JP2019032917A - Modulation code creating method, hologram recording/reproducing method, and hologram recording/reproducing device - Google Patents

Abstract

To provide a method for generating an n:r modulation code which is used for hologram recording/reproduction and which can improve error correction capability.SOLUTION: For all combinations of patterns of blocks consisting of r bit pixels required for n: r modulation, an Amatrix in which the sum of the Euclidean distances between a bright spot (white) between each pattern is arranged in a matrix is created, for all combinations of n bit strings, a Bmatrix in which the sum of the Euclidean distances of the respective bits between each bit string is arranged in a matrix is created, a squared-sum (D) of the differences between the elements of Amatrix_normalized and Bmatrix_normalized elements normalizing the elements of Amatrix and Bmatrix is calculated, the Amatrix that minimizes the squared-sum (D) is obtained, and, based on the correspondence relationship between Amatrix arrangement and Bmatrix arrangement at this time, the n bit strings and the r bit pattern are made to correspond to each other as an n: r modulation code.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a modulation code creating method, a hologram recording / reproducing method, and a hologram recording / reproducing apparatus, and more particularly to an n: r modulation code creating method and a hologram recording / reproducing method for recording / reproducing an n: r modulated signal, And a hologram recording / reproducing apparatus.

  In recent years, holographic optical memory media (hologram recording media) have attracted attention as media capable of efficiently recording large volumes of data. The holographic memory is expected to be used as a large-capacity memory for images, sounds and computers.

  In a holographic memory recording system, generally, an object beam carrying digital data is simultaneously irradiated onto a hologram recording medium together with a reference light, and interference fringes formed in the hologram recording medium are written on the optical recording medium to thereby generate the digital data. Record. On the other hand, when the hologram recording medium on which the digital data is recorded is irradiated with the reference light, light is diffracted by the interference fringes written in the hologram recording medium, and the digital data carried by the object light is reproduced. Can do. An example of a holographic memory recording system currently used will be briefly described with reference to FIGS.

  First, the recording will be described. FIG. 12 is a diagram showing an example of an optical arrangement and an optical path (thick one-dot chain line) at the time of recording in the holographic memory recording system 100. Note that optical elements that are not used during recording are drawn with thin two-dot chain lines.

  The laser light (here, S-polarized light (longitudinal polarized light)) output from the laser light source 101 and having passed through the shutter 102 has its polarization plane rotated to 45-degree polarized light by the half-wave plate 103, and then PBS (polarized beam splitter). ) 104 and divided into P-polarized light and S-polarized light. P polarized light passes through the shutter 105 after passing through the PBS 104. Thereafter, after being magnified by the magnifying lens 106, the light passes through the PBS 107 and is irradiated onto an SLM (spatial light modulation element) 108 made of a reflective liquid crystal element or the like. The irradiated light carries digital data of a two-dimensional image of a white and black bit pattern projected on the element surface of the SLM 108 and is converted to S-polarized light (actually, white display is performed). The light from the element is converted into S-polarized light) and returned to the PBS 107 as object light. The object light that has returned from the SLM 108 is reflected by the PBS 107, passes through the FT (Fourier transform) lens 109, passes through the Nyquist frequency by the spatial filter 110, cuts the frequency component beyond it, and again FT (Fourier). The hologram recording medium 113 is irradiated through a conversion) lens 111 and an FT (Fourier transform) lens 112.

  On the other hand, the S-polarized light reflected by the PBS 104 passes through the half-wave plate 117, but here, the half-wave plate 117 and the polarization axis of the beam are aligned, and the polarization plane of the beam is not rotated. Next, the light enters the PBS 116, where it is reflected, reflected by the mirror 120 and the galvanometer mirror 121, passes through the relay lens 122, and is irradiated onto the hologram recording medium 113. Since both the reference light and the object light irradiated onto the hologram recording medium 113 in this manner are S-polarized light, interference fringes are formed on the hologram recording medium 113, and the interference fringes are formed as holograms. It will be written on the recording medium 113.

  Next, playback will be described with reference to FIG. FIG. 13 is a diagram showing an example of an optical arrangement and an optical path (thick one-dot chain line) during reproduction of the holographic memory recording system 100. Note that optical elements that are not used at the time of reproduction are drawn with thin two-dot chain lines.

  Up to PBS 104 is the same as in recording, but the transmitted P-polarized light is stopped by the shutter 105. On the other hand, the reflected S-polarized light is changed to the setting value of 45 degrees by changing the axis of the half-wave plate 117 and the polarization plane is rotated by 90 degrees to become P-polarized light. The P-polarized light is reflected by the galvanometer mirror 115 after passing through the PBS 116, passes through the relay lens 114, and enters the hologram recording medium 113. The signal light diffracted by the interference fringes written on the hologram recording medium 113 passes through the FT lens 112, the FT lens 111, the spatial filter 110, and the FT lens 109, and then passes through the PBS 107 and is imaged by the two-dimensional image sensor 118. The digital data is restored by processing with the arithmetic unit 119.

  In such a holographic memory recording system, the light passing through the FT lens is subjected to the effect of a kind of low-pass filter, and the two-dimensional image sensor 118 that reproduces the signal has a large point image and is close to neighboring point images. In this case, the point image is a reconstructed image that is joined. Further, since the light emitted from the laser light source 101 is enlarged to the size of the SLM 108 by the magnifying lens 106, a reproduced image is obtained in which the central portion of the SLM 108 is bright and the peripheral portion is slightly dark.

  In the threshold determination in this case, the threshold must be changed between the peripheral part and the central part according to the luminance distribution. However, since the luminance distribution has various dependencies such as recording conditions and reproduction conditions, it cannot be determined unconditionally. In view of this, a differential code for determining white and black within a certain range has been proposed as a recording code (Patent Document 1). By adopting this method, there is a feature that data can be reproduced by discriminating between white and black within a certain range.

  On the other hand, in the holographic memory recording system, in addition to the luminance unevenness, various noises such as an optical system, noise from a recording medium, and leakage from a multiplexed recording page are added. For this reason, since it is difficult to record and reproduce without error using only the above-described difference code, a normal error correction code is added.

  The error correction code is roughly divided into a block code and a convolutional code. In recent years, LDPC (Low Density Parity Check) is often used for block codes, and turbo codes are often used for convolutional codes because of their error correction capability approaching the Shannon limit.

  Among these, the turbo code is not suitable from the viewpoint of error correction of the recording apparatus because the decoding process is complicated and the latency is relatively large. On the other hand, LDPC is used in various places such as satellite broadcasting, wireless LAN, and wireless Internet because it is linear time decoding and suitable for parallel implementation. Similarly, in the holographic memory recording system, it is promising to use LDPC for error correction (Patent Document 2).

  Here, an outline of LDPC encoding / decoding will be described.

  In LDPC, bits to be encoded are generally called “information bits”. In addition, when performing LDPC encoding, a “check matrix” (indicated as H) is determined in advance. In encoding, first, a “check bit string” (parity) is generated based on the input information bit string and the check matrix H. The data unit to which the check bit is added, that is, the unit of “information bit + check bit” is “1LDPC block” which is the minimum unit of LDPC encoding / decoding. Data thus LDPC-encoded (LDPC code string) is transmitted to a communication path or recorded on a recording medium.

  In decoding of an LDPC code, first, a “log Likelihood Ratio” (LLR) of each bit constituting an LDPC code string is calculated from a received signal (or read signal). This “log likelihood ratio” is used as information representing the likelihood of the value of each bit (“0” or “1”), and is hereinafter abbreviated as “LLR”.

  Here, a description will be given of how to obtain LLR (λn) when the transmission signal is Xn (Xn is +1 or -1) and the reception signal is Yn. From the conditional probability P (Yn | Xn) of the communication path, the LLR can be calculated by the following equation (1).

In the case of an LDPC encoding / decoding model assuming a general AWGN (additive white Gaussian noise) channel, the conditional probability of the channel can be expressed by the following equation (2). Here, σ ² is the variance of Gaussian noise, and b takes values of +1 and −1.

  Here, when the expression (2) is substituted into the expression (1), the LLR (λn) becomes the following expression (3).

  The LLR for each bit is expressed as λ (n). An LLR (λ (n)) for each bit is calculated from the received signal, and based on these λ (n) and a predetermined check matrix (H), each of the information bits for each LDPC block is calculated by the LDPC decoding algorithm. It is LDPC decoding that estimates the bit value.

  The LDPC decoding algorithm is based on a so-called MAP (Maximum A posteriori Possibility) decoding method. In the MAP decoding method, a conditional probability representing the probability that a received word Y is received when a codeword X is transmitted is calculated, and a symbol of “0” or “1” that maximizes the conditional probability P is estimated. Value. However, if the procedure for calculating the posterior probability for each bit by adding the values of the posterior probabilities P (Yn | Xn) for all the code words is executed as it is according to the definition, the calculation amount becomes enormous. For example, a sum-product algorithm has been proposed as an LDPC decoding algorithm for reducing the calculation amount. This sum-product algorithm can be said to be an approximate algorithm of the MAP decoding method. Next, the sum-product algorithm will be described.

  FIG. 14 is a flowchart showing the contents of the decoding process for briefly explaining the contents of the LDPC decoding process by the sum-product algorithm (Non-Patent Document 2).

  The outline of the flowchart is as follows. First, in step 1 (S1), a process for obtaining the message αmn from the check node m to the variable node n is performed, and then in step 2 (S2), the obtained αmn and the log likelihood ratio λn. Based on the above, a process for obtaining the message βnm from the variable node n to the check node m is performed. Thereafter, in step 3 (S3), an approximate value Ln of a log posterior probability ratio described later is obtained, and an estimated bit is determined based on this value.

  Thereafter, in step 4 (S4), a parity check is performed based on the obtained estimated bit. When the estimated bit satisfies the parity check, in step 5 (S5), this is output as a correct estimated bit, and is not satisfied. If so, return to step 1 to repeat the process.

  In each expression of the flowchart, “A (m)” represents a variable node set connected to the check node m, and “A (m) \ n” represents a difference set obtained by removing n from the set A (m). Represents. Similarly, “B (n)” represents a check node set connected to the variable node n, and “B (n) \ m” represents a difference set obtained by removing m from the set B (n). Further, as shown in the figure, the function f (x) is a function defined by the following equation (4), and has the property that f · f is an identity map.

  The function sign (x) is a sign function that takes +1 when x is positive, −1 when negative, and 0 when 0. In the decryption process, the calculation starts with the initial value of “message βnm from variable node n to check node m” being “0”.

  Ln calculated in the estimated bit determination process in step 3 (S3) is an approximate value of an amount called “logarithmic posterior probability ratio” related to the posterior probability P. The absolute value of Ln represents the reliability of estimation, and the larger the value, the higher the reliability of estimation. If the value of Ln is positive, “0” is determined as the value of the estimated bit (0 (Ln> 0)). If the value of Ln is negative, “1” is determined as the estimated bit value (1 (Ln <0)).

  In the parity check process in step 4 (S4), a predetermined check matrix H is used. If the estimated bit sequence satisfies the parity check condition, the estimated bit sequence is output as an estimated value of the information bit sequence transmitted (recorded) (S5).

  In this way, in the decoding process using the sum-product algorithm, the check node process, variable node process, and estimated bit determination process are performed as one round process, and this process is repeated until the estimated bit sequence satisfies the parity check condition. Details of the LDPC decoding algorithm including the sum-product algorithm are described in the literature (Non-Patent Document 1, Non-Patent Document 2, Non-Patent Document 3, etc.).

  By the way, since a general signal is a time-series one-dimensional signal, the likelihood value may be calculated by applying the amplitude value of the received signal to Equation (3). On the other hand, in the hologram recording, as described above, a difference code may be used for countermeasures such as uneven brightness. In such a case, the received signal cannot be directly applied to Equation (3).

  Therefore, an example of likelihood calculation when using a difference code will be described. In hologram recording, it has been attempted to record / reproduce 2 × 2 4-bit pixels by making only one bit white from the other and black the other, that is, using 2 bits of information of 4 bits. Hereinafter, a modulation method that expresses nbit information using rbit is referred to as “n: r modulation”. The method for recording / reproducing the 2-bit information using 4 bits is “2: 4 modulation”. The n: r modulation can be realized, for example, by expressing nbit information as rbit by a predetermined number of bit arrangements (pixel arrangements) in r locations. For example, when converting a signal into two-dimensional data, This is used to remove the direct current component of.

  When using 2: 4 modulation, the received value of 2 bits can be obtained by the following equation (5), with the measured values of each element of rbit (4 bits) as r1 to r4.

  Each received word Yn (reproduced signal) is 1 when there is no noise, and when there is noise, it has a normal distribution with 1 as an average value. Therefore, the conditional probability corresponding to equation (2) is (6) to (9).

  From this, for the original 2 bits, the first bit LLR is obtained by the following equation (10), and the second bit LLR is obtained by the following equation (11).

  LDPC error correction decoding can be performed using this LLR (Patent Document 2).

  In this way, an encoding and error correction decoding method combining n: r modulation and LDPC has been proposed. The original 2-bit LLR is obtained from the measurement value of 4-bit two-dimensional data in Patent Document 2, and this LLR is obtained. However, the method of correcting errors in LDPC using the method has a problem that the amount of calculation increases when the code length is increased.

  In addition, in 9:16 modulation in which 9-bit information is expressed by 16 bits, an LDPC likelihood calculation method has been proposed (Patent Document 3). However, since this calculation method also performs rearrangement many times and requires various calculations such as detection of the minimum value, it is not versatile and difficult to apply when the code length becomes large. There was a problem.

  Therefore, the present inventors do not perform a measurement bit estimation from the measurement value likelihood to obtain the final bit, but directly determine the path, that is, the measurement value (rbit) likelihood from the final bit. A method called (nbit) estimation has been proposed (Japanese Patent Application No. 2006-175893).

  Here, the likelihood determination method (LLR calculation procedure) proposed by the present inventors will be described based on the flowchart of FIG. 15 and the example of the reception (read) signal shown in FIG.

  An example of n: r modulation will be described using 5: 9 modulation. In the holographic memory recording system, 5: 9 modulation is a modulation code in which 5 bits of data are converted into 9 bits (3 × 3) pixels, two of the nine pixels are white, and the others are black. It is. Since two of nine pixels are white, the number of selections is 36 as shown in the following equation (12).

Since 5-bit data is 2 ⁵ = 32, 5: 9 modulation can be supported by selecting 32 out of 36 types.

  At the time of hologram recording / reproduction, two white pixels are identified in the reproduced 3 × 3 pixels, and 5 bits are decoded by the arrangement of the pixels. That is, if the LLR of 5-bit data can be finally determined as the likelihood from the reproduction (measurement) data, LDPC decoding with 5 bits before 5: 9 modulation may be performed.

In step 1 (S1) of the flowchart of FIG. 15, the rbit measurement data that has been blocked is read. Here, the _9- bit block input signal data (a _{1 to} a ₉ ) shown in FIG. For example, in the case of 8-bit gradation measurement data acquired by an image sensor in a holographic memory recording system, the data of each bit is a gradation signal of 0 to 255.

Next, in step 2 (S2), conversion from an rbit input signal to nbit (nbit hard decision) is performed. Here, ₉ bits of measurement data (a _{1 to} a ₉ ) of (1) is made to correspond to a black and white (1, 0) data pattern, and a hard decision is made as to what 5 bits are supported. In this case, for example, the measurement data is arranged in order from the data with the highest luminance, the upper two luminances are determined to be white, and the hard determination result is obtained from the position. In the example of FIG. 16, among the 9-bit measurement data of (1), the data with the highest luminance (for example, a ₆ ) and the data with the next highest luminance (for example, a ₇ ) are set to white [1], and the other data are Corresponding to black [0], 9-bit data “000001100” is obtained (corresponding to the data in FIG. 16 (4)), and “10011” in FIG. 16 (2) corresponding to the 9-bit data is obtained. This is derived as a hard decision result.

  Next, as step 3 (S3), k = 1 is set. This k means that the process is to obtain likelihood information (LLR) of the k-th bit from the top of nbit.

  As step 4 (S4), first, an nbit (first nbit) with the determination result of the k-th bit from the top as 1 is created for the nbit obtained in step 2 (S2). For example, when the likelihood (LLR) of the upper 1 bit (k = 1) of the hard decision result is obtained, only the upper 1 bit is set to “1”, and the other bits are the nbit (first nbit) that remains the hard decision result. create. In the example of FIG. 16, since the first bit of the hard decision result (“10011”) is 1, the first nbit is (2), which matches the nbit of the hard decision result. Next, for the nbit obtained in step 2 (S2), an nbit (second nbit) in which the determination result of the k-th bit from the top is set to 0 is created. For example, in the process for obtaining the likelihood (LLR) of the upper 1 bit (k = 1), an nbit (second nbit) is generated in which only the upper 1 bit is set to “0” and the other bits are left as a hard decision result. In the example of FIG. 16, the upper 1 bit (leftmost bit) of the 5-bit data “10011” of FIG. 16B is set to “0” (inverted), and the second nbit (3) of “00011” is created. A portion (in this case, upper 1 bit) surrounded by a thick frame of (2) and (3) is a bit for obtaining the likelihood (LLR).

  In step 5 (S5), a bit-by-bit difference between the converted data of the first nbit rbit obtained in step 4 (S4) and the converted data of the second nbit rbit is calculated. That is, 9 bits ((4) “00000100” in FIG. 16) assigned to the 5 bits are obtained from “10011” of the first nbit (= hard decision result) obtained in step 4 (S4). Similarly, 9 bits ((5) “100010000” in FIG. 16) allocated to 5 bits of the second nbit are obtained from the obtained second nbit (“00011”). Then, a 9-bit bit string (4) assigned to the first nbit with the likelihood determination bit (higher 1 bit) being “1” and a 9-bit assigned to the second nbit with the likelihood determination bit being “0”. The difference from the bit string (5) is taken. That is, ((4)-(5)) is obtained for each 9-bit bit to obtain the data string “−1000-11100” of (6). The part where the bit string (4) and the bit string (5) do not match (here, the first, fifth, sixth and seventh bits surrounded by a frame) becomes 1 or -1 in the data string of (6), and the other The bit is 0. In the case of 5: 9 modulation, since data 1 is 2 bits out of 9 bits, the number of mismatched bits is only 4 bits at maximum. As to whether to perform (4)-(5) or (5)-(4) as the calculation for obtaining the difference, the maximum value of the measurement data corresponds to “−1” in the next normalization process. Since it can change depending on whether it is made to correspond to “+1” or not, it is not fixed.

In step 6 (S6), the rbit measurement data is normalized. For example, the _9- bit measurement data (a _{1 to} a ₉ ) shown in FIG. 16 (1) is expressed by the following equation (13), with the maximum value (max (a ₁ ,..., A ₉ )) and the minimum among the 9 data. Based on the value (min (a ₁ ,..., A ₉ )), normalization from −1 to 1 is performed to obtain normalized data (a ₁ ′ to a ₉ ′) in FIG. For example, when the measurement data obtained by the image sensor is gradation data with a minimum of 15 and a maximum of 200, the data distributed in 185 gradations is normalized from -1 to 1 to correspond.

Note that whether the maximum / minimum of the measurement data (a _{1 to} a ₉ ) corresponds to −1 to +1 or +1 to −1 is calculated as (4) − (5) Or (5)-(4) is set, and an appropriate LLR is set as appropriate. Further, when the measurement data (a _{1 to} a ₉ ) is distributed from −1 to 1 as in the case of the received signal transmitted through the communication path, for example, it is particularly necessary to perform the normalization process. Absent.

As step 7 (S7), the difference data obtained in step 5 (S5) and the rbit data normalized in S6 (rbit measurement data if normalization is not required) are multiplied bit by bit ( Product). Note that even if multiplication is performed, the difference data is 1 or −1. Therefore, the multiplication is substantially only the operation of the sign of the measurement data, and the amount of calculation is small. Then, an average value of the entire multiplication results is obtained. For example, in the example of FIG. 16, (−a ₁ ′ −a ₅ ′ + a ₆ ′ + a ₇ ′) is obtained as the product of the difference data and the standardized measurement data, and this is calculated as the number of bits in which the difference occurs ( Here, the average value of the whole is obtained by dividing by 4). Then, this average value is regarded as a received signal Yn as shown in FIG.

In step 8 (S8), the LLR as the likelihood of the kth bit is calculated using the calculation result in step 7 (S7) as the received signal Yn. That is, Yn (average value) in FIG. 16 (8) is substituted for Yn in the above-described equation (3). At this time, the noise σ ² may be obtained as an actual measurement value or an appropriate value may be input as an estimated value. The obtained result is defined as the log likelihood ratio (LLR) of the upper 1 bit (k = 1) of the nbit data.

  Thereafter, in step 9 (S9), it is determined whether k = n. If the determination result is Yes (k = n), the process ends. If No (k <n), the process proceeds to step 10 (S10).

  In step 10 (S10), 1 is added to k, and the process is performed again from step 4 (S4). That is, in the above step, the most significant 1 bit in 5 bits has been described, but in the next process, the likelihood of the second bit in 5 bits is obtained with k = 2. When calculating the likelihood (LLR) of the second bit, similarly, based on the nbit data of the hard decision result, the second nbit (k = 2) is set to “1” (see FIG. In the example of “1611”, “11011”) and the second nbit (“10011” in the example of FIG. 16) in which the second bit is “0” are created, and the same calculation is performed.

  By performing such an arithmetic process, it is possible to determine the likelihood (LLR) of the bit string (nbit) from the rbit measurement data and further to determine the bit. In this calculation, only basic four arithmetic operations such as difference, multiplication, and average value are performed. Therefore, the likelihood (LLR) can be calculated very quickly and efficiently. After that, error correction based on the likelihood of n bits can be performed to realize highly accurate data decoding.

  In the description of FIG. 16, (2) is a hard decision result, but is replaced with an estimated bit in the LDPC iterative calculation.

Japanese Patent No. 3209493 JP 2007-272773 A JP 2010-186503 A

"Practical method of constructing LDPC codes (Part 1)" Nikkei Electronics August 15, 2005 (pages 126-130) "Practical construction method of LDPC code (middle)" Nikkei Electronics August 29, 2005 issue (pp. 127-132) "Practical construction method of LDPC code (2)" Nikkei Electronics September 12, 2005 issue (pp.137-145)

  In conventional recording systems using n: r modulation, an nbit bit string and an rbit pixel block are arbitrarily associated, and the correlation between a pixel (symbol) read error and a bit string bit error is It was not considered.

  This will be described by taking 5: 9 modulation as an example. As described above, 5: 9 modulation is a modulation code in which 5 bits of data are converted into 9 bits (3 × 3) pixels, two of the nine pixels are white, and the others are black. The number of selections is 36 as shown in equation (12). FIG. 2 shows all 36 patterns. FIG. 2 mechanically creates all 36 patterns in which 2 are white from 3 × 3 pixels, and is given temporary numbers from $ 0 to $ 35. In the pattern shown in FIG. 2, one white (white 1) is first arranged at the upper left and the other white (white 2) is arranged at the left center is set to $ 0, and then white 1 is fixed. The white 2 placed at the lower left is set to $ 1, and similarly the white 2 placement is moved sequentially to create a pattern of $ 2 to $ 7, and then the white 1 is fixed at the left center and the white 2 The arrangement is sequentially moved to create a pattern of $ 8 to $ 14, and similarly, the arrangement of white 1 and white 2 is sequentially moved to create 36 patterns mechanically.

  In the conventional 5: 9 modulation, these 36 patterns and a 5-bit bit string are arbitrarily associated with each other, so that a pattern reading error may cause a large bit error. For example, a pattern in which white is arranged in the upper left and the left center (pattern $ 0 in FIG. 2) corresponds to data 0 (bit string “00000”), and a pattern in which white is arranged in the upper center and the left center (in FIG. 2). Assume that data 7 (bit string “00111”) is associated with pattern $ 9). When the recorded pattern $ 0 is reproduced, there is a possibility that one of white of the pattern $ 0 is erroneously read as a neighboring pixel, and the pattern $ 0 may be determined as the pattern $ 9. That is, an error of 1 pixel (symbol) may occur in the reproduced signal for hologram recording, and an error of 3 bits may occur in the final bit string.

  As described above, in the conventional hologram recording / reproducing apparatus using n: r modulation, there is no correlation between the nbit data string and the rbit pattern, which is an error in decoding the nbit bit string data from the measured value. Was one of the causes.

  The present inventors further provide the proposed decoding method shown in FIGS. 15 and 16 with a correlation between the nbit data string and the rbit pattern, that is, the likelihood of the measured value and the final value. We found that the error correction capability can be improved by correlating with the likelihood of the correct bit.

  Accordingly, an object of the present invention made in view of the above problems is to provide an n: r modulation code generation method capable of improving the error correction capability.

  Another object of the present invention is to perform a recording / reproducing process based on an n: r modulation signal to improve the error correction capability, and to reduce the error rate of the reproduced signal. An object of the present invention is to provide a hologram recording / reproducing apparatus that can perform the above-described process.

In order to solve the above problems, a modulation code generation method according to the present invention is a modulation code generation method for n: r modulation, which is a pattern of a block composed of a number of rbit pixels necessary for n: r modulation. For all combinations, the sum of the Euclidean distances between the bright spots (white) is obtained, and the process of creating an Amatrix in which the sum of the Euclidean distances between the bright spots (white) between the patterns is arranged in a matrix, and all combinations of bit strings of nbits For each of the above, the sum of the Euclidean distances of the respective bits between the bit strings, the process of creating a Bmatrix in which the sum of the Euclidean distances of the respective bits between the bit strings is arranged in a matrix, and the matrix elements of each of the Amatrix and Bmatrix are standardized To create Amatrix_normalized and Bmatrix_normalized, standardized Calculating the sum of squares (D) of the differences between the elements of the matrixes by the following equation:
The sum of squares (D) is calculated by changing the array of Amatrix, the Amatrix that minimizes the sum of squares (D) is obtained, and the bit string of nbits is determined from the correspondence between the sequence of Amatrix and the sequence of Bmatrix at this time. And an rbit pattern in association with each other to form an n: r modulation code.

  In order to solve the above-described problem, the hologram recording method according to the present invention creates an n: r modulation code by the modulation code creation method, and, at the time of recording, converts nbit data to 2 bits of rbit by the n: r modulation code. A dimensional code is recorded on a recording medium.

  In order to solve the above problems, a hologram reproducing method according to the present invention creates an n: r modulation code by the modulation code creating method, and at the time of reproduction, from an n: r modulated signal reproduced from a recording medium, A bit for calculating the likelihood based on hard-decided nbit data, and a bit for calculating the likelihood based on the hard-decided nbit data from the rbit reproduction signal. The first nbit and the second nbit in which the bit for calculating the likelihood is 0 are created, and the difference between the rbit converted data corresponding to the first nbit and the rbit converted data corresponding to the second nbit is normalized. a step of calculating a likelihood of the bit based on an average value of a product of each bit of the rbit reproduction signal and an error correction of the nbit based on the calculated likelihood; Characterized in that it comprises a step of performing a decoding process.

In order to solve the above problems, a hologram recording / reproducing apparatus according to the present invention extracts an rbit from an n: r modulated signal reproduced from a recording medium, and converts the rbit reproduced signal into an n: r modulation table. In the hologram recording / reproducing apparatus that performs nbit determination based on the stored n: r modulation code, the n: r modulation code stored in the n: r modulation table is the entire block pattern composed of rbit pixels. Amatrix_normalized, which is a standardized Amatrix in which the sum of Euclidean distances between bright spots (white) between patterns is arranged in a matrix, and the sum of Euclidean distances of each bit string between each bit string for all combinations of nbit bit strings A matrix with Bmatrix_normalized that standardizes Bmatrix with matrix arrangement The sum of squares (D) of the differences between the elements of each of the nodes (the following equation) is 90 of the value of the square sum (D) obtained using Amatrix in which a block pattern composed of rbit pixels is randomly arranged. It is an n: r modulation code of an nbit bit string and an rbit pattern having a correspondence relationship between an Amatrix sequence and a Bmatrix sequence that are equal to or less than%.

In order to solve the above problems, a hologram recording / reproducing apparatus according to the present invention extracts an rbit from an n: r modulated signal reproduced from a recording medium, and converts the rbit reproduced signal into an n: r modulation table. In the hologram recording / reproducing apparatus that performs nbit determination based on the stored n: r modulation code, the n: r modulation table is a 5: 9 modulation table, and 5: 9 stored in the 5: 9 modulation table. The 9 modulation codes are Amatrix_normalized, which is a standardized Amatrix in which the sum of the Euclidean distances between the bright points (white) between the patterns is matrix-arranged for all combinations of 32 block patterns consisting of 9-bit pixels, and 5 bits. Matrix of sum of Euclidean distance of each bit string between all bit string combinations A bit string of n bits having a correspondence relationship between an Amatrix sequence and a Bmatrix sequence in which the sum of squares (D) of the elements of the difference between the matrix and the Bmatrix_normalized standardized Bmatrix is equal to or less than 2122 And a 5: 9 modulation code of the rbit pattern.

  In addition, the hologram recording / reproducing apparatus uses a block extraction unit that blocks the reproduced n: r modulated signal into rbit blocks, and an n: r modulation code from the blocked rbit input signal. Based on hard decision unit that performs nbit hard decision, based on nbit data that has been hard decided, create first nbit with 1 bit to calculate likelihood and second nbit with 0 bit to calculate likelihood Then, the likelihood of the bit is calculated based on the average value of the product of each bit of the difference between the rbit conversion data corresponding to the first nbit and the rbit conversion data corresponding to the second nbit and the rbit input signal. And an error correction decoding unit that performs an nbit error correction decoding process based on the likelihood calculated by the LLR determination unit. Desirable.

  In the hologram recording / reproducing apparatus, it is desirable that the reproduced n: r modulated signal is subjected to error correction coding processing using an LDPC code.

  According to the modulation code generation method of the present invention, it is possible to generate an n: r modulation code that can improve the error correction capability.

  Further, according to the hologram recording / reproducing method and the hologram recording / reproducing apparatus of the present invention, the error correction capability can be improved in the hologram recording / reproducing based on the n: r modulation signal, and the error rate of the reproduced signal is lowered. Can be

It is a figure explaining calculation of the sum of the Euclidean distance between the bright spots (white) between two patterns. It is a figure which shows a response | compatibility with 36 patterns of a 3x3 block, and a temporary number. It is an example of the result of the Euclidean distance sum between the bright spots (white) between the mutual patterns of 36 kinds of blocks. It is a figure which shows the pattern of 32 selected blocks. This is the result of the sum of distances between 32 bit strings. It is a figure explaining the derivation method of the optimal arrangement | sequence by a genetic algorithm. It is an example of the optimal solution of the correspondence between 5 bits and a 3 × 3 block pattern. It is a block diagram of an example of the decoding apparatus of the hologram recording / reproducing apparatus of this invention. It is a figure which shows the comparison of the hard decision result by 5: 9 modulation code of this invention and a prior art example. It is a figure which shows the comparison of the LDPC error correction by 5: 9 modulation code of this invention and a prior art example. It is a figure which shows the comparison of the LDPC error correction convergence frequency by 5: 9 modulation code of this invention and a prior art example. It is an example of the optical layout at the time of recording in a holographic memory recording system. It is an example of the optical arrangement | positioning figure at the time of reproduction | regeneration in a holographic memory recording system. It is a flowchart which shows the LDPC decoding process by a sum-product algorithm. It is a flowchart which shows the efficient likelihood determination method. It is a figure explaining an efficient likelihood determination method based on an example of a reception (reading) signal.

  In order to solve the problem of the present invention, a combination of an nbit data string and an rbit pixel pattern so that the sum of the Euclidean distances between measured patterns and the final inter-code distance have similar characteristics. By optimizing the error characteristics, the error characteristics are improved. Embodiments of the present invention will be described below.

  An example of n: r modulation will be described using 5: 9 modulation. The present invention is not limited to 5: 9 modulation but can be applied to other modulation schemes such as 9:16 modulation and 15:25 modulation.

  A modulation code (correspondence between the data string and the pattern) that increases the relationship between the nbit data (data string) and the rbit pixel pattern was obtained by the following steps [1] to [8].

[1] The sum of Euclidean distances between bright spots (white) between patterns of hologram recording (3 × 3 blocks) is calculated.

  “Sum of Euclidean distances between bright spots (white) between patterns” means that when the patterns of two blocks are overlapped, the bright spot (white) of the other pattern from the center of the bright spot (white) of one pattern ) Is the sum of all straight line distances (Euclidean distances) to the center.

  FIG. 1 will be described as an example. The block 1 on the left side of FIG. 1 has a pattern to which $ 3 is assigned in the block pattern list of FIG. Further, the block 2 on the right side has a pattern to which $ 30 is assigned in the pattern list of FIG. The “sum of Euclidean distances between bright spots (white)” (sometimes simply referred to as “sum of Euclidean distances”) of these two patterns is calculated as the following equation (14). (In the following equation (14), || means the absolute value of the distance.)

  Similarly, the sum of Euclidean distances between bright spots (white) is calculated in 36 × 36 mutual patterns to obtain a 36 × 36 matrix. Of course, since the relationship between the pattern $ 1 and the pattern $ 2 and the relationship between the pattern $ 2 and the pattern $ 1 are the same, the calculation can be omitted by entering the same value. Further, the sum of Euclidean distances between the same patterns of pattern $ 1 and pattern $ 1 is zero. The calculation results are shown in FIG.

[2] Select 32 patterns to be used for nbit (5 bits) display.

  Of the 36 calculated patterns, 32 patterns are required, so there is a high possibility that reading errors will increase, that is, there are many cases where the sum of the Euclidean distances between other patterns and bright points (white) is short. Select four patterns and delete them.

  The four patterns of $ 10, $ 21, $ 26, and $ 28 are targeted for deletion. These patterns are judged to be patterns having a large number of appearances of 3.414 (eight times) with the smallest sum of Euclidean distances between bright spots (white) (8 times) and short distances from other patterns (FIG. 3). Each of these four patterns was a pattern in which white was arranged at the center of the 3 × 3 block and above, below, left, and right.

  Next, numbers # 0 to # 31 are assigned again to 32 patterns obtained by excluding the above four patterns from 36 methods for taking two white colors out of 3 × 3, and used as pattern identification numbers. . FIG. 4 shows the patterns of 32 selected blocks.

[3] A 32 × 32 matrix is created for the 32 selected patterns, and the sum of the Euclidean distances between bright points (white) between the patterns is calculated again (not shown).

  The matrix thus obtained is designated as Amatrix (32, 32).

[4] The mutual Euclidean distance is similarly calculated for nbit (5-bit) bit strings.

  The sum of the distance of each bit between bit strings is calculated with 32 bit strings of n bits (5 bits). For example, the sum of the Euclidean distances of each bit between the bit string “00101” and the bit string “11111” (actually, the sum of the absolute values of the differences in the numerical values. Corresponding to “sum”, it is referred to as “sum of Euclidean distance” between bit strings.) Is calculated as the following equation (15). Since the bit difference can only take values of 1, 0, -1, a square value may be used instead of the absolute value.

  Similarly, the sum of Euclidean distances is calculated using 32 × 32 bit strings, and a 32 × 32 matrix is obtained. As in the above [1], 0 is set in the case of self-self.

  The matrix thus obtained is designated as Bmatrix (32, 32). FIG. 5 shows the result of the sum of the Euclidean distances between the 32 bit strings. The matrix thus obtained is designated as Bmatrix (32, 32).

[5] Normalize values in each matrix.

In each matrix, the maximum value and the minimum value (excluding 0) of each value are obtained, and the values are normalized. For example, the value is normalized to a value of 0 to 10. The diagonal matrix is 0.
Standardized Amatrix and Bmatrix are called as follows.
Amatrix_normalized (32,32)
Bmatrix_normalized (32,32)

[6] Next, the sum of squares (D) of the differences between the respective normalized matrices obtained in [5] is calculated.

  The sum of squares (D) is a sum obtained by squaring the difference between the elements (i, j) of the two normalized matrices (32 × 32), and is obtained by the following equation (16).

[7] The order of the Amatrix patterns is exchanged and the sum of squares (D) is recalculated.

It is preferable to calculate for all the rearranged sequences. In this case, 32! = 2.63 × 10 ³⁵ types.

  The reason why the sum of squares (D) is recalculated with various Amatrix patterns rearranged is to find a more preferable correspondence between Amatrix and Bmatrix. Therefore, since it takes a very long time to perform this calculation in all cases, it is possible to use a genetic algorithm as an optimization method.

  The genetic algorithm method is also described. FIG. 6 is a diagram for explaining a method for deriving an optimal arrangement (steps (1) to (3) among them).

(1) Arrange the patterns # 1 to # 32 at random. For example, make four of them. Furthermore, four patterns in which the patterns # 1 to # 32 are arranged at random are made.

(2) Divide a total of eight lines in half from the middle point.

(3) Multiply the halves in all streets and join (cross) each to create a new row. (At this time, 8 × 8 = 64 arrangements are possible.)

(4) A matrix (64 patterns) is created with the created arrangement, and the above-mentioned sum of squares (D) is calculated.

(5) Select four evaluation values with a small D, and return to (1). From the second time on, four new random sequences are added.

(6) After a certain number of times have passed, select the remaining matrix having the smallest evaluation value D.

  By using this genetic algorithm, the possibility of a local solution cannot be denied, but the intended matrix can be obtained at a relatively high speed.

[8] Amatrix that minimizes the sum of squares (D) is obtained.

  It is determined that the arrangement of Amatrix in which the sum of squares (D) at this time has the minimum value has a high correlation with the bit arrangement of nbits (final bits) in Bmatrix.

  By selecting this highly correlated sequence, it is possible to apply the likelihood of the measurement point to the likelihood of the final bit string at the time of calculation using likelihood such as LDPC.

  FIG. 7 shows a correspondence relationship between each Amatrix pattern in which the sum of squares (D) has the minimum value and the final bit nbit (5 bits), which is obtained using the genetic algorithm. FIG. 7 is an example of an optimal solution of the correspondence (5: 9 modulation code) between 5 bits and a 3 × 3 block pattern. The number corresponding to each pattern means a 5-bit bit string, where “1” indicates “00001” and “31” indicates “11111”.

  When the original FIG. 4 is mechanically associated with 5 bits (when pattern $ 0 is associated with “00000” and pattern $ 31 is associated with “11111”), the calculated square sum (evaluation value) D is Although it was 2358, the sum of squares (evaluation value) D decreased to 1965 by optimizing the arrangement of the patterns. In other words, it can be seen that the relevance between the matrices increased by performing the rearrangement.

  In the subsequent verification, in the case of the 5: 9 modulation code, if the square sum (D) of the difference between the standardized Amatrix and Bmatrix elements is “2122” or less, the error correction capability is greatly improved. Was confirmed. A modulation code based on Amatrix with the sum of squares (D) being the minimum value (1965) exhibits the highest error correction capability, but the modulation code when the sum of squares (D) is "2122" or less is the minimum value In this case, the error correction ability was almost comparable. Therefore, a 5: 9 modulation code having a correspondence relationship between an Amatrix sequence and a Bmatrix sequence whose square sum (D) is “2122” or less is hereinafter referred to as an “optimized 5: 9 modulation code”. And Note that “2122” of the sum of squares (D) is when the bit string and the pattern are mechanically associated with each other (this is because the bit string and the pattern are not intentionally associated with each other. This is equivalent to 90% of “2358” of the square sum (D) of the bit string and the pattern. Also, in other n: r modulation codes, modulation codes based on Amatrix that are square sums (D) of 90% or less of square sums (D) when bit strings and patterns are initially associated with random patterns are The error correction capability is greatly improved. Therefore, in general, the correspondence between the arrangement of Amatrix and the arrangement of Bmatrix in which the sum of squares (D) is 90% or less of the sum of squares (D) obtained by using Amatrix of randomly arranged patterns is shown. The modulation code that is included can be referred to as an “optimized modulation code”.

  The hologram recording / reproducing method and hologram recording / reproducing apparatus using the optimized n: r modulation code of the present invention will be described below.

  In the hologram recording method using the optimized n: r modulation code of the present invention, first, an optimized n: r modulation code is obtained in accordance with the steps [1] to [8] described above, and then the optimum Hologram recording with improved error correction capability by converting the nbit data (preferably error correction encoded nbit data) into a two-dimensional code of rbit and recording it on a recording medium using the converted n: r modulation code Can do.

  The hologram reproducing method of the present invention obtains an optimized n: r modulation code, and then obtains the nbit likelihood from the rbit measurement data according to the flowchart of FIG. Further error correction is performed. That is, rbit is extracted from the input signal modulated by the optimized n: r modulation code of the present invention, and nbit hard decision is performed from the rbit input signal. Based on the hard-determined nbit data, a first nbit with a bit for calculating likelihood is set to 1, and a second nbit with a bit for calculating likelihood is set to 0, and rbit conversion data corresponding to the first nbit is generated. The likelihood of the bit is calculated based on the difference between the rbit conversion data corresponding to the second nbit and the bitwise product of the rbit input signal. Thereafter, the n-bit error correction decoding process is performed based on the calculated likelihood.

  Next, the hologram recording / reproducing apparatus of the present invention includes the optimized n: r modulation code described above as an n: r modulation table. Then, n-bit data (preferably n-bit data subjected to error correction coding) is modulated with the optimized n: r modulation code, and recorded on the recording medium as rbit two-dimensional data. In this way, hologram recording with improved error correction capability can be performed during decoding.

  FIG. 8 is a block diagram of an example of a decoding device of the hologram recording / reproducing device as an embodiment of the present invention.

  The decoding apparatus 10 includes a block extraction unit 11, a hard decision unit 12, an LLR calculation unit 13, and an error correction decoding unit 14, and includes an optimized n: r modulation code as an n: r modulation table 15. . The decoding device 10 receives an n: r modulation signal and outputs nbit data subjected to error correction decoding. Here, it is desirable that the input n: r modulation signal is subjected to error correction coding (for example, LDPC coding) at the stage of the nbit signal (before conversion to rbit). This n: r modulation signal is modulated with the optimized n: r modulation code of the present invention. In the hologram recording / reproducing apparatus of FIG. 13, the measurement data imaged (read) by the two-dimensional image sensor 118 is obtained. Can be used.

  The block extraction unit 11 blocks the n: r modulated signal (n: r modulated input signal) into rbit blocks (rbit units corresponding to the original nbits), and the extracted blocks to the hard decision unit 12 Output. For example, when 5: 9 modulation is used in the holographic memory storage system of FIGS. 12 and 13, a 9-bit data unit composed of 3 × 3 pixels is one block.

  The hard decision unit 12 performs an nbit hard decision based on the rbit input signal data input from the block extraction unit 11 and outputs the decision result to the LLR calculation unit 13. For example, the rbit pattern is determined based on the intensity of the input signal, and the n: r modulation table 15 is referenced to output the nbit corresponding to this rbit as the hard decision result. Specifically, the processing of step 1 (S1) and step 2 (S2) in FIG. 15 is performed.

  The LLR calculation unit 13 calculates an LLR as likelihood information for each bit of the n-bit data input from the hard decision unit 12 and outputs the LLR to the error correction decoding unit 14. The LLR is calculated by creating a first nbit in which the LLR calculation target bit is 1 and a second nbit in which the LLR calculation target bit is 0 in the hard-decided nbit conversion data, and the difference between the respective rbit conversion data And the likelihood (LLR) is calculated based on the average value of values obtained by multiplying the input signal (rbit measurement data) for each bit. Specifically, the processing from step 3 (S3) to step 10 (S10) in FIG. 15 is performed. Although not shown, the LLR calculation unit 13 also refers to the n: r modulation table 15 for conversion between nbits and rbits.

  The error correction decoding unit 14 performs error correction decoding corresponding to the error correction coding of the input signal based on the LLR of the nbit signal input from the LLR calculation unit 13. For example, if the error correction coding is LDPC coding, the above-described LDPC decoding process is performed. Estimated bits are determined by error correction decoding processing, and the obtained estimated bits are output to the LLR calculator 13 to perform likelihood (LLR) calculation again. As a result of the iterative process, when an estimated bit satisfying the parity check is obtained, it is output from the decoding device 10 as nbit data subjected to error correction decoding.

  In the hologram recording / reproducing apparatus in FIG. 13, the decoding apparatus 10 can be realized by the arithmetic unit 119.

(inspection result)
Hologram recording / reproduction was performed using the n: r modulation code created by the n: r modulation code creation method of the present invention, and the resulting error rate and the like were verified.

  FIG. 9 is a diagram showing a comparison of hard decision results by the 5: 9 modulation code of the present invention and the conventional example. The horizontal axis represents the signal-to-noise ratio (SNR) (dB), and the vertical axis represents the error rate of the reproduction code. The graph of ● shown as “optimization” in FIG. 9 is a hard decision result when recording / reproducing with the 5: 9 modulation code according to the present invention shown in FIG. 7, and the graph of ○ shown as “conventional” Is a hard decision result when recording / reproduction is performed with a 5: 9 modulation code according to an arbitrary correspondence shown in FIG. Even in the hard decision result, the error rate is improved when the modulation code of the present invention is used than in the conventional case. Therefore, the n: r modulation code of the present invention is effective not only when performing error correction, but also by a normal hard decision result, and by having it as an n: r modulation table in a wide general hologram recording / reproducing apparatus, It can be applied.

  FIG. 10 is a diagram showing a comparison of LDPC error correction using the 5: 9 modulation code of the present invention and the conventional example. In FIG. 10A, the horizontal axis represents the signal-to-noise ratio (dB), and the vertical axis represents the error rate after error correction by LDPC. In FIG. 10B, the horizontal axis represents the signal-to-noise ratio (dB), and the vertical axis represents the total number of error correction repetitions by LDPC. Here, in order to perform verification with a sufficient number of data, data is acquired using 48 sets of 4577 LDPC blocks. The meanings of the “optimization” and “conventional” graphs in the figure are the same as those in FIG. The result of FIG. 10 shows the result of error correction using the likelihood (LLR) derived by the likelihood determination method shown in FIGS. 15 and 16.

  When the optimized n: r modulation code of the present invention is used, the error rate after LDPC error correction is reduced by one digit or more than before, and the number of repetitions is greatly reduced, so that the convergence is achieved quickly. Therefore, it was verified that the n: r modulation signal according to the present invention can improve the error correction capability in hologram recording and can reduce the error rate of the reproduced signal.

  FIG. 11 is a diagram showing a comparison of the number of LDPC error correction convergence using the 5: 9 modulation code of the present invention and the conventional example. FIG. 11A shows the number of LDPC error correction convergence times when recording / reproducing is performed with the 5: 9 modulation code according to the present invention shown in FIG. 7, and FIG. The number of times of LDPC error correction convergence when recording / reproducing with 5: 9 modulation code is shown. Here, verification was performed with 4577 LDPC blocks. In LDPC, calculations and determinations are repeated using rows and columns using the likelihood of measured values. Of course, when there are few errors, the number of repetitions decreases, and when there are many errors, the number of repetitions increases. Referring to FIG. 11, in the conventional case (B), the number of repetitions is large and there are many long lines (blocks with a large number of repetitions). However, in the case of optimization (A), the number of lines is large. It can be seen that is decreasing. In other words, it can be said that by optimizing the matrix, the error correction capability can be further exhibited.

  Although the above embodiment has been described as a representative example, it will be apparent to those skilled in the art that many changes and substitutions can be made within the spirit and scope of the invention. Therefore, the present invention should not be construed as being limited by the above-described embodiments, and various modifications and changes can be made without departing from the scope of the claims. For example, a plurality of constituent blocks described in the embodiments can be combined into one, or one constituent block can be divided.

DESCRIPTION OF SYMBOLS 10 Decoding apparatus 11 Block extraction part 12 Hard decision part 13 LLR calculation part 14 Error correction decoding part 15 n: r modulation table 101 Laser light source 102 Shutter 103 1/2 wavelength plate 104 PBS (polarization beam splitter)
105 Shutter 106 Magnifying Lens 107 PBS (Polarized Beam Splitter)
108 SLM (Spatial Light Modulator)
109 FT lens 110 Spatial filter 111 FT lens 112 FT lens 113 Hologram recording medium 114 Relay lens 115 Galvano mirror 116 PBS
117 half-wave plate 118 two-dimensional image sensor 119 arithmetic unit 120 mirror 121 galvanometer mirror 122 relay lens

Claims (7)

A modulation code generation method for n: r modulation,
n: Sum of Euclidean distances between bright points (white) for all combinations of block patterns composed of rbit pixels necessary for r modulation, and sum of Euclidean distances between bright points (white) between each pattern Creating an Amatrix with a matrix arrangement;
For all combinations of nbit bit strings, obtaining a sum of Euclidean distances of each bit between the bit strings, and creating a Bmatrix in which the sum of the Euclidean distances of each bit between the bit strings is arranged in a matrix;
Normalizing each matrix element of Amatrix and Bmatrix to create Amatrix_normalized and Bmatrix_normalized;
A step of calculating a sum of squares (D) of differences between the elements of the normalized matrix by the following equation (1):
The sum of squares (D) is calculated by changing the array of Amatrix, the Amatrix that minimizes the sum of squares (D) is obtained, and the bit string of nbits is determined from the correspondence between the sequence of Amatrix and the sequence of Bmatrix at this time. And an nbit modulation pattern in association with the rbit pattern;
A modulation code generating method comprising: An n: r modulation code is created by the modulation code creation method according to claim 1,
A hologram recording method for recording n-bit data into an rbit two-dimensional code by the n: r modulation code on a recording medium during recording. An n: r modulation code is created by the modulation code creation method according to claim 1,
Extracting rbit from an n: r modulated signal reproduced from a recording medium during reproduction;
Performing nbit hard decision based on the n: r modulation code from the rbit reproduction signal;
Based on the hard-determined nbit data, a first nbit with a bit for calculating likelihood is set to 1, and a second nbit with a bit for calculating likelihood is set to 0, and rbit conversion data corresponding to the first nbit is generated. Calculating the likelihood of the bit based on the difference between the rbit converted data corresponding to the second nbit and the bitwise product of the standardized rbit reproduction signal;
A hologram reproducing method comprising a step of performing an n-bit error correction decoding process based on the calculated likelihood. Rbit is extracted from the n: r modulated signal reproduced from the recording medium, and nbit is determined from the rbit reproduction signal based on the n: r modulation code stored in the n: r modulation table. In the hologram recording / reproducing apparatus,
The n: r modulation code stored in the n: r modulation table is:
For all combinations of block patterns of rbit pixels, Amatrix_normalized, which is a standardized Amatrix in which the sum of the Euclidean distances between the bright points (white) between the patterns is arranged in a matrix, and for all combinations of nbit bit strings, A block in which the sum of squares (D) [Expression (1)] of the difference between each element of the matrix and Bmatrix_normalized, which is a standardized Bmatrix in which the sum of Euclidean distances of each bit between the bit strings is arranged in a matrix, is composed of rbit pixels. Between an nbit bit string and an rbit pattern having a correspondence relationship between an Amatrix sequence and a Bmatrix sequence that are 90% or less of the value of the sum of squares (D) obtained by using an Amatrix in which a pattern of Rb is randomly arranged n: r modulation code That, hologram recording and reproducing apparatus.
Rbit is extracted from the n: r modulated signal reproduced from the recording medium, and nbit is determined from the rbit reproduction signal based on the n: r modulation code stored in the n: r modulation table. In the hologram recording / reproducing apparatus,
The n: r modulation table is a 5: 9 modulation table, and the 5: 9 modulation code stored in the 5: 9 modulation table is:
Amatrix_normalized standardized Amatrix, which is a matrix arrangement of the sum of the Euclidean distances between bright points (white) between each pattern, and all combinations of 5 bit bit strings for all combinations of 32 block patterns consisting of 9 bit pixels , The sum of squares (D) [Equation (1)] of the difference between each element of the matrix and Bmatrix_normalized, which is a standardized Bmatrix in which the sum of the Euclidean distances of each bit between the bit strings is arranged in a matrix, is 2122 or less. A hologram recording / reproducing apparatus, which is a 5: 9 modulation code of an n-bit bit string and an rbit pattern having a correspondence relationship between an Amatrix sequence and a Bmatrix sequence.
The hologram recording / reproducing apparatus according to claim 4 or 5,
A block extractor that blocks the regenerated n: r modulated signal into rbit blocks;
A hard decision unit that performs an nbit hard decision by the n: r modulation code from the blocked rbit input signal;
Based on the hard-determined nbit data, a first nbit with a bit for calculating likelihood is set to 1, and a second nbit with a bit for calculating likelihood is set to 0, and rbit conversion data corresponding to the first nbit is generated. And an LLR determination unit that calculates the likelihood of the bits based on the difference between the rbit conversion data corresponding to the second nbit and the bitwise product of the rbit input signal,
A hologram recording / reproducing apparatus comprising: an error correction decoding unit that performs n-bit error correction decoding processing based on the likelihood calculated by the LLR determination unit. 7. The hologram recording / reproducing apparatus according to claim 6, wherein the reproduced n: r modulated signal is subjected to error correction coding processing using an LDPC code.