JP7212543B2 - Decoding device, hologram reproducing device, and decoding method - Google Patents

Description

The present invention relates to a decoding device, a hologram reproducing device, and a decoding method, and more particularly to a decoding device, a hologram reproducing device, and a decoding method suitable for decoding two-dimensional encoded signals. Although the present invention will be described based on an example of a hologram reproducing apparatus, the decoding apparatus and decoding method of the present invention are not limited to the hologram reproducing apparatus.

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

In a holographic memory recording system, generally, a holographic recording medium is irradiated with an object beam carrying digital data together with a reference beam at the same time, and interference fringes formed in the holographic recording medium are written in the optical recording medium to obtain the digital data. record. On the other hand, when a hologram recording medium on which digital data is recorded is irradiated with reference light, diffraction of light occurs due to interference fringes written in the hologram recording medium, and the digital data carried by the object light is reproduced. can be done. An example of a currently used holographic memory recording system will be briefly described with reference to FIGS. 10 and 11. FIG.

First, the recording will be explained. FIG. 10 is a diagram showing an example of an optical arrangement and an optical path (thick chain line) during recording in the holographic memory recording system 100 . Optical elements that are not used during recording are drawn with thin two-dot chain lines. A hologram recording apparatus can be configured using only optical elements used for recording.

After the laser light (here, S-polarized light (vertically polarized light)) that is output from the laser light source 101 and has passed through the shutter 102 is rotated by the half-wave plate 103 to have its plane of polarization rotated by 45 degrees, it passes through a PBS (polarizing beam splitter). ) 104 into P-polarized light and S-polarized light. P-polarized light passes through the shutter 105 after passing through the PBS 104 . After that, the light is magnified by a magnifying lens 106, passes through a PBS 107, and is irradiated onto an SLM (spatial light modulator) 108 made of a reflective liquid crystal element or the like. This irradiated light carries digital data of a two-dimensional image by a black and white bit pattern (pixel pattern) projected on the element surface of the SLM 108, and is converted into S-polarized light (actually, The light from the element displayed in white is converted into S-polarized light), reflected, and returned to the PBS 107 as object light. The object light returned from the SLM 108 is reflected by the PBS 107, passes through an FT (Fourier transform) lens 109, passes through a Nyquist frequency component through a spatial filter 110, cuts frequency components higher than that, and is processed again by an FT (Fourier transform) lens. A hologram recording medium 113 is irradiated with the light through a transformation) lens 111 and an FT (Fourier transformation) lens 112 .

On the other hand, the S-polarized light reflected by the PBS 104 passes through the half-wave plate 117. Here, the half-wave plate 117 and the polarization axis of the beam are aligned, and the plane of polarization of the beam is not rotated. Next, the light enters the PBS 116 , is reflected there, is reflected by the mirror 120 and the galvanomirror 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 by interference on the hologram recording medium 113, and the interference fringes form the hologram. It is written in the recording medium 113 . Thus, the two-dimensional data projected on the SLM 108 are recorded.

Next, reproduction will be described with reference to FIG. FIG. 11 is a diagram showing an example of an optical arrangement and an optical path (thick chain line) during reproduction of the holographic memory recording system 100. FIG. Optical elements that are not used during playback are drawn with thin two-dot chain lines. A hologram reproducing apparatus can be configured by using only the optical element used for reproducing.

Up to the PBS 104, it is the same as during recording, but the transmitted P-polarized light is stopped by the shutter 105. FIG. On the other hand, the reflected S-polarized light has its plane of polarization rotated by 90 degrees by changing the axis of the half-wave plate 117 to the setting of 45 degrees, and becomes P-polarized light. After passing through the PBS 116 , this P-polarized light is reflected by the galvanomirror 115 and enters the hologram recording medium 113 after passing through the relay lens 114 . 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, passes through the PBS 107, and is imaged by the two-dimensional imaging element 118. , the arithmetic unit 119 restores the recorded digital data.

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 spreads the point image widely, and the neighboring point images are close to each other. In such a case, a reproduced image is obtained in which the point images are joined together. 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, the reproduced image is bright in the center of the SLM 108 and slightly dark in the periphery.

In the pixel pattern threshold determination in this case, the threshold must be changed between the peripheral portion and the central portion according to the luminance distribution. However, since the luminance distribution has various dependencies such as recording conditions and reproduction conditions, it cannot be determined in a general way. Therefore, as a recording code, a difference code has been proposed for determining white and black within a certain range. By adopting this method, there is a feature that data can be reproduced by distinguishing between white and black within a certain range.

Further, in the holographic memory recording system, a two-dimensional code (two-dimensional code) developed from the differential code is also used. For example, in hologram recording, only one pixel out of 2×2=4 pixels (pixels) is made white and the others are made black. In other words, 2-bit information is recorded and reproduced using 4 pixels. (Patent Document 1). Hereinafter, a modulation method for expressing n-bit information using r pixels will be referred to as "n:r modulation". A method of recording and reproducing the above 2-bit information using 4 pixels is "2:4 modulation". The n:r modulation can convert n-bit information into a two-dimensional signal using a two-dimensional code (hereinafter referred to as a "symbol") of r pixels.

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

Error correction codes (error correction codes) are roughly divided into block codes and convolutional codes. In recent years, LDPC (Low Density Parity Check) has been widely used in block codes, and turbo codes have been widely used in convolutional codes because they show an error correction capability approaching the Shannon limit.

Among them, the turbo code is not suitable from the point of view of error correction of the recording device because the decoding process is complicated and the latency is relatively large. On the other hand, LDPC is used in various fields 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, the use of LDPC as an error correction code is promising (Patent Documents 2 and 3).

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

In LDPC, the bits to be encoded are generally called "information bits". Also, when performing LDPC encoding, a “parity check matrix” (denoted 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 parity check matrix H described above. A data unit to which check bits are added, that is, a unit of “information bit+check bit” becomes “one LDPC block” which is the minimum unit of LDPC encoding/decoding. The data (LDPC code string) LDPC-encoded in this way is transmitted to a communication channel or recorded on a recording medium.

In the decoding of the LDPC code, first, the "Log Likelihood Ratio (LLR)" of each bit forming the LDPC code string is calculated from the received signal (or the readout signal). This "log-likelihood ratio" is used as information representing the likelihood of each bit value ("0" or "1"), and is abbreviated as "LLR" below.

Here, how to obtain the LLR (where λn is assumed) when the transmission signal is Xn (Xn is +1 or -1) and the reception signal is Yn will be described. LLR can be generally calculated by the following equation (1) from the conditional probability P(Yn|Xn) of the communication channel.

In the case of an LDPC encoding/decoding model assuming a general AWGN (Additive white Gaussian noise) channel, the conditional probability P _AWGN of the channel is given by the following equation (2). be able to. where σ ² is the variance of Gaussian noise and μ takes values of +1 and -1.

Here, when formula (2) is substituted for formula (1), LLR(λn) is given by formula (3) below.

Therefore, the final log-likelihood ratio (LLR) takes the form of equation (4).

LDPC is to calculate the LLR for each bit from the received signal, and estimate each bit value of the information bit for each LDPC block by the LDPC decoding algorithm based on the obtained LLR and a predetermined parity check matrix (H). Decryption.

The LDPC decoding algorithm is based on the 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 the symbol of "0" or "1" that maximizes the conditional probability P is estimated. value. However, if the procedure of calculating the posterior probability for each bit by adding the posterior probability P(Yn|Xn) for all codewords is executed as it is according to the definition, the amount of calculation will be enormous. , for example, a sum-product algorithm has been proposed as an LDPC decoding algorithm for reducing the amount of calculation. This sum-product algorithm can be said to be an approximation algorithm of the MAP decoding method. The sum-product algorithm has already been described in many documents (Non-Patent Documents 1-3).

The inventors of the present invention have already proposed a decoding device and a decoding method for efficiently decoding a signal error-correction coded by LDPC and n:r modulated (Patent Document 4). With this decoding device and decoding method, it is possible to simply and accurately determine the likelihood (LLR) of nbit data from an n:r modulated signal only by arithmetic operations. In this decoding method, since the likelihood of each bit is calculated based on the standardized measurement value (signal value), the method for obtaining LLR based on Patent Document 4 will be described below as the "measurement value reference method". sometimes called

In this way, the development of encoding/decoding devices using two-dimensional codes based on n:r modulated signals is progressing. Multi-valued recording is also actively researched to increase capacity and transfer speed. For example, there has been proposed an optical information recording/reproducing apparatus that utilizes amplitude multi-values that convert to multi-values using intermediate values between white and black, and phase multi-values that converts to multi-values using phase information of light (Patent Reference 5).

Japanese Patent No. 3209493 JP 2007-272973 A JP 2010-186503 A JP 2018-41525 A Japanese Patent No. 6297219

"Practical Method of Constructing LDPC Codes (Part 1)" Nikkei Electronics, August 15, 2005 (pp.126-130) "Practical Method of Constructing LDPC Codes (Part 2)" Nikkei Electronics, August 29, 2005 (pp.127-132) "Practical Method of Constructing LDPC Codes (Part 2)" Nikkei Electronics, September 12, 2005 (pp.137-145)

A signal reproduced via a transmission path or from a recording medium, such as a two-dimensional coded signal, suffers from reading errors with respect to noise intensity. In addition, the luminance level of each pixel also fluctuates due to various factors. Therefore, there is a problem that errors are likely to occur in the decoded data, and even if the error correction code is added, the accuracy of the likelihood becomes small, and the error correction capability cannot be exhibited.

This problem also applies to the holographic memory recording system. When recording and reproducing using two-dimensional encoded data, errors are likely to occur in the reproduced data. There was a problem that the correction ability could not be exhibited.

In addition, the holographic memory recording system uses various multiplexing methods such as angle multiplexing, phase code multiplexing, and spherical reference beam shift multiplexing, enabling multiplex recording of holograms at the same location. can be recorded. However, dirt such as dust adhering to the optical system or recording medium causes bit defects in the reproduced signal, and aberration of optical parts such as lenses blurs the page data image, causing intersymbol interference. All of these noises are fixed noises that occur depending on the position of page data, but no suitable means for removing the fixed noises has been proposed.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention, which has been made in view of the above problems, is to eliminate fixed noise and reduce data errors when decoding information from a reproduced encoded signal. A further object of the present invention is to provide a decoding device, a hologram reproducing device, and a decoding method capable of exhibiting sufficient error correction capability.

In order to solve the above problems, a decoding device according to the present invention is a decoding device for decoding a reproduced coded signal, wherein the reproduced coded signal is demodulated and determined by a trained neural network to generate a reproduced bit string, A log-likelihood ratio of each bit is obtained from the class probabilities calculated by the neural network, and error correction of the reproduced bit string is performed.

Moreover, it is preferable that the decoding device uses the reproduced encoded signal as a two-dimensional encoded signal and the neural network as a convolutional neural network.

Further, the decoding device includes a symbol extraction unit for extracting a symbol consisting of a predetermined number of pixels from the two-dimensional encoded signal, and a convolutional neural network that has been trained to demodulate and judge the extracted symbol and reproduce it. Based on a CNN (convolutional neural network) demodulation determination unit that generates a bit string and a normalized probability obtained by normalizing the class probability calculated by the CNN demodulation determination unit, the log likelihood ratio (LLR) of each bit of the reproduced bit string ), and an error correction decoding unit that performs error correction on the reproduced bit string based on the log-likelihood ratio.

Also, in the decoding device, the symbol extraction unit preferably extracts the symbol including surrounding pixels of the symbol.

Further, the decoding device obtains normalized probabilities obtained by normalizing the class probabilities, and, based on the reproduced bit string, obtains a first reproduced bit string in which a bit for calculating the likelihood is set to 1 and a bit for calculating the likelihood. creating a second reproduced bit string set to 0, and calculating the difference between the normalized probability corresponding to the first reproduced bit string and the normalized probability corresponding to the second reproduced bit string as the logarithmic likelihood ratio in error correction; It is desirable to

Further, the decoding device obtains normalized probabilities obtained by normalizing the class probabilities, and, based on the reproduced bit string, obtains a first reproduced bit string in which a bit for calculating the likelihood is set to 1 and a bit for calculating the likelihood. A second reproduced bit string with 0 is created, and the square of the difference between the normalized probability corresponding to the first reproduced bit string and the normalized probability corresponding to the second reproduced bit string is defined as the logarithmic likelihood in error correction. It is desirable to use the degree ratio.

In order to solve the above problems, a hologram reproducing apparatus according to the present invention is a holographic reproducing apparatus comprising the above-described decoding device, wherein the reproduced encoded signal is a signal reproduced from a hologram recording medium. do.

A decoding method according to the present invention for solving the above problems is a decoding method for decoding a reproduced coded signal, comprising a step of determining demodulation of the reproduced coded signal by a trained neural network to generate a reproduced bit string. and calculating a log-likelihood ratio of each bit from the class probabilities calculated by the neural network; and performing error correction on the reproduced bit string based on the calculated log-likelihood ratio. characterized by

According to the decoding device, hologram reproducing device, and decoding method of the present invention, fixed noise can be removed and data errors can be reduced when information is decoded from a reproduced encoded signal, and furthermore, Sufficient error correction capability can be exhibited.

1 is a block diagram of an example of a decoding device according to Embodiment 1; FIG. It is a figure which shows the system example of image (symbol) recognition by CNN. FIG. 4 is a diagram showing an outline of a demodulation system for reproduced page data; FIG. 10 is a diagram showing the error rate of hard decision results by the measurement value reference method; It is a figure which shows an example of the error correction by a measurement reference method. FIG. 10 is a diagram showing an error rate of demodulation determination results by the CNN system; It is a figure which shows an example of the error correction by a CNN system. FIG. 4 is a diagram comparing error correction characteristics of various LLR calculation methods; FIG. 4 is a diagram showing a comparison of error rate and error correction capability between the CNN scheme and the measurement-based scheme; 1 is an example of an optical arrangement during recording of a holographic memory recording system; It is an example of an optical arrangement during playback of the holographic memory recording system.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described with reference to the drawings.

(Embodiment 1)
A decoding apparatus that uses a two-dimensional coded signal as a reproduced signal (reproduced coded signal) and decodes information from the reproduced signal will be described. FIG. 1 is a block diagram of an example of a decoding device according to Embodiment 1 of the present invention. In this embodiment, a reproduced signal (for example, a signal reproduced from a hologram recording medium) is input to the decoding device 1, and a bit string subjected to error correction decoding is output. A two-dimensional coded signal that is n:r-modulated using pixels (multi-valued pixels) having multi-valued information will be described as an example of a reproduced signal.

The decoding device 1 includes a symbol extraction unit 10, a CNN demodulation determination unit 20, an LLR calculation unit 30, and an error correction decoding unit 40. As the reproduced signal (two-dimensional encoded signal) to be input, measurement data captured (read) by the two-dimensional imaging element 118 in the holographic memory recording system (hologram reproducing apparatus) of FIG. 11 can be used.

[Two-dimensional encoded signal]
A two-dimensional coded signal that is n:r-modulated using pixels having multilevel information and used in this embodiment will be described.

As an example of n:r modulation, 10:9 modulation will be used for explanation. 10:9 modulation is a modulation method that expresses 10-bit data with a two-dimensional code consisting of 9 (3×3) pixels (symbols). Here, amplitude multi-value recording (multi-value recording using light luminance) will be described as an example of the multi-value recording method. Three of the nine pixels are set as bright points, the others are set as dark points (black), and an intermediate value (intermediate brightness) is set for the bright points.

The brightness to be set is, for example, an 8-bit gradation in the range of minimum 0 to maximum 255, and bright points are set to three brightness levels of 255, 170, and 85. One of the three bright points must be 255 (maximum brightness) is entered. The luminance level of dark spots (black) is set to 0 (minimum luminance). This is to facilitate detection of other luminance levels (170, 85) by embedding the reference luminance (maximum luminance 255, minimum luminance 0) in the data. That is, for all two-dimensional codes used for encoding, at least one maximum value pixel and at least one minimum value pixel are included within the set signal value range in r pixels, which are unit symbols. A two-dimensional code containing

If there are 3 brightness levels from 9 pixels and 3 bright spots, and one of them always has the maximum brightness of 255, the total number of ways is 1596. Of these 1596 patterns, the portion actually used as data (two-dimensional code) is 10 bits, so 2 ¹⁰ =1024.

From the 1596 patterns, a data sequence with a high probability of error (for example, when three bright spots are 255, 85, 85, etc.) is deleted, and from the remaining patterns, 1024 patterns are determined as two-dimensional codes, and recorded and reproduced. to use.

Here, although there are three brightness levels, more bit data can be recorded by using a larger number of intermediate brightness levels. Even if a larger number of intermediate luminance levels are used, the decoding method of the invention described below is equally applicable.

[Symbol extractor]
Returning to FIG. 1, the symbol extractor 10 converts the input reproduced signal (two-dimensional encoded signal) into a symbol consisting of a predetermined number of pixels (r pixels corresponding to the original nbit, here 3×3=9). pixels) and extracted, and outputs the extracted symbols to the CNN demodulation determination unit 20 . The extraction may be performed in units of symbols (3×3 pixels), but in order to learn and remove the influence of intersymbol interference, an image including surrounding pixels of the symbol (for example, 5×5 pixels) is used. is desirable.

[CNN demodulation determination unit]
The demodulation determination unit 20 performs demodulation determination of the symbols input from the symbol extraction unit 10 using a neural network. In this embodiment, a convolutional neural network (CNN), which is highly effective for two-dimensional signals (images), is used as a machine learning algorithm used in demodulation determination. Therefore, in this embodiment, it is described as a CNN (convolutional neural network) demodulation determination unit 20 .

The CNN demodulation determination unit 20 performs processing using a pre-trained CNN on the input image (symbol), determines the input symbol based on the output class probability, and determines the determined symbol The corresponding nbit is output to the LLR calculator 30 as a reproduced bit string (bit string data). In addition, as will be described later, the output of the CNN processing (internal potential P _CNN or class probability C _CNN ) is also output to the LLR calculator 30 . The CNN demodulation determination unit 20 can remove fixed noise such as noise caused by the optical system by image recognition using machine learning (for example, deep learning).

FIG. 2 shows a system example of image (symbol) recognition by CNN. The input signal may be each symbol image (for example, 3×3 pixels) in the reproduced page data. The input was an image containing pixels (eg, 5×5 pixels). The CNN has an input layer 21 consisting of a plurality of neuron groups (here, 9 or 25 neurons whose input is the luminance value of each pixel) that receives input signals, and an excitation pattern of neuron groups in the preceding layer. After pattern conversion is performed by using the following function, a neuron group that outputs excitation patterns to the next stage (a convolutional layer 22 that performs filtering to detect features between adjacent pixels, and a connection that combines the results of the convolutional layers and an intermediate layer consisting of layer 23). It receives, converts, and outputs the excitation pattern of neurons in the final intermediate layer.

At the output, neurons (10 ¹⁰ =1024 neurons) corresponding to n bits (here 10 bits) of n:r modulation output internal potentials P _CNN , which are CNN outputs. By processing this internal potential P _CNN with a Softmax function, the respective class probabilities of the estimated symbols are output. Of the 1024 class probabilities for the input symbol (denoted as a bar graph image in FIG. 2), the demodulation decision result (decided symbol = demodulated 10-bit reproduced bit string) is immediately displayed from the one with the highest probability. can get.

[Learning CNN]
Prior machine learning is required for demodulation determination by CNN. Training a CNN can be done as follows.

FIG. 3 shows an outline of a demodulation system for reproduced page data (image data read from a recording medium). The CNN demodulation determination unit 20 in FIG. 1 is actually an aggregate of a plurality of CNN demodulation determination units corresponding to each area (3×3 pixels) of the page data, and the CNN demodulation determination unit to be constructed (convolutional neural network model ) is the same as the number of symbols included in the reproduction page data. The size of the page data in this embodiment is, for example, 1740 pixels×1044 pixels, and there are 201,840 symbols in one page data. Build 840 convolutional neural network models. With this configuration, the reproduced bit strings 1 to 201840 can be reproduced simultaneously from the CNN demodulation decision units 20-1 to 20-201840, respectively, and one page data can be read at once. The reproduced bit strings output in parallel are arranged in a predetermined order, and the input recording bit strings of 1,009,200 bits are demodulated.

Page data (a part of multiplexed data) reproduced from the same hologram recording/reproducing apparatus and a recording bit string (recorded original data) are used as teacher data used for algorithm learning. A large number of reproduced page data are grouped for each symbol position in the page data and input to a CNN (convolutional neural network). The results output from the CNN are compared with the recorded bit string, and each parameter of the CNN is learned using the error backpropagation method. By dividing the page data and performing machine learning on a per-symbol basis (or per 5 x 5 pixels including surrounding pixels) for each position, noise and optical transfer functions that occur depending on each position in the page data The 10:9 modulation demodulation algorithm is mechanically acquired in consideration of (that is, the optical characteristics such as noise and aberration included in the optical system of the hologram recording and reproducing device and the page data demodulation algorithm are acquired at the same time), and high accuracy data can be demodulated. That is, by using CNN, fixed noise can be learned and its influence can be removed.

[LLR calculation unit]
The LLR calculator 30 calculates the log-likelihood ratio (LLR) of each bit based on the output of the CNN (internal potential P _CNN or class probability C _CNN ) and outputs it to the error correction decoder 40 . A method of calculating the likelihood of LDPC using the internal potential P _CNN calculated by CNN will be described.

For example, assuming that the determination result of the CNN demodulation determination unit 20 indicates that the symbol with the highest class probability is a symbol indicating 512 in 10:9 modulation, the demodulated determined reproduced bit string is "1000000000" (=512 ). At this time, internal potentials P _CNN (n): n=0 to 1023 of 1024 symbols corresponding to each 10-bit bit string are obtained simultaneously.

First, with the above equation (3) in mind, the exp of the internal potential P _CNN was taken and normalized from -1 to 1 to calculate the normalized probability P _{CNN-exp-normalize} (n).

The class probability C _CNN of the CNN is generally represented by the following equation (6) from the internal potential P _CNN using the softmax function.

Then, the above equation (5) can also be expressed as the following equation (7) using the class probability C _CNN . That is, the normalized probability P _{CNN-exp-normalize} (n) can be said to be the class probability normalized from −1 to 1.

Next, to find the LLR of the upper 1 bit of the reproduced bit string "1000000000" (=512), the normalized probability P of the bit string (first reproduced bit string) "1000000000" (=512) when the relevant bit is set to 1 _{CNN-exp-normalize} (512) and the normalized probability P _{CNN-exp-normalize} (0) of the bit string (second reproduced bit string) "0000000000" (=0) when the relevant bit is set to 0 are obtained. The conditional probability is obtained by taking the exp of P _{CNN-exp-normalize} (n). From these, LLR (λ _n ) of the upper 1 bit is calculated as shown in the following equation (8).

Therefore, the LLR of the first high-order bit is represented by the following equation (9).

Note that, according to the verification results described later, the LLR may be obtained by the equation (10) obtained by squaring the value of the equation (9). (10) can be used to similarly perform error correction.

For reference, if you want to find the LLR of the second bit from the uppermost bit of the reproduced bit string "1000000000" (=512), the P _{CNN-exp-normalize} (768) and P _{CNN-exp-normalize} (512) of the second reproduced bit string "1000000000" (=512) when the relevant bit is set to 0 are obtained. From these, the LLR (λ _n ) of the second bit from the high order is calculated by the following equation (11).

[Error correction decoder]
The error correction decoding unit 40 performs error correction decoding based on the logarithmic likelihood ratio (LLR) of each bit input from the LLR calculation unit 30, and outputs an error-corrected bit string. This bit string is the output of the decoding device 1 . In the present invention, LDPC is used as encoding means, and the error correction decoding unit 40 can perform decoding using, for example, the above-described sum-product algorithm.

As described above, CNN can be used to perform demodulation determination of reproduced signals and error correction decoding using LLRs.

(Embodiment 2)
So far, the decoding device 1 that decodes information from a two-dimensional encoded signal having multilevel information has been described. A hologram reproducing apparatus that reproduces/decodes a multivalued two-dimensional signal can be realized by constructing the apparatus. This hologram reproducing apparatus uses a reproduced signal (two-dimensional encoded signal) as a reproduced signal read from a hologram recording medium, and can output recorded data after error correction. Effective.

(Embodiment 3)
Further, although the configuration and operation of the decoding device 1 have been described in the first embodiment, the present invention is not limited to this, and is configured as a decoding method for decoding information from a reproduced signal (two-dimensional encoded signal). may That is, according to the data flow of FIG. 1, a step of extracting two-dimensionally encoded symbols from the reproduced signal, and demodulating the reproduced signal (symbol) by a trained neural network (for example, CNN) to determine the reproduced bit string. A decoding method comprising a step of generating, a step of calculating a log-likelihood ratio of each bit from the class probabilities calculated by the neural network, and a step of correcting errors in the reproduced bit string based on the calculated log-likelihood ratio. may be configured as

(Other application forms of the present invention)
The above description is based on the decoding of the n:r-modulated two-dimensional encoded signal reproduced from the hologram recording medium. Other two-dimensional coded signals such as a QR code (registered trademark) transmitted through the transmission may also be used. An LDPC-encoded two-dimensional signal can be decoded in exactly the same manner as in the first embodiment.

Furthermore, the reproduced signal is not limited to a two-dimensional encoded signal, and may be a time-series encoded signal transmitted through a certain transmission path. In this case, a recurrent neural network (RNN: Recurrent Neural Network) or the like, which can process time-series data, can be used as a neural network to perform demodulation determination. In this case, fixed noise generated in the transmission path (for example, in the case of transmitting television broadcasting by terrestrial waves, reflected wave noise generated from a specific building, etc.) can be removed, and the received signal It is possible to perform highly accurate demodulation determination and error correction for (reproduced signal).

[Verification of effect]
Various noises were assumed and added, and the difference between the CNN method of the present invention and the measurement value reference method was verified.

First, the measurement value reference method to be compared will be briefly described. In the measurement-based hard decision, 3 pixels are selected from r pixels (for example, 9 pixels) in descending order of luminance based on the measured value of the reproduced signal, and the pixel with the highest luminance is set as the maximum luminance pixel, and the other pixels are selected. are determined based on a predetermined threshold to determine which luminance level they are. As a result, the luminance and the arrangement of the three pixels with the highest luminance are determined. Based on this, the matching r-pixel symbol (two-dimensional code) is determined from among the 1024 patterns, and the corresponding nbit ( 10 bits) is output as a hard decision result.

In addition, for the error correction decoding of the measurement value standard method, the method of Patent Document 4 was extended to a two-dimensional code using multilevel pixels to calculate LLRs. Specifically, the LLRs used for error correction decoding are set to the first nbit in which the bit for calculating the likelihood is 1 and the second nbit in which the bit for calculating the likelihood is 0, based on the hard-decided nbit data. and convert the 1st nbit to the corresponding 1st r pixel data, the 2nd nbit to the corresponding 2nd r pixel data, and square the distance between the 1st and 2nd r pixel data and the measured value (signal value) of the r pixel It was calculated based on the difference between

The bit error rates and error correction decoding results of the measurement-based method and the CNN method are compared. Here, the LDPC block (information bit+check bit) is assumed to have a configuration of 19500 bits, and the calculation is performed for each of 100 blocks.

FIG. 4 shows the error rate of the hard decision result by the measurement value reference method. The horizontal axis is the 100 block number, and the vertical axis is the bit error rate ber. The average error rate in hard decision was 6.45×10 ⁻² .

FIG. 5 is an example of error correction by the measurement value reference method. The horizontal axis is the number of iterations of the sum-product algorithm for LDPC error correction, and the vertical axis is the error rate after iterative processing. Here, the 30th block (ber=0.0588) is used as a sample, and when the LLR is calculated by the above-described method and LDPC error correction is performed, the error diverges as shown in FIG. Met. Moreover, this tendency was the same for all 100 blocks.

On the other hand, FIG. 6 shows the error rate of the demodulation decision result by the CNN system. As in FIG. 4, the horizontal axis is 100 block numbers, and the vertical axis is the bit error rate ber. The average error rate in the demodulation judgment result was 5.57×10 ⁻³ . A comparison of FIG. 6 and FIG. 4 reveals that the average error rate in CNN demodulation is improved by one order of magnitude compared to hard decision.

Furthermore, FIG. 7 is an example of error correction by the CNN method. As in FIG. 5, the horizontal axis represents the number of iterations of the sum-product algorithm for LDPC error correction, and the vertical axis represents the error rate after iterative processing. Here, the third block (ber = 0.0062) is used as a sample, and the LLR is calculated using equation (9) using the normalized probability P _{CNN-exp-normalize} (n) described above, LDPC error corrected. As can be seen from FIG. 7, the LDPC correction algorithm also converges quickly with 3 iterations. The CNN method is also superior to the measurement-based method in terms of error correction capability.

FIG. 8 compares the error correction characteristics of various LLR calculation methods using the internal potential P _CNN of the CNN. +1 and -1 in parentheses of the function in FIG. 8 are standardized when the predetermined bit is set to 1 (corresponding to +1 of μ) and when the predetermined bit is set to 0 (corresponding to -1 of μ). It means using probabilities.

In addition to formulas (9) and (10), the likelihood (LLR) calculation method includes formula (12) for subtracting the square of the normalized probability and formula (13) for not calculating exp. Formulas were also compared.

The horizontal axis of FIG. 8 is the block number, and indicates the result of calculation for each of the 100 blocks. The vertical axis indicates the number of times of convergence, and the upper limit of iterative calculation is set to 30 times. In other words, points less than 30 converge at that number of times, and 30 times indicates that convergence has not occurred even with the upper limit of 30 times. As is clear from FIG. 8, the two methods of equations (9) and (10) converge immediately, but none of the equations (12) converge, and some of the equations (13) only converges.

Therefore, by using the CNN method of the present invention (particularly, the method using the difference of normalized probabilities), it is possible to correct all data, and furthermore, it is possible to reduce the number of iterations during correction.

FIG. 9 shows a comparison of the error rate and error correction capability between the CNN scheme and the measurement-based scheme. The horizontal axis of FIG. 9 is the hard decision error rate by the measured value reference method, and the vertical axis is the demodulation decision error rate by the CNN method of the present invention. rate. As shown in the comparison between FIG. 4 and FIG. 6, the demodulation decision of the CNN system improves the error rate by about one order of magnitude compared to the hard decision.

In FIG. 9, the error rate of the determination result before correction is plotted on the horizontal axis, and the error correction limit when error correction decoding is performed by each of the CNN method and the measurement value reference method is indicated by a dashed line. The allowable limit of the correctable area by the measurement value standard method was 1.8×10 ^-2 , but by using the CNN method, it is possible to expand the allowable limit to 2.7×10 ^-1 became. Therefore, by using the method according to the CNN method of the present invention, it becomes possible to correct even data that cannot be corrected by the measurement value standard method.

A computer can be suitably used to function as the decryption device 1 described above, and such a computer stores a program describing processing details for realizing each function of the decryption device 1 in a storage unit of the computer. It can be realized by reading out and executing this program by the CPU of the computer. This program can be recorded on a computer-readable recording medium.

Although the above embodiments have been described as representative examples, it will be apparent to those skilled in the art that many modifications and substitutions may be made within the spirit and scope of the invention. Therefore, the present invention should not be construed as limited by the embodiments described above, and various modifications and changes are possible without departing from the scope of the appended claims. For example, it is possible to combine a plurality of configuration blocks described in the embodiments into one or divide one configuration block.

1 decoding device 10 symbol extraction unit 20 CNN demodulation determination unit 21 input layer 22 convolution layer 23 coupling layer 30 LLR calculation unit 40 error correction decoding unit 100 holographic memory recording system 101 laser light source 102 shutter 103 half-wave plate 104 PBS ( polarizing beam splitter)
105 shutter 106 magnifying lens 107 PBS (polarizing 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 Galvanomirror 116 PBS
117 1/2 wavelength plate 118 two-dimensional image sensor 119 arithmetic device 120 mirror 121 galvanomirror 122 relay lens

Claims (8)

A decoding device for decoding a reproduced encoded signal,
determining demodulation of the reproduced coded signal by a trained neural network to generate a reproduced bit string;
A decoding device, wherein a log-likelihood ratio of each bit is obtained from the class probabilities calculated by the neural network, and error correction is performed on the reproduced bit string. 2. The decoding device according to claim 1, wherein said reproduced coded signal is a two-dimensional coded signal, and said neural network is a convolutional neural network. In the decoding device according to claim 2,
a symbol extraction unit for extracting a symbol consisting of a predetermined number of pixels from the two-dimensional encoded signal;
a CNN (convolutional neural network) demodulation determination unit that demodulates and determines the extracted symbols by the trained convolutional neural network to generate a reproduced bit string;
an LLR calculation unit that calculates a logarithmic likelihood ratio (LLR) of each bit of the reproduced bit string based on a normalized probability obtained by normalizing the class probability calculated by the CNN demodulation determination unit;
an error correction decoding unit that performs error correction on the reproduced bit string based on the logarithmic likelihood ratio;
A decoding device, characterized by comprising: 4. The decoding device according to claim 3, wherein said symbol extractor extracts said symbol including surrounding pixels of said symbol. 5. The decoding device according to any one of claims 1 to 4, wherein normalized probabilities obtained by normalizing the class probabilities are obtained, and a first reproduction is performed using 1 as a bit for calculating likelihood based on the reproduced bit string. A bit string and a second reproduced bit string with bits for calculating likelihood set to 0 are created, and the difference between the normalized probability corresponding to the first reproduced bit string and the normalized probability corresponding to the second reproduced bit string is calculated. , the log-likelihood ratio in error correction. 5. The decoding device according to any one of claims 1 to 4, wherein normalized probabilities obtained by normalizing the class probabilities are obtained, and a first reproduction is performed using 1 as a bit for calculating likelihood based on the reproduced bit string. A bit string and a second reproduced bit string with bits for calculating the likelihood set to 0 are created, and the difference between the normalized probability corresponding to the first reproduced bit string and the normalized probability corresponding to the second reproduced bit string is calculated. A decoding device, wherein a square is the logarithmic likelihood ratio in error correction. A hologram reproducing device comprising the decoding device according to any one of claims 1 to 6,
A hologram reproducing apparatus, wherein the reproduced encoded signal is a signal reproduced from a hologram recording medium. A decoding method for decoding a reproduced encoded signal,
determining demodulation of the reproduced coded signal by a trained neural network to generate a reproduced bit string;
calculating a log-likelihood ratio of each bit from the class probabilities calculated by the neural network;
error correction of the reproduced bit string based on the calculated log-likelihood ratio;
A decoding method, characterized in that it comprises:

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