13. The position difference determination unit calculates the predicted value p ^* [i−1] of the output value o [i−1] predicted without using the external data string e and the output value o [i−1]. The absolute value of the residual r ^* [i-1] is smaller than the absolute value of the residual r [i-1] between the predicted value p [i-1] and the output value o [i-1]. The data decompression device according to claim 10 or 11, wherein the position difference m is newly determined when the reference number of times continues for a reference time.
14. The data decompression device further includes:
    For a certain output value o [j] generated by the output value calculator, the predicted value p [j] predicted using the position difference m determined by the position difference determiner, and the output value o [j ] The verification part which makes the said position difference determination part re-determine the said position difference m when the absolute value of the residual r [j] with respect to a reference value or more is provided. The data decompression device according to item.
15. The input value d [i] of the target position i in the input data string d is used by using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. ] Prediction processing for predicting the predicted value p [i] of
    A residual calculation process for calculating a difference between the input value d [i] and the predicted value p [i] predicted by the prediction process as a residual r [i];
    A data compression program for causing a computer to execute an encoding process for encoding a residual r [i] calculated by the residual calculation process and generating a code c [i] for the input value d [i].
16. The output value o [i] of the target position i in the output data string o is used by using the external value e [im] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e. ] Prediction processing for predicting the predicted value p [i] of
    A decoding process for decoding the code c [i] to generate a residual r [i];
    The computer executes an output value calculation process for calculating the sum of the predicted value p [i] predicted by the prediction process and the residual r [i] generated by the decoding process as an output value o [i]. Data decompression program to be executed.
17. The processor uses the external value e [i−m] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e, and the input value of the target position i in the input data string d. predict a predicted value p [i] of d [i],
    A processor calculates a difference between the input value d [i] and the predicted value p [i] as a residual r [i];
    A data compression method in which a processor encodes the residual r [i] to generate a code c [i] for the input value d [i].
18. The processor uses the external value e [i−m] at a position shifted by a positional difference m from the external value e [i] of the target position i in the external data string e, and the output value of the target position i in the output data string o. predict the predicted value p [i] of o [i],
    A processor decodes the code c [i] to generate a residual r [i];
    A data expansion method in which a processor calculates the sum of the predicted value p [i] and the residual r [i] as the output value o [i].

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