JP4176097B2 - Encoding system, encoding computer program, decoding system, and decoding computer program - Google Patents

Description

  The present invention repeats the process of dividing the code range into sections according to the symbol type of the symbol to be processed, and encodes the operation result obtained by the repetition process, thereby forming a symbol composed of a plurality of symbols. The present invention relates to a technique for encoding a sequence.

  One of the entropy coding is arithmetic coding. Arithmetic coding is coding in which a symbol string is a single code word, and the process of dividing the appearance probability of a symbol into segments corresponding to the symbol type (symbol type) of the line segment (code range). By repeating the process, the process finally outputs one real number included in the section. Patent Document 1 discloses a technique for increasing the processing speed in this arithmetic coding. More specifically, the division process is executed only by the shift process by maintaining the maximum value of the appearance frequency of the symbol type at a power of 2.

JP-A-10-32496

  However, the encoding described in Patent Document 1 has a multiplication process, and it is necessary to separately provide a circuit for performing the division process. This division process requires a complicated circuit like the multiplication process, and causes a reduction in processing speed and an increase in the scale of the circuit in the encoding process. Further, it cannot be applied to a range coder similar to the code range of arithmetic coding.

  The present invention has been made in view of such circumstances, and an object of the present invention is to reduce multiplication / division processing in encoding or decoding, and to increase the overall processing speed.

  Another object of the present invention is to reduce the size of the circuit by reducing the number of circuits that perform multiplication and division.

In order to solve such a problem, the first invention is obtained by repeating the process of dividing the code range set by the code range specific value into sections according to the symbol type of the symbol to be processed. An encoding system is provided that encodes a symbol string composed of a plurality of symbols by encoding the calculated result. This system includes a storage unit, an update unit, a code range update unit, and a shift amount calculation unit. The storage unit stores a plurality of count values that can specify the appearance frequency of each symbol type included in the symbol string. The update unit updates the count value corresponding to the symbol type of the read symbol each time a symbol is read from the symbol string as a processing target. When one symbol is read as the current processing target, the code range update unit is stored in the storage unit before the update unit updates the count value corresponding to the symbol type of the one symbol. Read the frequency. The code range update unit includes at least a shift process that shifts the count value corresponding to the symbol type of one symbol by a shift amount of n (n is a natural number) bits used in the current processing target. By performing the processing, the code range specific value is updated. The shift amount calculation unit approximates a division value obtained by dividing the width of the code range specified by the code range specification value updated by the code range update unit by the total appearance frequency specified by the count value by 2 ⁿ , The value n obtained by approximation is set as the shift amount used in the next processing target.

  Here, in the first invention, when the width of the code range becomes smaller than the predetermined value due to the update process of the code range update unit, or when the upper bits of the predetermined range of the code range specific value no longer change In addition, a determination unit that outputs the code range specific value updated by the current process to be processed as encoded data may be further provided.

  In the first invention, the shift amount calculation unit calculates a value calculated by a shift process for performing bit shift with a shift amount obtained by approximation with respect to the total appearance frequency, and a code range used in the current processing target. It is preferable to calculate an approximation error which is a difference value with respect to the width of. In this case, the code range update unit apportions the approximation error at a predetermined ratio according to the symbol type, and assigns it to each section of the symbol type constituting the code range used for the next processing target.

2nd invention repeats the process which divides | segments the code range set by a code range specific value into the area according to the symbol kind of the symbol used as a process target, and encodes the calculation result obtained by this repetition process Thus, there is provided an encoding computer program for causing a computer to execute an encoding method for encoding a symbol string composed of a plurality of symbols. This program includes a first step of reading one symbol as a current processing target from among a symbol string composed of a plurality of symbols, and a plurality of symbols that can specify the appearance frequency of each symbol type included in the symbol string Of the count values, the second step of updating the count value corresponding to the symbol type of one symbol and the symbol type of one symbol prior to updating the count value corresponding to the symbol type of one symbol The code range specific value is updated by performing an arithmetic process including at least a shift process for performing a bit shift with a shift amount of n (n is a natural number) bits used in the current process target, on the count value corresponding to And the total frequency of occurrences specified by the count value in step 3 and the width of the code range specified by the updated code range specification value. In the division was divided value is approximated by 2 ^n, and a fourth step of setting the value n obtained by the approximation as a shift amount used in the next processing object in the symbol sequence, one symbol to be processed The computer is caused to execute an encoding method including a fifth step that repeats the processing from the first step to the fourth step until a predetermined output condition is satisfied.

  Here, in the second invention, the output condition is that when the code range width becomes smaller than the predetermined value due to the update of the code range specific value, or the upper bits of the predetermined range of the code range specific value change. It may be a case where it disappears.

  In the second invention, the fourth step includes a value calculated by a shift process for performing a bit shift with a shift amount obtained by approximation with respect to the total appearance frequency, and a code range used in the current processing target. It is preferable to include a sixth step of calculating an approximation error which is a difference value with respect to the width of. In this case, the third step includes a step of assigning the approximation error to each section for each symbol type constituting the code range used in the next processing target after apportioning the approximation error by a predetermined ratio corresponding to the symbol type. May be.

The third invention specifies a section corresponding to the value of the encoded data from the code range set by the code range specifying value and divided into sections according to the symbol type of the symbol, and the specified section Provided is a decoding system for decoding encoded data into a symbol string composed of a plurality of symbols by repeating search processing for outputting corresponding symbols and arranging symbols obtained by the repetition. This system includes a storage unit, an update unit, a code range update unit, and a shift amount calculation unit. The storage unit stores a plurality of count values that can specify the appearance frequency of each symbol type output by the search process. The update unit updates the count value corresponding to the symbol type of the output symbol each time the symbol is output by the search process. When one symbol is output as the current process, the code range update unit reads the appearance frequency stored in the storage unit. The code range update unit includes at least a shift process that shifts the count value corresponding to the symbol type of one symbol by a shift amount of n (n is a natural number) bits used in the current process. To set a code range specific value used in the next processing. The shift amount calculation unit approximates a division value obtained by dividing the width of the code range specified by the code range specification value set by the code range update unit by the total appearance frequency specified by the count value by 2 ⁿ , The value n obtained by approximation is set as the shift amount used in the next processing.

  Here, in the third invention, when the width of the code range becomes smaller than the predetermined value due to the update process of the code range update unit, or when the upper bits of the predetermined range of the code range specific value no longer change In addition, a determination unit that performs a shift process for bit-shifting the encoded data by the shift amount by the number of upper bits may be further provided.

  In the third invention, the shift amount calculation unit calculates a value calculated by a shift process for performing bit shift with a shift amount obtained by approximation with respect to the total appearance frequency, and a code range used in the current processing target. It is preferable to calculate an approximation error which is a difference value with respect to the width of. In this case, it is desirable that the code range update unit apportions the approximation error at a predetermined ratio according to the symbol type, and then assigns it to each section for each symbol type constituting the code range used in the next processing target.

The fourth invention specifies a section corresponding to the value of the encoded data from the code range set by the code range specifying value and divided into sections according to the symbol type of the symbol, and the specified section Decoding that causes a computer to execute a decoding method for decoding encoded data into a symbol string composed of a plurality of symbols by repeating search processing for outputting corresponding symbols and arranging the symbols obtained by the repetition. Provide a computer program. The program includes a first step of outputting the symbol type of one symbol from the encoded data by the search process, and a plurality of count values that can specify the appearance frequency of each symbol type output by the search process. Second step of updating the count value corresponding to the symbol type of one symbol, and n (n is a natural number) bits used in the current processing target for the count value corresponding to the symbol type of one symbol A third step of updating the code range specific value by performing a calculation process including at least a shift process for performing bit shift by the shift amount of the code, and a count value for the width of the code range specified by the updated code range specific value the quotient obtained by dividing the total frequency of occurrence is identified approximated by 2 ^n, the value n obtained by the approximation in the next processed by The fourth step to be set as the shift amount, and the processing from the first step to the fourth step until one predetermined condition is satisfied while sequentially shifting one symbol to be processed in the symbol string And causing the computer to execute a decoding method having a fifth step of repeating

  Here, in the fourth invention, the determination condition is that the code range width becomes smaller than the predetermined value due to the update of the code range specific value, or the upper bits of the predetermined range of the code range specific value change. It may be a case where it disappears.

  In the fourth invention, the fourth step includes a value calculated by a shift process for performing a bit shift with a shift amount obtained by approximation with respect to the total appearance frequency, and a code range used in the current processing target. There may be included a sixth step of calculating an approximation error that is a difference value from the width of. In this case, the third step includes a step of apportioning the approximation error by a predetermined ratio corresponding to the symbol type and assigning it to each section for each symbol type constituting the code range used in the next processing target. Is preferred.

  Furthermore, in any one of the first to fourth inventions, the code range is preferably specified by a predetermined combination of an upper limit value, a lower limit value, or a width that is a code range specifying value.

  According to the first or second invention, the width of the code range specified by the code range specifying value is approximated by the shift amount by dividing the divided value by the total appearance frequency specified by the count value. Then, the code range specific value is updated by performing an arithmetic process including at least a shift process for performing a bit shift by this shift amount. Thus, regarding the update of the code range specific value, it is possible to increase the speed of the encoding process by replacing the multiplication process and the division process with the shift process. At the same time, according to the first aspect of the present invention, it is possible to reduce the number of circuits that perform multiplication / division, and thus it is possible to reduce the circuit scale.

  Further, according to the third or fourth invention, the speed of the decoding process can be increased for the same reason as the first or second invention described above. It becomes possible to reduce the scale.

<First Embodiment (Encoding)>
FIG. 1 is a configuration diagram of an encoding system. In this encoding system, the process of dividing the code range set by the code range specific value into sections corresponding to the symbol type of the symbol to be processed is repeatedly executed. Then, the symbol string is encoded by encoding the calculation result obtained by this iterative process. Subscripts (i) and (i-1) attached to data such as the count value CNT indicate one cycle in the iterative process. The subscript (i) indicates a value calculated based on the symbol to be processed in the current cycle (i), and the subscript (i-1) has been processed in the previous cycle (i-1). Indicates the value calculated based on the symbol.

  The encoding system includes an appearance frequency management unit 1, a code range management unit 2, a shift amount calculation unit 3, and a first output management unit 4. The appearance frequency management unit 1 manages how many times each symbol type included in the symbol string to be processed is input at the current stage. The appearance frequency management unit 1 includes a storage unit 11 and an update unit 12.

  The storage unit 11 stores a plurality of count values that can specify the appearance frequency of each symbol type included in the symbol string. The storage content of the storage unit 11 has a configuration as an appearance frequency table, and thus count values are stored. The appearance frequency of the symbol type is managed by two types of count values such as the appearance frequency CNT [j] and the cumulative appearance frequency SUM [j] (j: one symbol).

The appearance frequency CNT [j] is the number of appearances of a certain symbol type j. The initial value is 1. For example, when the symbol “a” is read (input) twice, the appearance frequency CNT [a] of the symbol “a” is counted up from 1 (initial value) to 3. . The cumulative appearance frequency SUM [j] is a cumulative value of the appearance frequency CNT lower than the symbol type in a predetermined order from the lower order to the higher order in the appearance frequency table. For example, when the appearance frequency table is arranged in the order of symbols “a”, “b”, and “c” from the lower order, the cumulative appearance frequency SUM [a] of the symbol “a” and the cumulative appearance frequency SUM of the symbol “b” [b] and the cumulative appearance frequency SUM [c] of the symbol “c” are expressed by the following equations.

SUM [a] = 0 (or “NULL”)
SUM [b] = CNT [a]
SUM [c] = CNT [a] + CNT [b]

The appearance frequency table of the storage unit 11 also stores a total appearance frequency SUMALL obtained by accumulating the appearance frequencies CNT [j] of all symbol types. For example, when the appearance frequency table is composed of three symbols “a”, “b”, and “c”, the total appearance frequency SUMALL can be expressed by the following equation.
SUMALL = CNT [a] + CNT [b] + CNT [c]

  As the appearance frequency table, the appearance frequency CNT [j] and the cumulative appearance frequency SUM [j] for each symbol type are managed. However, it is not always necessary to manage both, and if at least one of them is managed It ’s enough. This is because the cumulative appearance frequency SUM [j] can be uniquely specified by the addition process based on the appearance frequency CNT, and the appearance frequency CNT [j] can also be uniquely specified by the subtraction process based on the cumulative appearance frequency SUM. It is. The same applies to the total appearance frequency SUMALL. If the appearance frequencies CNT [j] of all symbol types can be calculated from the appearance frequency table stored in the storage unit 11, the storage unit 11 displays the appearance frequencies CNT [ j] need not be managed.

  In the present embodiment, the appearance frequency CNT [j] manages the number of appearances of the symbol type, but it is sufficient that at least the appearance ratio of the symbol type can be grasped. For example, the appearance frequency table is composed of symbols “a”, “b”, and “c”, and the appearance frequencies are CNT [a] = 2, CNT [b] = 4, and CNT [c] = 2. In each case, each occurrence frequency is multiplied by 1/2 (1-bit right shift processing is performed) to update CNT [a] = 1, CNT [b] = 2, and CNT [c] = 1. May be. Note that the update condition and update timing of the appearance frequency [j] are required to be the same as those of a later-described decoding system in order to ensure reproducibility in decoding.

  The updating unit 12 updates the count value (CNT, SUM) corresponding to the input symbol type each time the symbol Sym (i) is input as a processing target from the symbol string. For example, when the appearance frequency table is arranged in the order of symbols “a”, “b”, “c” from the lower order, and the symbol “a” is input as a processing target, 1 is added to the appearance frequency CNT [a]. Is updated to the value In response to this, the cumulative appearance frequencies SUM [b], SUM [c], and the total appearance frequency SUMALL are each updated to a value obtained by adding one by one.

  The code range management unit 2 repeatedly updates the code range corresponding to the symbol string to be processed every time a symbol is input. The code range management unit 2 includes a code range storage unit 21 and a code range update unit 22. The code range storage unit 21 stores a code range specifying value that specifies a code range. The code range specification value is information for specifying the absolute position of the code range expressed by a one-dimensional line segment, and as an example, the lower limit value LOW and the width RNG of the code range are used. However, as the code range specification value, there is an upper limit value UP indicating the upper limit of the code range in addition to the lower limit value LOW and the width RNG. If at least two of these are managed, the code range is uniquely specified. it can. Therefore, the code range specifying value to be managed is not limited to the combination as in the present embodiment, but the combination of the lower limit value LOW and the upper limit value UP, the combination of the upper limit value UP and the width RNG, or the lower limit. A combination of the value LOW, the upper limit value UP, and the width RNG may be used. Note that the initial values of the lower limit value LOW and the width RNG stored in the code range storage unit 21 are assumed to be the same as those of a later-described decoding system in order to ensure data reproducibility at the time of decoding.

  The code range update unit 22 updates the code range (code range specific value) when one symbol Sym (i) that is the current processing target is input. It should be noted here that the code range is updated before the update of the appearance frequency table, in other words, before the count value corresponding to the symbol type of this symbol Sym (i) is updated. is there. Specifically, the code range update unit 22 first counts CNT [j] (i−1), SUM [j stored in the storage unit 11 before updating the appearance frequency table in the storage unit 11. ] (i-1) is read. The count value CNT [Sym (i)] (i-1), SUM [Sym (i)] (i-1) corresponding to the symbol type of the symbol Sym (i) includes at least a shift process. An arithmetic process is performed, and a lower limit value LOW (i) and a width RNG (i) are calculated as new code range specifying values. The shift process is an arithmetic process in which a bit shift is performed with an n-bit shift amount SFT used in the current processing target. The calculated code range specific value is stored in the code range storage unit 21.

FIG. 2 is a configuration diagram of the code range update unit 22. The code range update unit 22 includes a lower limit value calculation unit 22a and a width calculation unit 22e. The lower limit calculator 22a includes a shifter 22b, a shifter 22c, and an adder 22d. The shifter 22b reads the count value SUM [Sym (i)] (i-1) before update corresponding to the input symbol type Sym (i), and this count value SUM [Sym (i)] (i-1). ) Is subjected to left bit shift processing with a shift amount SFT (i−1). Further, the shifter 22c reads the approximate error RMD (i-1) and performs right bit shift processing with a predetermined value (for example, value L) corresponding to the symbol Sym (i) input to the lower limit calculation unit 22a. Further, the adder 22d adds the respective values shifted by the shifters 22b and 22c and the value of the lower limit value LOW (i-1) before update stored in the code range storage unit 21 to obtain a new value. The lower limit value LOW (i) of the code range (used in the next processing target) is calculated. The calculated lower limit value LOW (i) is stored in the code range storage unit 21. The lower limit value LOW (i) calculated by the lower limit value calculation unit 22a is expressed by the following equation. "<<" indicates left bit shift processing, and ">>" indicates right bit shift processing. For example, "SUM [Sym (i)] (i-1) << SFT (i-1)" This is a process of shifting the value SUM [Sym (i)] (i-1) to the left by the shift amount SFT (i-1) bits, that is, multiplying by 2 ^{SFT (i-1)} .

LOW (i) = SUM [Sym (i)] (i-1) << SFT (i-1) + RMD (i-1) >> L + LOW (i-1)

Similar to the lower limit calculation unit 22a, the width calculation unit 22e includes a shifter 22f, a shifter 22g, and an adder 22h, but the count values to be processed are different. Another difference is that the adder 22h does not use the pre-update code range specific value stored in the code range storage unit 21. The shifter 22f reads the pre-update count value CNT [Sym (i)] (i-1) corresponding to the input symbol type Sym (i), and this count value CNT [Sym (i)] (i-1 ) Is subjected to left bit shift processing with a shift amount SFT (i−1). The shifter 22g reads the approximate error RMD (i-1) and performs a right bit shift process with a predetermined value (for example, value R) corresponding to the symbol Sym (i) input to the width calculation unit 22e. The adder 22h adds the values shifted by the shifters 22f and 22g and calculates a new code range width RNG (i) (used for the next processing target). The calculated width RNG (i) is stored in the code range storage unit 21. The lower limit value RNG (i) calculated by the width calculation unit 22e is expressed by the following equation.

RNG (i) = CNT [Sym (i)] (i-1) << SFT (i-1) + RMD (i-1) >> R

The shift amount calculation unit 3 uses the code range width RNG (i−1) specified by the code range specification value updated by the code range management unit 2 as the total appearance frequency SUMALL (i−1) specified by the count value. ) Is approximated by 2 ⁿ (2 factorial). Then, the value n obtained by this approximation is set as the shift amount SFT used for the next processing target.

FIG. 3 is a configuration diagram of the shift amount calculation unit. The shift amount calculation unit 3 includes an approximation unit 31, a shifter 32, and a subtracter 33. The approximating unit 31 divides the division value obtained by dividing the width RNG (i−1) stored in the code range storage unit 21 by the total appearance frequency SUMALL (i−1) before update stored in the storage unit 11. Approximate by factorial and calculate shift amount SFT (i-1). In this embodiment, the shift amount SFT (i-1) is calculated by comparing the value obtained by shifting the total appearance frequency SUMALL (i-1) with the left bit and the value comparing the width RNG (i-1). Is done. Specifically, a shift amount SFT (i−1) that satisfies the following equation is calculated. For approximation, simply calculate the shift amount n by obtaining the division value of the width RNG (i-1) and the total appearance frequency SUMALL and comparing this division value with the factorial of 2. It may be calculated.

(SUMALL (i-1) << SFT (i-1)) ≤RNG (i-1) << (SUMALL << SFT (i-1) +1)

The shifter 32 performs a left bit shift process with the shift amount SFT (i−1) calculated by the approximating unit 31 for the total appearance frequency SUMALL (i−1) before the update. The subtractor 33 subtracts the value calculated by the shifter 32 and the pre-update width RNG (i−1) stored in the code range storage unit 21 to obtain the approximate error RMD (i−1). calculate. As a result of approximation to the shift amount SFT (i-1), the approximation error RMD (i-1) is a value calculated by a shift process in which the total appearance frequency is bit-shifted by the shift amount SFT (i-1). The difference value from the width of the code range used in the current processing target. The approximate error RMD is as follows. If SUMALL << SFT = RNG, no approximation error is calculated.

RMD (i-1) = RNG (i-1) − (SUMALL (i-1) << SFT (i-1))

  The first output management unit 4 reads the code range specific value updated by the code range update unit 22 when the symbol Sym (i) to be processed is input from the code range storage unit 21 and satisfies a predetermined condition. Thus, a part of the code range specific value is output as encoded data. The first output management unit 4 includes a determination unit 41 and an output update unit 42. The determination unit 41 reads the lower limit value LOW (i) and the width RNG (i) of the code range in the code range storage unit 21, determines whether or not predetermined output conditions and end conditions are satisfied, and based on this determination The output update unit 42 is controlled. Further, the output update unit 42 outputs the value of the lower limit value LOW (i) stored in the code range storage unit 21 as encoded data based on the determination of the determination unit 41, and also outputs the lower limit value LOW (i) and width. Renew RNG (i).

  FIG. 4 is a flowchart of the encoding process. This processing flow as a whole repeats the process of dividing the code range set by the code range specific value into sections corresponding to the symbol type of the symbol to be processed (step 103 to step 112). Then, a calculation result obtained by this iterative process is output (step 107, step 111), thereby encoding a symbol string composed of a plurality of symbols.

  First, in step 101, before the symbol to be processed Sym (i) is read (input), the count values CNT and SUM and the shift amount SFT stored in the storage unit 11 and the code range storage unit 21 are stored. The stored lower limit value LOW and width RNG are initialized. Specifically, the update unit 12 updates all the count values CNT [j] of the symbol types stored in the appearance frequency table of the storage unit 11 to 1 (the appearance probabilities of all symbols are processes with equal probability).

  For example, when the symbol type included in the symbol string to be processed is composed of only “a”, “b”, and “c”, the count values CNT [a] (0) and CNT [b] in the appearance frequency table (0) and CNT [c] (0) are all 1. Accordingly, the total appearance frequency SUMALL (0) is also updated to 3. Also, the code range specifying value of the code range storage unit 21 is also updated to a predetermined value (for example, a natural number such as LOW (0) = 0, RNG (0) = 65535). At this time, since the total appearance frequency SUMALL (0) and the width RNG (0) are already set, the shift amount calculation unit 3 determines the shift amount SFT (0) and the approximate error RMD based on these values. Calculate (0). The calculated shift amount SFT (0) and approximate error RMD (0) are stored in a buffer (not shown) provided in the shift amount calculation unit 3 or the code range update unit 22.

  In step 102, a loop variable i is set. This loop variable indicates the update timing of the appearance frequency table and the code range for the input of the symbol, and is set to 1 as an initial value. Note that the loop variable i may be stored in any buffer (for example, the updating unit 12) inside or outside the encoding system as long as the timing of updating the appearance frequency table and the code range for the input of the symbol can be managed.

  In step 103, the i-th symbol (1 if the initial value is one) in the symbol string to be processed is input. The input symbol Sym (i) is input to the update unit 12 of the appearance frequency management unit 1 and the code range update unit 22 of the code range management unit 2 respectively. At this time, the updating unit 12 does not update the count value (appearance frequency table) for the input symbol Sym (i).

  In step 104, the code range update unit 22 counts CNT [Sym (i)] (i-1), SUM [Sym (i)] (i-1) corresponding to the input symbol Sym (i). ), The shift amount SFT (i−1) calculated by the shift amount calculation unit 3, and the approximation error RMD (i−1). As described above, the update unit 12 updates the appearance frequency table of the storage unit 11 with respect to the count values CNT [Sym (i)] (i-1) and SUM [Sym (i)] (i-1). The previous one is used. In this embodiment, the shift amount SFT (i-1) is calculated (set) in advance in step 112 (or step 101) described later. For example, in step 104, the shift amount SFT (i-1) is calculated. As described above, it is sufficient if it is calculated before the processing of the next step 105.

  In step 105, the code range update unit 22 is based on these values CNT (i-1), SUM (i-1), SFT (i-1), and RMD (i-1) read in step 104. Then, a new lower limit value LOW (i) and a new width RNG (i) used for the update process by the next symbol input are calculated. The code range is updated by storing the new code range specifying value in the code range storage unit 21.

In step 106, the determination unit 41 of the first output management unit 4 determines an end condition whether or not to end the encoding of the symbol string. If this end condition is satisfied, the process proceeds to step 107; otherwise, the process proceeds to step 108. This termination condition may be any condition as long as it can be applied (determined) in common to a decoding system described later and prevents repeated processing in the encoding process. In the present embodiment, the end conditions are as follows, for example.
(Example 1)
When a symbol indicating the end of encoding (for example, symbol “EOF”) is set in advance before encoding processing and is input as a symbol processing target (Sym (i) = “EOF”).
(Example 2)
A threshold value (LAST) of the number of loops is set in advance before the encoding process, and the loop variable i reaches the threshold value (i = LAST).

  When the end condition is satisfied and the process proceeds to step 107, the determination unit 41 outputs the lower limit value LOW (i) stored in the code range storage unit 21 to the output update unit 42 as encoded data. The process is terminated. On the other hand, when the end condition is not satisfied and the process proceeds to step 108, the count value is updated. Specifically, the updating unit 12 updates the count values CNT [j] and SUM [j] to the storage unit 11. As in step 101, the calculated shift amount SFT (i) and approximate error RMD (i) are stored in a buffer (not shown) provided in the shift amount calculation unit 3 or the code range update unit 22. Thereafter, the process proceeds to step 109.

  Next, step 109 and step 110 described below are output conditions for outputting the code range specific value updated in step 105. In the output condition of the present embodiment, step 110 is executed after step 109, but step 109 may be executed after step 110.

  In step 109, it is determined whether or not the width RNG (i) used for the next processing target is smaller than a predetermined value. Specifically, the determination unit 41 of the first output management unit 4 reads the width RNG (i) stored in the code range storage unit 21, and determines whether the width RNG (i) is smaller than a predetermined value. judge. When the width RNG (i) is not smaller than the predetermined value, that is, when there is room to reduce the value of the width RNG (the further arithmetic processing is not affected even if the width RNG (i) is further reduced) , The process proceeds to step 110. On the other hand, when the width RNG (i) is smaller than the predetermined value, that is, the width RNG has no room to reduce the value (if the width RNG (i) is further reduced, the subsequent arithmetic processing is affected). , The process proceeds to step 111.

  In step 110, it is determined whether or not the upper bits of the predetermined range of the code range specific value are not changed by the update process of the code range update unit 22. This determination is performed by comparing the upper bits of the predetermined range of the code range specific value used in the processing target with the upper bits of the predetermined range of the code range specific value used in the current processing target. Specifically, the determination unit 41 of the first output management unit 4 stores the lower limit value LOW (i−1) calculated for the previous processing target, and is stored in the code range storage unit 21. The lower limit value LOW (i) is read and compared with the lower limit value LOW (i-1). If the upper 8 bits of the lower limit value (i) and the lower limit value (i-1) are different, that is, if there is a large difference in the value of the lower limit value LOW (i), the process proceeds to step 112. If the upper 8 bits of the lower limit value (i) and the lower limit value (i-1) are unchanged, that is, if the value of the lower limit value LOW (i) does not change even if the code range is updated more than this, the processing is performed at step 111. Proceed to In the present embodiment, the lower limit value LOW (i−1) calculated for the previous processing target is stored in the determination unit 41, but may be stored in the code range storage unit 21. In this case, the determination unit 41 reads the lower limit value LOW (i−1) as well as the lower limit value LOW (i) from the code range storage unit 21 and performs the above comparison.

  When the output conditions in step 109 and step 110 are satisfied and the process proceeds to step 111, the lower limit value LOW (i) is output as encoded data code, and the lower limit value LOW (i) and width RNG (i) Will be updated again. Specifically, the determination unit 41 controls the output update unit 42 to output and update the lower limit value LOW (i). Then, the output update unit 42 reads the lower limit value LOW (i) and the width RNG (i) from the code range storage unit 21 according to this control, and outputs the upper 8 bits of the lower limit value LOW (i). A bit shift process for shifting the lower limit value (i) and the width RNG (i) by 8 bits to the left is performed. In other words, the output update unit 42 shifts the lower limit value LOW (i) to the left, and outputs the bits that have overflowed digits as encoded data code.

  Note that 0 is inserted in the lower 8 bits that become blank (or “NULL”) by shifting the lower limit (i) to the left. Similarly, a bit shift process for shifting the width RNG to the left by 8 bits is performed. In this process, the code range specific value whose value has been reduced is increased again at the same time as the output of the encoded data code, and it is possible to suppress a decrease in the calculation process of the encoding process using the lower limit value LOW and the width RNG. it can. Then, the shift amount calculation unit 3 reads the width RNG (i) of the code range storage unit 21, and calculates the shift amount SFT (i) and the approximate error RMD (i) (step 112). Finally, after the loop variable is incremented (step 113), the process proceeds to step 103.

  Next, a specific case of the code range according to the present embodiment will be described with reference to a code range transition diagram in FIG. In this case, count values of three symbol types “a”, “b”, “c” are set in advance in the appearance frequency table, and symbols in the symbol sequence are input in the order of “b”, “a”. When the input of these two symbols is completed, the encoding ends (LAST = 2). Note that the output conditions described in steps 109 and 110 are not satisfied, and accordingly, the processing in step 111 is not performed.

  FIG. 5A shows the state of the code range in the initial state (i = 0) (step 101). The width RNG (0) and the lower limit value LOW (0) stored in the code range storage unit 21 are initial values set in advance before the encoding process. In addition, the code range in the figure has a line segment divided for each symbol type, but this is described for the sake of simplicity, and is a value that identifies a section indicating each symbol type in implementation. (Boundary value) is not stored in the code range storage unit 21.

  In FIG. 5B, the shift amount calculation unit 3 calculates the shift amount SFT (0) and the shift amount SFT (0) from the count values CNT [j] and SUM [j] of the storage unit 11 and the width RNG (0) of the code range storage unit 21. The state of the code range in which the approximate error RMD (0) is calculated is shown (step 104). The code range updating unit 22 apportions this approximation error at a predetermined ratio (a: b: c = 1: 2: 1) and assigns it to each section for each symbol type constituting the code range.

Allocation of the approximate error can be performed by dividing and multiplying the approximate error RMD, but in the case of this embodiment, bit shift processing can also be used. This is because a 1-bit right shift makes the value 1/2, and a 2-bit right shift makes the value 1/4. When the approximate error division is fixed and assigned at the above ratio, the correspondence between the input symbol Sym (i), the newly calculated lower limit LOW (i), and the width RNG (i) can be expressed by the following equation: .

(1) When Sym (i) = "a"
LOW (i) = SUM [a] (i-1) << SFT (i-1) + LOW (i-1)
RNG (i) = CNT [a] (i-1) << SFT (i-1) + RMD (i-1) >> 2
(2) When Sym (i) = "b"
LOW (i) = SUM [b] (i-1) << SFT (i-1) + RMD (i-1) >> 2 + LOW (i-1)
RNG (i) = CNT [b] (i-1) << SFT (i-1) + RMD (i-1) >> 1
(3) When Sym (i) = “c”
LOW (i) = SUM [c] (i-1) << SFT (i-1) + RMD (i-1) >> 2 +++ RMD (i-1) >> 1 + LOW (i-1)
RNG (i) = CNT [c] (i-1) << SFT (i-1) + RMD (i-1) >> 2

Therefore, in this case, since the input symbol is “b”, the newly calculated lower limit value LOW (1) and width RNG (1) are expressed by the following equations. FIG. 5C shows a state in which the approximate error calculated by this equation is allocated to each section for each symbol type and then assigned to a new code range. (Step 105).

LOW (1) = SUM [b] (0) << SFT (0) + RMD (0) >> 2 + LOW (0)
RNG (1) = CNT [b] (0) << SFT (0) + RMD (0) >> 1

  Note that the approximation error can be statically assigned at a ratio set in advance before the encoding process as in this case, but the approximation error may be dynamically assigned. For example, the allocation of the approximation error may be changed according to the symbol Sym (i−1) input immediately before the current encoding process or the distribution of count values in the current appearance frequency table in the encoding process. Specifically, when there is a high possibility that the same symbol will appear (input) continuously, an approximate error RMD is assigned to the width RNG of this symbol, or the count value CNT of each current symbol type is assigned. It can also be assigned as a ratio as it is. However, similar to the static allocation, the allocation setting of the approximation error RMD needs to be the same as the decoding described later.

  FIG. 5D shows the state of the code range in which the first symbol input is completed (i = 1). Similar to the initial state, the value (boundary value) for specifying the section indicating each symbol type is not stored in the code range storage unit 21. FIG. 8E shows that the shift amount calculation unit 3 performs the shift amount SFT (1) and the shift amount SFT (1) based on the count value SUMALL (1) of the storage unit 11 and the width RMG (1) of the code range storage unit 21. The state of the code range in which the approximate error RMD (1) is calculated is shown (step 104). Then, as in FIG. 5B, the approximate error is allocated equally to the symbols “a”, “b”, and “c” at a ratio of 1: 2: 1.

  FIG. 5F shows a state where the calculated approximate error RMD (1) is assigned according to the symbol type and updated to a new code range (step 105). Note that since the value is not stored in the cumulative appearance frequency SUMALL [a] (1) (0 or “NULL”), the value is 0 even if the left shift process is performed. Therefore, the newly set lower limit value LOW (2) remains the lower limit value LOW (1). Then, the lower limit value LOW (2) and the width RNG (2) corresponding to the next symbol processing as shown in (g) in the figure are updated, and the lower limit value LOW (2) of them encodes the symbol string. The data code is output from the output update unit 42 (step 107).

As described above, according to the present embodiment, the shift amount calculation unit 3 sets the division value obtained by dividing the code range width RNG (i-1) by the total appearance frequency SUMALL (i-1) into 2 in the encoding. Approximate with ⁿ , and set the value n obtained by this approximation as the shift amount SFT (i-1) used in the next processing target. The code range update unit 22 then generates a new lower limit value LOW (i) and a new lower limit value LOW (i) based on the shift amount SFT and the count values CNT [j] (i-1) and SUM [j] (i-1). Set a reasonable width RNG (i). Thereby, in the next update of the code range specific value, the multiplication process and the division process can be changed to the shift process, so that the overall processing speed can be increased. Further, since the division / multiplication processing is also reduced, it is possible to reduce the scale of the entire circuit.

  Further, according to the present embodiment, in the above approximation, the shift amount calculation unit 3 calculates the total appearance frequency SUMALL (i-1) by the shift amount SFT (i-1) by the shift process, and the current time An approximate error RMD (i-1) that is a difference value from the width RNG (i-1) of the code range used in the processing target is calculated. Then, the code range update unit 22 divides the approximate error RMD (i-1) at a predetermined ratio according to the symbol type, and the divided value is used as the lower limit value LOW ( The calculation process is distributed to i) and the width RNG (i). As a result, the newly set lower limit value LOW (i) and width RNG (i) can be suppressed from being reduced more than necessary, so in subsequent iterations, the increase in the amount of computation due to the reduction in the number of digits is suppressed, A decrease in calculation processing speed can be prevented.

<Second Embodiment (Decoding)>
FIG. 6 is a configuration diagram of the decoding system. Similar to the above-described encoding system, this decoding system repeats the process of dividing the code range into sections corresponding to the symbol type of the symbol to be output. Then, by searching the code range for the section corresponding to the input encoded data code, the symbol corresponding to the corresponding section is output.

  The decoding system includes an appearance frequency management unit 1, a code range management unit 2, a shift amount calculation unit 3, and a second output management unit 5. The appearance frequency management unit 1 of the present embodiment counts the appearance frequency table corresponding to the symbol type of the output symbol Sym (i) every time the symbol Sym (i) is output from the second output management unit 5. Update the values CNT [j] and SUM [j]. The shift amount calculation unit 3 calculates the shift amount SFT (i-1) and the approximate error RMD (i-1) in accordance with the update of the count value, and the code range management unit 2 calculates the shift amount SFT ( A new lower limit value LOW (i) and width RNG (i) are calculated based on i-1) and the approximation error RMD (i-1). The configurations of the appearance frequency management unit 1, the code range management unit 2, and the shift amount calculation unit 3 are the same as those of the encoding system described above.

  The second output management unit 5 divides the code range for each symbol type based on the shift amount SFT (i-1), the approximation error RMD (i-1), and the count value (cumulative appearance frequency SUM [j]). The boundary value BASE [j] to be calculated is calculated, and a section corresponding to each symbol type is set. Then, a section including the value of the encoded data code input to the decoding system is searched and specified, and a symbol type corresponding to the specified section is output as an output symbol Sym (i). The second output management unit 5 includes a storage unit 51, a determination unit 52, an update unit 53, a boundary calculation unit 54, and an output unit 55.

  The storage unit 51 stores encoded data code generated by encoding a symbol string. As in the first embodiment, the determination unit 52 reads the lower limit value LOW (i) and the width RNG (i) stored in the code range storage unit 21, and determines whether or not predetermined update conditions and end conditions are satisfied. The storage unit 51 and the update unit 53 are controlled according to the determination result. The update unit 53 re-updates the lower limit value LOW (i) and the width RNG (i) stored in the code range storage unit 21 according to the determination result of the determination unit 52.

  The boundary calculation unit 54 is based on the shift amount SFT (i−1) and the approximation error RMD (i−1) calculated by the shift amount calculation unit 3 and the count value SUM [j] stored in the appearance frequency management unit 1. The boundary value BASE [j] for dividing the code range for each symbol type is calculated. The output unit 55 sets a section of a code range based on the boundary value BASE [j] calculated by the boundary calculation unit 54, and searches and specifies a section corresponding to the encoded data code stored in the storage unit 51. The symbol type corresponding to this section is output as the output symbol Sym (i).

FIG. 7 is a configuration diagram of the boundary calculation unit 54. The boundary calculation unit 54 includes a shifter 54a, a shifter 54b, and an adder 54c. The shifter 54a reads the count value SUM [j] (i-1) before update corresponding to all symbol types, and shifts SFT (i) for each count value SUM [j] (i-1). The left bit shift process is performed in -1). The shifter 54b reads the approximate error RMD (i-1), and performs a right shift process on the approximate error RMD (i-1) with a predetermined value (for example, value B) corresponding to the symbol. Further, the adder 54c adds the respective values shifted by the shifters 54a and 54b and the lower limit value LOW (i-1) of the code range used in the previous symbol, thereby obtaining the boundary value BASE [j] ( i) is calculated. The calculated boundary value BASE [j] (i) is output to the output unit 55. The boundary value BASE [j] (i) calculated by the boundary calculation unit 54 is expressed by the following equation.

BASE [j] (i) = BASE [j-1] (i) + SUM [j] (i-1) << SFT (0) + RMD (i-1) >> B + LOW (i-1)

  The output unit 55 reads the encoded data code stored in the storage unit 51 and the boundary value BASE [j] calculated by the boundary calculation unit 54. Then, the output unit 55 sets a section of the code range divided by the boundary value BASE [j], searches and specifies a section corresponding to the value of the encoded data code, and a symbol type corresponding to the specified section Is output as a symbol by Sym (i).

  FIG. 8 is a flowchart of decoding. Overall, first, a boundary value of the code range is provided, a section corresponding to the symbol type is set, a symbol type of a section corresponding to the value of the encoded data code is output, and finally the code range and count value are updated. . By repeating these series of processes and arranging the symbol types, decoding is performed into a symbol string corresponding to the encoded data code.

  First, in step 201, the count values CNT, SUM, shift amount SFT, etc. are initialized, and in the subsequent step 201, the loop variable i is set to 1 (similar to steps 101 and 102 in FIG. 4). In step 203, the count value SUM (i-1), the shift amount SFT (i-1), and the like are read as in step 104 of FIG. In this embodiment, the shift amount SFT (i-1) is calculated (set) in advance in step 213 (or step 201) described later. In step 203, the shift amount SFT (i-1) is calculated. As long as it is calculated, it suffices if it is calculated before the calculation of the boundary value BASE [j] in step 204.

  In step 204, based on the shift amount SFT (i-1) and approximate error RMD (i-1) calculated in step 203, and the count value (SUM [j]) stored in the appearance frequency management unit 1, The boundary calculation unit 54 calculates a boundary value BASE [j] that divides the code range into sections for each symbol type. In the subsequent step 205, the encoded data code is read. The read encoded data code is stored in the storage unit 51, and the process proceeds to step 206.

  In step 206, based on the boundary value BASE [j] calculated in step 204 and the encoded data code stored in the storage unit 51, the output unit 55 is divided into sections corresponding to the symbol type of the symbol. The section corresponding to the value of the encoded data code is searched and specified from the code range. The symbol type corresponding to the section specified by this, that is, the section including the value of the encoded data code is output. In subsequent step 207, the determination unit 52 determines whether or not it is the last symbol as in step 107 of FIG. 4. If the end condition is satisfied, the process ends. If the end condition is not satisfied, the process proceeds to step 208.

  In step 208, the updating unit 53 updates the lower limit value LOW (i) and the width RNG (i), similarly to step 105 in FIG. In step 209, the determination unit 52 updates the count values CNT (i) and SUM (i) as in step 108 of FIG. In step 210 and step 211, the determination unit 52 determines an update condition. These update conditions are the same as the output conditions shown in steps 109 and 110 in FIG. If any one of the update conditions is satisfied, the process proceeds to step 212; otherwise, the process proceeds to step 213.

  When the update conditions in step 210 and step 211 are satisfied and the process proceeds to step 212, the encoded data code is updated, and the lower limit value LOW (i) and width RNG (i) are updated again. Specifically, the determination unit 52 controls the storage unit 51 to update the encoded data code. Then, in accordance with this control, the storage unit 51 shifts the upper 8 bits of code to the left bit and adds a new code to the lower 8 bits. That is, the storage unit 51 deletes an unnecessary part of the encoded data code, and new encoded data is inserted into the lower bits where a blank (or “NULL”) is created.

  Similarly, the storage unit 51 performs bit shift processing for shifting the lower limit value LOW (i) and the width RNG (i) to the left by 8 bits. In this process, the code range specific value whose value has been reduced is increased again at the same time as the update of the encoded data code, and it is possible to suppress a decrease in the calculation process of the encoding process using the lower limit value LOW and the width RNG. it can. In step 213, the shift amount calculation unit 3 reads the width RNG (i) of the code range storage unit 21 and calculates the shift amount SFT (i) and the approximate error RMD (i) as in step 112 of FIG. To do. When the process of step 213 is completed, the loop variable is incremented (step 214), and the process proceeds to step 203.

  Next, a specific case of the code range according to the present embodiment will be described with reference to the code range transition diagram in the decoding of FIG. In this case, count values of three symbol types “a”, “b”, “c” are preset in the appearance frequency table, and “b”, “encoded by the above-described encoding system as input. The encoded data code corresponding to a ″ is used. When the output of these two symbols Sym (i) is completed, the decoding is also finished (LAST = 2).

  FIG. 9A shows the state of the code range in the initial state (i = 0). The initial width RNG (0) and the lower limit value LOW (0) stored in the code range storage unit 21 are values set in advance before the encoding process (step 201). Further, the values of the lower limit value LOW (0) and the width RNG (0) are the same as those of the encoding system described in the first embodiment. FIG. 9B shows that the shift amount calculation unit 3 uses the shift amount SFT (0) based on the count value (total appearance frequency SUMALL) of the storage unit 11 and the width RNG (0) of the code range storage unit 21. And the state of the code range in which the approximate error RMD (0) is calculated is shown (step 203). In the present embodiment, as in the first embodiment, the code range update unit 22 distributes the approximation error to the symbols “a”, “b”, and “c” at a ratio of 1: 2: 1. assign.

FIG. 9C shows the state of the code range set by the boundary calculation unit 54 when the symbol “b” is output (steps 204 to 206). The boundary calculation unit 54 is based on the shift amount SFT (0) and the approximate error RMD (0) calculated by the shift amount calculation unit 3 and the cumulative appearance frequency SUM [j] (0) stored in the appearance frequency management unit 1. Thus, the boundary value BASE [j] (0) for dividing the code range for each symbol type is calculated. In this case, each boundary value can be expressed by the following equation.

BASE [a] (1) = SUM [a] (0) << SFT (0) + LOW (0)
BASE [b] (1) = SUM [b] (0) << SFT (0) + RMD (0) >> 2 + LOW (0)
BASE [c] (1) = SUM [c] (0) << SFT (0) + RMD (0) >> 2 + 2 + RMD (0) >> 1 + LOW (0)

  Then, the output unit 55 searches for a section including the encoded data code stored in the storage unit 51 based on these boundary values. In this case, the encoded data code encoded by the first embodiment is SUM [b] << SFT (0) + RMD (0) << 2 + LOW (0). Therefore, since the code is included in the section corresponding to the symbol “b”, the symbol “b” is output.

  FIG. 9D shows the state of the code range in which the first symbol output is completed (i = 1). Similar to the initial state, the value (boundary value) specifying the section indicating each symbol type is not stored in the code range storage unit 21 (step 208). FIG. 8E shows that the shift amount calculation unit 3 calculates the shift amount SFT (1) and the approximate error RMD from the count value SUMALL (1) of the storage unit 11 and the width RMG (1) of the code range storage unit 21. The state of the code range for which (1) has been calculated is shown (step 209). Then, as in FIG. 5B, the approximate error is allocated equally to the symbols “a”, “b”, and “c” at a ratio of 1: 2: 1.

  FIG. 9F shows a state where the calculated approximate error RMD (1) is assigned according to the symbol type and updated to a new code range (steps 204 to 206). Note that since the value is not stored in the cumulative appearance frequency SUMALL [a] (1) (0 or “NULL”), the value is 0 even if the left shift process is performed. Therefore, the newly set lower limit value LOW (2) remains the lower limit value LOW (1). Then, the lower limit value LOW (2) and the width RNG (2) corresponding to the next symbol processing as shown in FIG. 5G are updated, and the lower limit value LOW (2) of them encodes the symbol string. Data code is output from the output update unit 42. Then, the output unit 55 searches for a section including the encoded data code stored in the storage unit 51 based on these boundary values. In this case, the encoded data code encoded by the first embodiment is SUM [a] (1) << SFT (1) + LOW (1) (= SUM [b] << SFT (0) + RMD (0) << 2 + LOW (0)). Accordingly, since code is included in the section corresponding to the symbol “a”, the symbol “a” is output.

  As described above, according to the present embodiment, the decoding process can be speeded up and the circuit can be reduced in size for the same reason as in the first embodiment.

The basic processing flow of the first and second embodiments described above is summarized as follows.
(1) The shift amount SFT (i-1) is calculated using the width RNG (i-1) of the code range and the total appearance frequency SUMALL (i-1).
(2) Acquire symbols to be processed before updating the appearance frequency table.
(3) Update lower limit value LOW (i) and width RNG (i).
(4) The appearance frequency table is updated based on the symbols acquired in (2).
(5) Return to (1) and repeat until a predetermined condition is satisfied.

  The difference between encoding and decoding lies in input data (symbol) to be processed in (2). Specifically, in the encoding system, the input data is a symbol string symbol, and in the decoding system, the input data is a symbol output by decoding. Therefore, by matching the initial value of the code range (specific value) and the update rule of the appearance frequency table (number of symbol types prepared in the appearance frequency table, end condition, etc.) Both the decoding system and the reproducibility can be ensured.

  In the first and second embodiments, the processing target is text (character) data such as “a” or “b”. For example, numerical values such as “0” to “255” are processing targets. Also good. Therefore, encoding is possible without being limited to data formats such as image data and audio data. In this case, it is necessary to secure an appearance frequency table (count value) corresponding to the number of symbol types that can be input (j = 256) in the storage unit 11.

  Further, in the above-described two embodiments, a program that realizes the functions of the encoding system of FIG. 1 or the decoding system of FIG. 6 is recorded on a computer-readable recording medium, and recorded on this recording medium. It can also be realized by introducing the program into a computer system. The “computer system” here includes an OS and hardware. The “computer system” also includes a WWW system having a homepage providing environment or a display environment. The “computer-readable recording medium” refers to a portable medium such as a ROM (Read Only Memory), a magnetic disk, an optical disk, a magneto-optical disk, and a hard disk. Further, “a computer-readable recording medium includes a server to which a program is transmitted via a network line such as the Internet, and a volatile memory inside the computer system. Further,“ program ”stores this program. It may be transmitted from a computer system stored in a medium to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program may be a part for realizing a part of information such as a network such as the Internet or a communication line (communication line) such as a telephone line. Moreover, the difference file which can implement | achieve these functions with the combination with the program already recorded by the computer system may be sufficient.

Configuration diagram of encoding system Configuration diagram of code range update unit Configuration diagram of shift amount calculation unit Encoding process flowchart Transition diagram of code range in encoding Configuration diagram of decryption system Configuration of output unit Flow chart of decryption process Transition diagram of code range in decoding

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Appearance frequency management part 11 Storage part 12 Update part 2 Code range management part 21 Code range storage part 22 Code range update part 22a Lower limit calculation part 22b Shifter 22c Shifter 22d Adder 22e Width calculation part 22f Shifter 22g Shifter 22h Adder 3 Shift amount calculation unit 31 Approximation unit 32 Shifter 33 Subtractor 4 First output management unit 41 Determination unit 42 Output update unit 5 Second output management unit 51 Storage unit 52 Determination unit 53 Update unit 54 Boundary calculation unit 55 Output unit 54a Shifter 54b Shifter 54c Adder 55 Output section

Claims (16)

By repeating the process of dividing the code range set by the code range specific value into sections according to the symbol type of the symbol to be processed, and encoding the operation result obtained by the repetition process, a plurality of symbols can be obtained. In an encoding system for encoding a configured symbol sequence,
A storage unit for storing a plurality of count values capable of specifying the appearance frequency of each symbol type included in the symbol string;
An update unit that updates a count value corresponding to the symbol type of the read symbol each time a symbol is read from the symbol string as a processing target;
When one symbol is read as the current processing target, the appearance frequency stored in the storage unit is read before the update unit updates the count value corresponding to the symbol type of the one symbol. By performing an arithmetic process including at least a shift process for performing a bit shift with a shift amount of n (n is a natural number) bits used in the current processing target, on the count value corresponding to the symbol type of the one symbol. A code range update unit for updating the code range specific value;
The division value obtained by dividing the width of the code range specified by the code range specification value updated by the code range update unit by the total appearance frequency specified by the count value is approximated by 2 ⁿ , and obtained by the approximation And a shift amount calculation unit that sets a value n as a shift amount to be used in the next processing target.   When the width of the code range becomes smaller than a predetermined value by the update process of the code range update unit, or when the upper bits of the predetermined range of the code range specific value no longer change, the current processing target The encoding system according to claim 1, further comprising a determination unit that outputs the code range specific value updated by the processing as encoded data. The shift amount calculation unit calculates a difference between a value calculated by a shift process for performing a bit shift with the shift amount obtained by the approximation with respect to the total appearance frequency, and a width of a code range used in the current processing target. Calculate the approximation error that is the value,
The code range update unit apportions the approximation error at a predetermined ratio according to a symbol type, and assigns it to each section of the symbol type constituting the code range used in the next processing target. An encoding system according to claim 1 or 2.   The encoding system according to any one of claims 1 to 3, wherein the code range is specified by a predetermined combination of an upper limit value, a lower limit value, or a width that is the code range specifying value. By repeating the process of dividing the code range set by the code range specific value into sections corresponding to the symbol type of the symbol to be processed, and encoding the operation result obtained by the repetition process, In an encoding computer program for causing a computer to execute an encoding method for encoding a configured symbol string,
A first step of reading one symbol as a current processing target from among a symbol string composed of a plurality of symbols;
A second step of updating a count value corresponding to the symbol type of the one symbol among a plurality of count values capable of specifying the appearance frequency of each symbol type included in the symbol sequence;
Prior to updating the count value corresponding to the symbol type of the one symbol, n (n is a natural number) bits used in the current processing target with respect to the count value corresponding to the symbol type of the one symbol A third step of updating the code range specific value by performing an arithmetic process including at least a shift process for performing a bit shift by a shift amount of:
The division value obtained by dividing the width of the code range specified by the updated code range specification value by the total appearance frequency specified by the count value is approximated by 2 ⁿ , and the value n obtained by the approximation is processed next time A fourth step of setting as a shift amount used in the object;
And a fifth step of repeating the processing from the first step to the fourth step until a predetermined output condition is satisfied while sequentially shifting one symbol to be processed in the symbol string. An encoding computer program for causing a computer to execute a characteristic encoding method.   The output condition is when the width of the code range becomes smaller than a predetermined value due to the update of the code range specific value, or when the upper bits of the predetermined range of the code range specific value no longer change. 6. An encoded computer program as claimed in claim 5, wherein: In the fourth step, the difference between the value calculated by the shift process for performing the bit shift with the shift amount obtained by the approximation with respect to the total appearance frequency and the width of the code range used in the current process target Including a sixth step of calculating an approximation error that is a value;
The third step includes a step of allocating the approximation error at a predetermined ratio according to a symbol type and assigning the approximation error to each section for each symbol type constituting the code range used in the next processing target. An encoding computer program according to claim 5 or 6, characterized in that   8. The encoding computer according to claim 5, wherein the code range is specified by a predetermined combination of an upper limit value, a lower limit value, and a width, which are the code range specification values. 9. program. A section corresponding to the value of the encoded data is specified from the code range set by the code range specifying value and divided into sections corresponding to the symbol type of the symbol, and a symbol corresponding to the specified section is output. In a decoding system that decodes encoded data into a symbol string composed of a plurality of symbols by repeating search processing and arranging symbols obtained by the repetition,
A storage unit that stores a plurality of count values that can specify the appearance frequency of each symbol type output by the search process;
An update unit that updates a count value corresponding to the symbol type of the output symbol each time a symbol is output by the search process;
When one symbol is output as the processing target this time, before the count value corresponding to the symbol type of the one symbol is updated by the update unit,
The appearance frequency stored in the storage unit is read, and the count value corresponding to the symbol type of the one symbol is bit-shifted by the shift amount of n (n is a natural number) bits used in the current process. A code range update unit that sets a code range specific value used in the next process by performing an arithmetic process including at least a shift process;
The division value obtained by dividing the width of the code range specified by the code range specification value set by the code range update unit by the total appearance frequency specified by the count value is approximated by 2 ⁿ , and obtained by the approximation And a shift amount calculation unit that sets a value n as a shift amount used in the next processing.   When the width of the code range becomes smaller than a predetermined value by the update process of the code range update unit, or when the upper bits of the predetermined range of the code range specific value no longer change, the encoded data is The decoding system according to claim 9, further comprising a determination unit that performs a shift process for performing a bit shift by a shift amount of the number of upper bits. The shift amount calculation unit calculates a difference between a value calculated by a shift process for performing a bit shift with the shift amount obtained by the approximation with respect to the total appearance frequency, and a width of a code range used in the current processing target. Calculate the approximation error that is the value,
The code range update unit apportions the approximation error at a predetermined ratio according to a symbol type, and assigns it to each section of the symbol type constituting the code range used in the next processing target. The decoding system according to claim 9 or 10.   The decoding system according to any one of claims 9 to 11, wherein the code range is specified by a predetermined combination of an upper limit value, a lower limit value, or a width that is the code range specifying value. A section corresponding to the value of the encoded data is specified from the code range set by the code range specifying value and divided into sections corresponding to the symbol type of the symbol, and a symbol corresponding to the specified section is output. In a decoding computer program for causing a computer to execute a decoding method for decoding encoded data into a symbol string composed of a plurality of symbols by repeating search processing and arranging symbols obtained by the repetition,
A first step of outputting a symbol type of the one symbol from the encoded data by the search process;
A second step of updating a count value corresponding to the symbol type of the one symbol among a plurality of count values capable of specifying the appearance frequency of each symbol type output by the search process;
Prior to updating the count value corresponding to the symbol type of the one symbol, n (n is a natural number) bits used in the current processing target with respect to the count value corresponding to the symbol type of the one symbol A third step of updating the code range specific value by performing an arithmetic process including at least a shift process for performing a bit shift by a shift amount of:
The division value obtained by dividing the width of the code range specified by the updated code range specification value by the total appearance frequency specified by the count value is approximated by 2 ⁿ , and the value n obtained by the approximation is processed next time A fourth step of setting as a shift amount used in the object;
And a fifth step of repeating the processing from the first step to the fourth step until a predetermined determination condition is satisfied while sequentially shifting one symbol to be processed in the symbol string. A decryption computer program for causing a computer to execute a characteristic decryption method.   The determination condition is when the width of the code range becomes smaller than a predetermined value due to the update of the code range specific value, or when the upper bits of the predetermined range of the code range specific value no longer change. 14. A decryption computer program as claimed in claim 13. In the fourth step, the difference between the value calculated by the shift process for performing the bit shift with the shift amount obtained by the approximation with respect to the total appearance frequency and the width of the code range used in the current process target Including a sixth step of calculating an approximation error that is a value;
The third step includes a step of allocating the approximation error at a predetermined ratio according to a symbol type and assigning the approximation error to each section for each symbol type constituting the code range used in the next processing target. 15. A decoding computer program according to claim 13 or 14, characterized in that:   The decoding computer according to any one of claims 13 to 15, wherein the code range is specified by a predetermined combination of an upper limit value, a lower limit value, or a width that is the code range specifying value. program.

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