JP3673222B2 - Variable length encoding method and apparatus, and variable length decoding method and apparatus - Google Patents

Description

【００３４】
次に、これらの整数値ｍと符号値ｎから次式の計算によって符号語Ｃ（ｎ）を得る。
まず、ｎの値が左辺(1/2)ｍ（ｍ−１）と等しい場合は、符号語Ｃ（ｎ）は次のようにする。
【数２】

それ以外の場合は、
【数３】

として、次の符号語を生成する。
【数４】

【００３５】
一方、復号値生成部３０１では次のような操作を行う。最初のビットが０ならば、それに続く連続する１の数ｒをカウントし、次式で計算される値を復号値ｎとする。
【数５】

【００３６】
もし、最初のビットが１ならば、１が合計３回に出現するまでＬビットの符号化データを読み込み、２番目の１が出現した位置をＳビット目とすると、復号値ｎは次の式で計算される。
【数６】

【００３７】
上述した符号語生成方法によって得られる符号語では、図６に示されるように予め定められた０と１の数によって符号語の区切りが分かり、また同一の符号語長の符号語間のハミング距離が必ず２以上になる。ハミング距離とは周知のように、同一の符号語長の符号語間で０と１が一致しないビットの数のことを指す。さらに、これらの符号語は複数の符号語を語尾を揃えて並べたときに各符号語が一致することがない。したがって、符号語のビットに誤りが入った場合でも自己同期しない性質をもっている。
【００３８】
次に、図７を用いて符号語生成部２０２における符号語生成のための計算手法の他の具体例について説明する。まず、符号値ｎに対して次の不等式を満足する１以上の整数値ｍを求める。
【数７】

【００３９】
次に、この整数値ｍと符号値ｎから次の数式の計算によって符号語Ｃ（ｎ）を得る。
【数８】

ここで、β（ｎ、ｍ）は、整数ｎのｍビット表現である。
一方、復号値生成部３０１では次のような操作を行う。符号化データを２進系列ｂ₁ ｂ₂ …ｂ_L を次の不等式がはじめて成り立つＬビットまで読み込む。
【数９】

次に、得られた２進系列ｂ₁ ｂ₂ …ｂ_L とＬの値から、次式の計算により復号値ｎを計算する。
【数１０】

【００４０】
図６と図７によって生成される符号語は、いずれも最も短い符号語が２ビットであり、それから符号語長は１ビットづつ増加し、同一の符号語長の符号語数は１、２、３、４…と増加してゆく。つまり、幾何分布よりも確率分布の裾が長い分布に対して最適な符号となっている。そのような確率分布は、画像符号化の変換係数の量子化値をランレングス符号化した場合や、動きベクトルの差分値などにおいてしばしば見受けられることから、実用的にも効果が高い。
【００４１】
なお、情報シンボルの生起確率に応じて、符号語生成切り替え信号を使うことで、図６または図７に示した符号とＥｌｉａｓのδ符号と切り替えて使用してもよい。
【００４２】
上述した本発明の可変長符号化及び復号化の処理は、ハードウェアにより実現してもよいし、処理の一部または全部をコンピュータを用いてソフトウェアにより実行することも可能である。
【００４３】
【発明の効果】
以上説明したように本発明によれば、より符号化効率の高い符号語を生成及び復号でき、さらに誤りを検出することができる。
【図面の簡単な説明】
【図１】 本発明の一実施形態に係る可変長符号化／復号化装置を含む符号化／復号化システムの構成を示すブロック図
【図２】 同実施形態における可変長符号化部の構成を示すブロック図
【図３】 同実施形態における可変長復号化部の構成を示すブロック図
【図４】 区間設定の例を示す図
【図５】 情報シンボル対応表の例を示す図
【図６】 同実施形態における符号語生成結果の例を示す図
【図７】 同実施形態における符号語生成結果の他の例を示す図
【図８】 従来の可変長符号での自己同期の例を示す図
【図９】 従来のＥｌｉａｓのδ符号の例を示す図
【符号の説明】
１００…符号化システム
１０１…可変長符号化部
１０２…区間設定部
１０３…伝送／蓄積系
１０４…復号化システム
１０５…区間検出部
１０６…可変長復号化部
１０７…長さ判定部
２０１…情報シンボル対応部
２０２…符号語生成部
３０１…復号値生成部
３０２…情報シンボル対応部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a variable length encoding / decoding method and apparatus.
[0002]
[Prior art]
Variable length coding is a technique for outputting a code word having a code length corresponding to an input information symbol as encoded data. In variable-length coding, based on the appearance frequency (probability of occurrence) of each information symbol, a short code length code is used for frequently appearing information symbols, and a long code length is used for rarely appearing information symbols. By assigning each of these codes, the code word output as encoded data has an average short code length. As a result, the data amount of information can be significantly compressed compared to before encoding. As a method for constructing such a variable length code, an optimum Huffman algorithm for a memoryless information source is known.
[0003]
In general, variable-length coding is performed using a codeword table that associates codewords of variable-length codes with information symbols. In the method using the codeword table, when the number of information symbols to be encoded by the variable length encoding is very large, for example, as a transform coefficient in moving image encoding, the size of the codeword table is excessively large. There is a problem of becoming.
[0004]
There has also been proposed a method for generating a code word by calculation for an information symbol without using a code word table. As a method for generating a code word by calculation, Elias δ code (IEEE Trans. IT vol.IT-21, no.2.pp.194-203, 1975) shown in FIG. Encoding for Golomb's geometric distribution (IEEE Trans. IT vol.IT-12, no.3.pp.399-401, 1966) has been known for some time. There is a problem that the distribution is limited and the coding efficiency is low.
[0005]
Furthermore, a general problem with variable-length codes is that if an error is mixed into the encoded data for some reason, the data after the error is mixed is propagated and correctly decoded by the decoding device. In addition, it is impossible to detect errors. This phenomenon is called self-synchronization, and occurs because the codeword decoded in error when the error is propagated matches the end of the correct codeword, so that the synchronization of the codeword itself is restored.
[0006]
FIG. 8 shows this state. An error occurs in the first bit of the code word c (= 001) of the encoded data shown in FIG. 8A and becomes the same as the code word b. In the decoded data shown in FIG. The ending is coincident with the code word b. At this time, in the decoded data, the synchronization is restored at the code word a next to the code word c in which an error has occurred (self-synchronization), but the number of code words in the decoded data has increased by one. When self-synchronization occurs, codeword synchronization is restored and the codeword itself is correctly decoded.
[0007]
However, in actual coding seen in video coding etc., self-synchronization occurred because prediction was performed at a higher level than the code word or coding was performed based on some kind of grammar. In some cases, grammatically or semantically correct decoding cannot be performed, and no error is detected. Therefore, there is a problem that error countermeasures cannot be taken and the influence of errors appears in the decoding result.
[0008]
[Problems to be solved by the invention]
As described above, the method using the codeword table in the variable length coding based on the prior art has an excessively large table size when the number of information symbols is large, and the information symbol appears in the method of generating the codeword by calculation. Depending on the probability distribution, there is a problem that the encoding efficiency is lowered.
[0009]
Furthermore, the variable-length code based on the prior art has a problem that self-synchronization is likely to occur, so that correct decoding cannot be performed and errors cannot be detected.
[0010]
An object of the present invention is to provide a variable-length encoding / decoding method and apparatus capable of realizing high encoding efficiency without using a large table.
[0011]
Furthermore, another object of the present invention is to provide a variable length encoding / decoding method and apparatus capable of detecting errors.
[0012]
[Means for Solving the Problems]
In order to solve the above problems, in the present invention, a codeword having a codeword length corresponding to the occurrence probability of each information symbol is assigned to each information symbol, and a codeword corresponding to the input information symbol is encoded. In variable-length coding to be output as data, according to one correspondence method selected from a plurality of correspondence methods, a code word is associated with the input information symbol, and a code value representing the value of the associated code word is According to one generation method selected from the plurality of generation methods, a code word is generated by calculation from the code value.
[0013]
On the other hand, in variable-length decoding that decodes variable-length encoded data composed of codewords corresponding to the information symbols thus obtained and outputs a decoding result, one generation method selected from a plurality of generation methods In accordance with the above, a decoded value is generated by calculation from each codeword included in the variable-length encoded data, and the decoded value is associated with an information symbol according to one correspondence method selected from a plurality of correspondence methods, and the associated information The symbol is output as a decoding result.
[0014]
As described above, in the present invention, the code word is made to correspond to the information symbol, the code word is generated by calculation from the code value obtained thereby, and the correspondence method and the generation method can be switched. It is also possible to cope with fluctuations in the occurrence probability of information symbols. In addition, since the code word is generated by calculation, the memory amount required for making the information symbol correspond to the code word and the memory amount for the code word table do not increase even if these are switched.
[0015]
In addition, when the length of the encoded data is known for each predetermined section, if there is no self-synchronization when an error is mixed in the encoded data, a difference occurs in the length of the decoded data. By checking the data length, it can be determined whether or not an error in that section is mixed.
[0016]
Here, when generating a code word by calculation, (a) the code word delimiter is known by a predetermined number of 0s and 1s, and (b) each when a plurality of code words are arranged with their tails aligned. It is desirable to generate codewords configured to satisfy the conditions that the codewords do not match and (c) the Hamming distance between the codewords having the same codeword length is 2 or more.
[0017]
When a codeword is generated in this way, even if a one-bit error occurs in a certain codeword, it does not change to the same codeword as other codewords with the same codeword length. Therefore, the code word configured in this way has the property that it is very difficult to self-synchronize. Therefore, if the length of the encoded data is known in advance, even if an error is mixed in the encoded data, it is self-synchronized. In addition, an error can be detected by finding a bit pattern that is not used, or the possibility that an error can be detected increases because data that cannot be decoded at the end of the encoded data is generated.
[0018]
Further, according to the present invention, a code word having a code word length corresponding to the occurrence probability of each information symbol is assigned to each information symbol, and a code word corresponding to the input information symbol is output as encoded data. A program for causing a computer to perform variable-length coding processing, which associates a code word with an input information symbol according to one correspondence method selected from a plurality of correspondence methods, and associates the associated code word In accordance with a process for outputting a code value representing the value of one and a generation method selected from a plurality of generation methods, the codeword is divided by a predetermined number of 0s and 1s by calculation from the code value (a) As can be seen, (b) when the codewords are arranged with their tails aligned, the codewords do not match, and (c) the Hamming distance between the codewords having the same codeword length Above, it can provide because of the program configured to a process of generating the codeword to perform the computer so as to satisfy the condition that.
[0019]
Further, according to the present invention, (a) a codeword delimiter can be identified by a predetermined number of 0s and 1s corresponding to an information symbol, and (b) each codeword when a plurality of codewords are arranged with their tails aligned. And (c) variable-length encoded data composed of codewords configured to satisfy the condition that the Hamming distance between codewords having the same codeword length is 2 or more A program for causing a computer to perform a variable-length decoding process that outputs a decoding result, calculated from each codeword included in the variable-length encoded data according to one generation method selected from a plurality of generation methods In accordance with a process for generating a decoded value by one and a corresponding method selected from a plurality of corresponding methods, the decoded value is associated with an information symbol, and the associated information symbol is defined as a decoded result. And processing for outputting Te can provide a program for causing the computer.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a configuration of an encoding / decoding system including a variable-length encoding / decoding device according to an embodiment of the present invention. The encoding / decoding system includes an encoding system 100 that encodes information symbols 10 that are roughly divided and outputs variable-length encoded data, and a transmission / storage system that transmits or stores variable-length encoded data. 103 and a decoding system 104 that decodes variable-length encoded data input from the transmission / storage system 103 to generate a decoding result 24 and an error detection result 26.
[0021]
The encoding system 100 includes a variable length encoding unit 101 and an interval setting unit 102 that perform variable length encoding on the input information symbol 10. The variable length coding unit 101 generates a code word of a variable length code corresponding to the value of the input information symbol 10 without using a code word table prepared in advance, and uses this as variable length coded data 14 Output.
[0022]
In the variable length coding unit 101, a plurality of methods (corresponding methods) are prepared for associating information symbols 10 and codewords, and a plurality of methods are associated with a plurality of methods (codeword generating methods) for generating codewords. (Corresponding method) is prepared, and one corresponding method and codeword generating method are selected according to the switching signals 11 and 12 supplied from the outside. It is assumed that the switching signals 11 and 12 are separately encoded and then sent to the decoding system 104 or can be obtained from the values of other encoding parameters in the decoding system 104.
[0023]
The variable length encoded data 14 output from the variable length encoding unit 101 is divided into predetermined intervals by the interval setting unit 102 (referred to as interval setting) and output from the encoding system 100. The encoded data 15 after the section setting from the section setting unit 102 is input to the transmission / storage system 103, and the variable length encoded data 16 output from the transmission storage system 103 is input to the decoding system 104.
[0024]
The decoding system 104 includes a section detection unit 105, a variable length decoding unit 106, and a length determination unit 107. The section detection unit 105 detects the section set by the section setting unit 102 from the input variable length encoded data 16. The variable length encoded data 16 is input to the variable length decoding unit 106 as the variable length encoded data 20 for each section detected by the section detection unit 105. The variable length decoding unit 106 generates a decoded value by calculation from each codeword included in the input variable length encoded data 20 without using a codeword table prepared in advance, and an information symbol is added to the decoded value. Are output as a decoding result 24.
[0025]
In the variable length decoding unit 106, a plurality of methods (decoded value generating methods) are prepared for generating decoded values, and a plurality of methods (corresponding methods) are prepared for associating decoded values with information symbols. , For example, depending on the switching signals 21 and 22 supplied from the encoding system 100 as described above or generated based on the values of other encoding parameters in the decoding system 104 as described above. A correspondence method and a codeword generation method are selected.
[0026]
Further, the variable length decoding unit 106 performs error detection as will be described later, outputs an error detection result 26, and codeword length information 25 indicating the length of a codeword included in the variable length encoded data 20. Is generated and sent to the length determination unit 107. In the length determination unit 107, error detection is performed by checking the codeword length information 25 for each section detected by the section detection unit 105.
[0027]
FIG. 2 shows the configuration of the variable length coding unit 101. The variable length coding unit 101 includes an information symbol correspondence unit 201 and a code word generation unit 202. The information symbol corresponding unit 201 outputs a code value 13 corresponding to the value of the input information symbol 10. The information symbol correspondence unit 201 includes a plurality of correspondence tables, in other words, a plurality of correspondence methods, which are switched by the information symbol correspondence switching signal 11 to select one correspondence table.
[0028]
The codeword generation unit 202 receives the code value 13 from the information correspondence unit 201 as an input and generates the codeword 14 by calculation using a calculation method determined in advance for each code. The codeword generation unit 202 includes a plurality of codeword generation methods, which are switched by the codeword generation switching signal 12 to select one codeword generation method.
[0029]
FIG. 3 shows the configuration of the variable length decoding unit 104. The variable length decoding unit 104 includes a decoded value generation unit 301 and an information symbol correspondence unit 302. In the decoded value generation unit 301, the decoded value 23 is calculated for each section detected by the section detecting unit 105 shown in FIG. 1 from the input variable length encoded data 20 by a calculation method determined in advance for each code. Generate by. The decoded value generation unit 301 includes a plurality of generation methods, which are switched by the decoded value generation switching signal 21 to select one decoded value generation method. Further, the decoded value generation unit 301 has a function of checking the length of the variable-length encoded data 20 for each section detected by the section detection unit 105, detecting an error from the check result, and outputting the error detection result 26. Have.
[0030]
The information symbol corresponding unit 302 receives the decoded value 23 generated by the decoded value generating unit 301 as an input, and outputs the corresponding information symbol as a decoded result 24. The information symbol correspondence unit 302 includes a plurality of correspondence tables, in other words, a plurality of correspondence methods, which are switched by the information symbol correspondence switching signal 21 to select one correspondence table.
[0031]
Next, an example of a section setting method for variable length encoded data in the section setting unit 102 will be described with reference to FIG. In the section setting method of FIG. 4A, the length information of the variable length encoded data exists immediately after the header, and the number of bits of the variable length encoded data is described here. In the section detection unit 105, the number of bits of the encoded data is determined by decoding the length information of the encoded data. The interval setting method in FIG. 4B uses a synchronization code. In this case, the section detection unit 105 counts the number of bits until the next synchronization code, and subtracts the number of bits from the header and stuffing to determine the number of bits of the encoded data.
[0032]
FIG. 5 shows an example of a correspondence table used in the information symbol correspondence unit 201 in FIG. 2 and the information symbol correspondence unit 302 in FIG. 3, and an example of a correspondence relationship between information symbols and code values in each correspondence table. ing. In this example, the value obtained by quantizing a coefficient (for example, DCT coefficient) obtained by orthogonal transform of an image signal for each block in moving image coding is variable length coded by run length coding. It is. In this example, the information symbol is a combination of an EOB (End Of Block) symbol indicating that there is no non-zero coefficient thereafter in the block, a run, and a level. Here, there are two types of symbol correspondence tables A and B, and the correspondence between information symbols and code values can be switched by an information symbol correspondence switching signal.
[0033]
Next, a specific example of a calculation method for codeword generation in the codeword generation unit 202 will be described with reference to FIG. First, an integer value m of 1 or more that satisfies the following inequality is obtained for the code value n.
[Expression 1]

[0034]
Next, a code word C (n) is obtained from the integer value m and the code value n by calculating the following equation.
First, when the value of n is equal to the left side (1/2) m (m−1), the code word C (n) is as follows.
[Expression 2]

Otherwise,
[Equation 3]

Then, the next code word is generated.
[Expression 4]

[0035]
On the other hand, the decoded value generation unit 301 performs the following operation. If the first bit is 0, the number r of successive 1s is counted, and a value calculated by the following equation is set as a decoded value n.
[Equation 5]

[0036]
If the first bit is 1, L-bit encoded data is read until 1 appears three times in total, and the position where the second 1 appears is the S-th bit. Calculated by
[Formula 6]

[0037]
In the code word obtained by the above-described code word generation method, as shown in FIG. 6, the code word delimiter can be identified by a predetermined number of 0 and 1, and the Hamming distance between code words having the same code word length Is always 2 or more. As is well known, the Hamming distance refers to the number of bits in which 0 and 1 do not match between codewords having the same codeword length. Further, these codewords do not match each other when a plurality of codewords are arranged with their tails aligned. Therefore, even if an error occurs in the bit of the code word, it has a property that it does not self-synchronize.
[0038]
Next, another specific example of a calculation method for codeword generation in the codeword generation unit 202 will be described with reference to FIG. First, an integer value m of 1 or more that satisfies the following inequality is obtained for the code value n.
[Expression 7]

[0039]
Next, a code word C (n) is obtained from the integer value m and the code value n by calculating the following mathematical formula.
[Equation 8]

Here, β (n, m) is an m-bit representation of an integer n.
On the other hand, the decoded value generation unit 301 performs the following operation. Encode data into binary sequence b ₁ b ₂ ... b _L Is read up to L bits for which the following inequality holds for the first time.
[Equation 9]

Next, the obtained binary sequence b ₁ b ₂ ... b _L And the value of L, the decoded value n is calculated by the following equation.
[Expression 10]

[0040]
The codewords generated by FIGS. 6 and 7 are both the shortest codeword of 2 bits, and then the codeword length increases by 1 bit, and the number of codewords of the same codeword length is 1, 2, 3 It increases with 4 .... That is, the code is optimal for a distribution having a longer tail of the probability distribution than the geometric distribution. Such a probability distribution is often seen in the case where the quantized value of the transform coefficient of image coding is run-length coded or the difference value of the motion vector.
[0041]
It should be noted that the code shown in FIG. 6 or FIG. 7 and the Elias δ code may be switched and used by using a code word generation switching signal according to the occurrence probability of the information symbol.
[0042]
The above-described variable length coding and decoding processing of the present invention may be realized by hardware, or part or all of the processing may be executed by software using a computer.
[0043]
【The invention's effect】
As described above, according to the present invention, a codeword with higher encoding efficiency can be generated and decoded, and an error can be detected.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of an encoding / decoding system including a variable length encoding / decoding device according to an embodiment of the present invention. FIG. 2 shows a configuration of a variable length encoding unit in the embodiment. FIG. 3 is a block diagram showing a configuration of a variable length decoding unit in the embodiment. FIG. 4 is a diagram showing an example of interval setting. FIG. 5 is a diagram showing an example of an information symbol correspondence table. The figure which shows the example of the codeword production | generation result in the same embodiment. FIG. 7 The figure which shows the other example of the codeword production | generation result in the same embodiment. The figure which shows the example of the self-synchronization in the conventional variable-length code. FIG. 9 is a diagram showing an example of a conventional Elias δ code.
DESCRIPTION OF SYMBOLS 100 ... Coding system 101 ... Variable length encoding part 102 ... Section setting part 103 ... Transmission / storage system 104 ... Decoding system 105 ... Section detection part 106 ... Variable length decoding part 107 ... Length determination part 201 ... Information symbol Corresponding unit 202 ... codeword generating unit 301 ... decoded value generating unit 302 ... information symbol corresponding unit

Claims (7)

In a variable length coding method, codewords having codeword lengths corresponding to the occurrence probability of information symbols are assigned to a plurality of information symbols, respectively, and codewords corresponding to the input information symbols are output as coded data ,
According to one corresponding method selected from a plurality of corresponding methods, associating a codeword with the input information symbol, and outputting a code value representing the value of the associated codeword;
According to one generation method selected from a plurality of generation methods, the code value is calculated from (a) a predetermined number of 0s and 1s by calculation from the code value , and (b) a plurality of code words are terminated. Generate the codeword configured to satisfy the conditions that the codewords do not match when aligned and (c) the Hamming distance between codewords having the same codeword length is 2 or more A variable length encoding method comprising: steps. In a variable-length coding apparatus that assigns a code word having a code word length corresponding to an occurrence probability of an information symbol to a plurality of information symbols, and outputs a code word corresponding to the input information symbol as coded data ,
According to one correspondence method selected from a plurality of correspondence methods, an information symbol correspondence unit that associates a code word with an input information symbol and outputs a code value representing a value of the associated code word;
According to one generation method selected from a plurality of generation methods, the code value is calculated from (a) a predetermined number of 0s and 1s by calculation from the code value , and (b) a plurality of code words are terminated. Generate the codeword configured to satisfy the conditions that the codewords do not match when aligned and (c) the Hamming distance between codewords having the same codeword length is 2 or more A variable length encoding device comprising a codeword generation unit. Corresponding to the information symbol (a) the codeword delimiter can be identified by a predetermined number of 0s and 1s, (b) the codewords do not match when multiple codewords are aligned and c) Variable that decodes variable-length encoded data composed of codewords configured to satisfy the condition that the Hamming distance between codewords having the same codeword length is 2 or more and outputs a decoding result met method length decoding,
Generating a decoded value by calculation from each codeword included in the variable-length encoded data according to one generation method selected from a plurality of generation methods;
A variable-length decoding method comprising the steps of: associating the decoded value with an information symbol according to one correspondence method selected from a plurality of correspondence methods; and outputting the associated information symbol as the decoding result. Corresponding to the information symbol (a) the codeword delimiter can be identified by a predetermined number of 0s and 1s, (b) the codewords do not match when multiple codewords are aligned and c) Variable that decodes variable-length encoded data composed of codewords configured to satisfy the condition that the Hamming distance between codewords having the same codeword length is 2 or more and outputs a decoding result met length decoding apparatus,
According to one generation method selected from a plurality of generation methods, a decoded value generation unit that generates a decoded value by calculation from each codeword included in the variable length encoded data;
Variable length decoding comprising: an information symbol corresponding unit that associates the decoded value with an information symbol and outputs the associated information symbol as the decoding result according to one corresponding method selected from a plurality of corresponding methods apparatus. The variable length decoding device according to claim 4, wherein the decoded value generation unit further detects an error by checking a codeword length of each codeword for each predetermined section detected for the variable length encoded data. A variable-length encoding process for assigning a code word having a code word length corresponding to the occurrence probability of the information symbol to a plurality of information symbols, and outputting a code word corresponding to the input information symbol as encoded data A program for causing a computer to perform
In accordance with one correspondence method selected from a plurality of correspondence methods, a process for associating a code word with an input information symbol and outputting a code value representing the value of the associated code word;
According to one generation method selected from a plurality of generation methods, the code value is calculated from (a) a predetermined number of 0s and 1s by calculation from the code value , and (b) a plurality of code words are terminated. Generate the codeword configured to satisfy the conditions that the codewords do not match when aligned and (c) the Hamming distance between codewords having the same codeword length is 2 or more program order to perform a process on the computer. Corresponding to the information symbol (a) the codeword delimiter can be identified by a predetermined number of 0s and 1s, (b) the codewords do not match when multiple codewords are aligned and c) Variable that decodes variable-length encoded data composed of codewords configured to satisfy the condition that the Hamming distance between codewords having the same codeword length is 2 or more and outputs a decoding result A program for causing a computer to perform a long decoding process,
In accordance with one generation method selected from a plurality of generation methods, a process of generating a decoded value by calculation from each codeword included in the variable length encoded data;
A program for causing the computer to perform processing for associating the decoded value with an information symbol and outputting the associated information symbol as a decoding result in accordance with one correspondence method selected from a plurality of correspondence methods.

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