Softness detection device, softness detection method, and program

Abstract

The present invention provides a soft decision device that performs a soft decision on the (n+1)th symbol of a transmitted signal with a symbol multi-value degree of m, the soft decision device comprising a control unit that estimates a branch metric which is a distance obtained using a Viterbi algorithm on the basis of an estimated transfer function which is the estimation result of a transfer function of a transmission path, and a received signal, and is the distance in a distance function that indicates the likelihood of transitioning from the nth symbol of the transmitted signal to each candidate for the (n+1)th symbol, estimates a path metric which is the sum of the distance that is obtained using the Viterbi algorithm on the basis of the result of the branch metric estimation process, is the distance in the distance function, and is the distance indicating the likelihood that each candidate for the (n+1)th symbol of the transmitted signal is a symbol of the transmitted signal, and the distance of a prescribed remaining path of the transmitted signal, and estimates the likelihood that the kth bit in the (n+1)th symbol of the transmitted signal is a prescribed bit.

Description

[Technical Field]

[0001] The present invention relates to a softness determination device, a softness determination method, and a program. This application claims priority based on PCT / JP2022 / 030392, which was filed internationally on 9 August 2022, and the contents of that application are incorporated herein by reference. [Background technology]

[0002] In order to cope with the recent increase in network traffic, research is underway to increase the speed and distance of optical transmission systems. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] DD Falconer, et al., 'Adaptive channel memory truncation for maximum likelihood sequence estimation,' The Bell System Technical Journal, vol. 52, no. 9, pp. 1541 - 1562 (1973) [Overview of the project] [Problems that the invention aims to solve]

[0004] However, in optical transmission systems, signal distortion and noise increase with increasing speed and distance. Therefore, a technique is needed to estimate the symbol of the transmitted signal, which is the optical signal transmitted by the transmitter. It has been proposed to estimate the symbol of the transmitted signal using the inverse function of the transfer function of the transmission line. However, estimation using the proposed technique has sometimes been inaccurate.

[0005] In view of the above circumstances, the present invention aims to provide a technique for estimating the symbol of a transmitted signal with higher accuracy. [Means for solving the problem]

[0006] One aspect of the present invention is a soft determination device that performs a soft determination for the (n+1)th symbol (n is an integer from 1 to N, N is an integer from 1 to N) of a transmitted signal with a symbol multi-level index of m (m is an integer of 2 or more), comprising: a branch metric estimation process that estimates a branch metric, which is a distance obtained by the Viterbi algorithm, a distance indicated by a predetermined distance function, and a distance indicating the likelihood of transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal, based on an estimated transfer function, which is a previously obtained estimated result of the transfer function of the transmission path through which the transmitted signal propagates, and a received signal, which is the result of receiving the transmitted signal; and a branch metric estimation process that estimates a branch metric, which is a distance obtained by the Viterbi algorithm, a distance indicated by a predetermined distance function, and a distance indicating the likelihood of transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal, based on the result of the branch metric estimation process. The soft decision device comprises a control unit that performs: a path metric estimation process that estimates a path metric which is the sum of the distance indicating the likelihood that each candidate for the (n+1)th symbol of the signal is the symbol of the transmitted signal and the distances of the first to nth remaining paths of the transmitted signal; and a bit likelihood estimation process that uses the path metrics of each candidate for the (n+1)th symbol of the transmitted signal obtained by the path metric estimation process, and without using any path metrics other than the path metric of each candidate for the (n+1)th symbol of the transmitted signal, estimates the likelihood that the kth bit (k is an integer between 1 and m) of the transmitted signal is a predetermined bit, and the control unit obtains the likelihood estimated by the bit likelihood estimation process as the result of the soft decision.

[0007] One aspect of the present invention is a soft determination method for performing a soft determination on a primary symbol which is the (n+1)th symbol (n is an integer from 1 to N; N is an integer from 1 to N) of a transmitted signal with a symbol multi-level index of m (m is an integer of 2 or more), comprising: a branch metric estimation process which estimates a branch metric which is a distance obtained by the Viterbi algorithm, is a distance indicated by a predetermined distance function, and represents the likelihood of transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal, based on an estimated transfer function which is a previously obtained estimated result of the transfer function of the transmission path through which the transmitted signal propagates, and a received signal which is the result of receiving the transmitted signal; and a branch metric estimation process which estimates a branch metric which is a distance obtained by the Viterbi algorithm, is a distance indicated by a predetermined distance function, and represents the likelihood of transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal, based on the result of the branch metric estimation process A soft decision method comprising: a path metric estimation process that estimates a path metric which is the sum of the distance indicating the likelihood that each candidate for the (n+1)th symbol is the symbol of the transmitted signal and the distances of the first to the nth remaining paths of the transmitted signal; and a bit likelihood estimation process that uses the path metrics of each candidate for the (n+1)th symbol of the transmitted signal obtained by the path metric estimation process, and without using any path metrics other than the path metric of each candidate for the (n+1)th symbol of the transmitted signal, estimates the likelihood that the kth bit (k is an integer between 1 and m) of the transmitted signal is a predetermined bit, wherein the control step obtains the likelihood estimated by the bit likelihood estimation process as the result of the soft decision.

[0008] One aspect of the present invention is a program for causing a computer to function as the above-mentioned soft judgment device. [Effects of the Invention]

[0009] This invention makes it possible to estimate the symbol of a transmitted signal with higher accuracy. [Brief explanation of the drawing]

[0010] [Figure 1] An explanatory diagram illustrating an optical transmission system according to an embodiment. [Figure 2] An explanatory diagram illustrating the Viterbi algorithm in an embodiment. [Figure 3] A diagram showing an example of the hardware configuration of the soft judgment device in the embodiment. [Figure 4] A flowchart showing a first example of the processing flow performed by the soft judgment device in the embodiment. [Figure 5] A flowchart showing a second example of the processing flow performed by the soft determination device in the embodiment. [Figure 6] Figure 1 shows an example of experimental results in an embodiment. [Figure 7] Figure 2 shows an example of experimental results in an embodiment. [Figure 8] A diagram showing an example of the configuration of the control unit in the embodiment. [Figure 9] A flowchart showing a third example of the processing flow performed by the soft judgment device in the embodiment. [Figure 10] A figure showing an example of a bit likelihood histogram in an embodiment. [Figure 11] Figure 3 shows an example of experimental results in the embodiment. [Modes for carrying out the invention]

[0011] (First Embodiment) Figure 1 is an explanatory diagram illustrating an optical transmission system 100 of an embodiment. The optical transmission system 100 comprises a transmitter 1, a transmission line 2, a receiver 3, and a soft determination device 4. The transmitter 1 transmits an optical signal. Hereinafter, the optical signal transmitted by the transmitter 1 will be referred to as the transmitted signal. In the optical transmission system 100, the symbol multi-level index of the transmitted signal was m (where m is an integer of 1 or more). Hereinafter, the symbol of the transmitted signal will be referred to as the main symbol.

[0012] Transmission path 2 is a transmission path through which optical signals propagate, such as an optical fiber. The transmission signal sent by transmitter 1 propagates through transmission path 2 and reaches receiver 3. Receiver 3 receives the optical signal that has propagated through transmission path 2. Hereinafter, the result of the receiver receiving the optical signal that has propagated through transmission path 2 will be referred to as the received signal.

[0013] The transfer function of transmission line 2 is given by the vector H = {h1, ..., h l Represented as}, the received signal y n is, x n H+W n Therefore, H is a vector whose elements are the weight coefficients. Thus, h1, ..., h l These are all weight coefficients. l is the memory length. That is, l is the time extension of the transfer function. x n This is a sequence of symbols representing the transmitted signal, and it is a sequence of symbols containing symbols from the (n-l+1)th symbol to the nth symbol. The dot (·) represents the inner product. W n This represents the white noise added to the optical signal as it propagates through transmission path 2.

[0014] The soft determination device 4 performs a soft determination on the (n+1)th symbol of the transmitted signal (where n is an integer between 1 and N, and N is an integer greater than or equal to 1). The soft determination device 4 includes a control unit 40 which has a processor 91 such as a CPU (Central Processing Unit) and memory 92 connected by a bus, and executes a program.

[0015] <Vitabi Algorithm> The soft determination performed by the soft determination device 4 uses quantities defined in the Viterbi algorithm. Therefore, before explaining the soft determination performed by the soft determination device 4, we will briefly explain the Viterbi algorithm. For simplicity, we will explain using the case where the memory length l=3 and the symbol multi-level index m=2 as an example. We will also explain using the case where the signal is a sequence of two bits, 0 and 1.

[0016] Figure 2 is an explanatory diagram illustrating the Viterbi algorithm in an embodiment. More specifically, Figure 2 is a trellis diagram illustrating the Viterbi algorithm.

[0017] Since the symbol multiplicity m = 2 and the memory length l = 3, the number of candidates for the state at each time n of the transmission signal is (R + 1). R is the value obtained by subtracting 1 from m to the power of (l - 1). In FIG. 2, the number of candidates for the state at time n of the transmission signal is 4, and R = 3. The state at time n of the transmission signal is, specifically, the symbol at time n of the transmission signal. Note that the symbol at time n of the transmission signal means the n-th symbol in the transmission signal. In FIG. 2, each of the four states is represented as S0, S1, S2, S3.

[0018] State S0 is a symbol represented by an ordered set of a "0" bit and a "0" bit. State S1 is a symbol represented by an ordered set of a "0" bit and a "1" bit. State S2 is a symbol represented by an ordered set of a "1" bit and a "0" bit. State S3 is a symbol represented by an ordered set of a "1" bit and a "1" bit.

[0019] p M n+1 (where M is an integer from 0 to R) is a quantity called a path metric in the Viterbi algorithm. Therefore, the path metric p M n+1 is the distance obtained by the Viterbi algorithm, the distance indicated by a predetermined distance function, and the distance indicating the likelihood that the symbol at time (n + 1) of the transmission signal is S r That is, the distance indicating the likelihood. The path metric p M n+1 is the sum of the distance indicating the likelihood that the symbol at time (n + 1) of the transmission signal is S r and the distance of the remaining path from the first to the n-th of the transmission signal. Note that the distance of the predetermined distance function may be, for example, the square error or the sum of the square errors.

[0020] b q n+1 (where q is an integer from 1 to Q. Q = (R + 1) × m.) is a quantity called a branch metric in the Viterbi algorithm. Therefore, the branch metric b qn+1 Q is the distance obtained by the Viterbi algorithm, the distance represented by a given distance function, and the likelihood of transitioning from the nth symbol of the transmitted signal to each candidate of the (n+1)th symbol. Since the symbol multi-level index is m=2, the (n+1)th symbol has a next bit following each candidate of the nth symbol that is either 0 or 1. Thus, the branch metric Q is (R+1)×m.

[0021] The distance represented by the branch metric may be, for example, the squared error or the sum of the squared errors. The distance represented by a given distance function in the path metric may be different from the distance represented by a given distance function in the branch metric. Therefore, for example, if the distance represented by the branch metric is the squared error, the distance represented by the path metric is the sum of the squared errors.

[0022] In the example in Figure 2, for example, if the symbol at time (n-1) is state S0, then the distance indicated by the branch metric when the state becomes S1 at time n is b 1 n That is the case.

[0023] The branch metric value is calculated based on the estimated transfer function, which is a pre-obtained estimated result of the transfer function of transmission path 2, and the received signal. The estimated transfer function is estimated, for example, based on the result of propagating a pre-prepared training signal through transmission path 2 to receiver 3.

[0024] The process for calculating the branch metric value based on the estimated transfer function and the received signal can be any existing process. For example, the process for calculating the branch metric value based on the estimated transfer function and the received signal is to obtain the squared error between the received signal and the result of applying the estimated transfer function to the symbol sequence indicated by the branch metric. The symbol sequence indicated by the branch metric refers to the candidate sequence corresponding to the branch corresponding to the branch metric.

[0025] The (n+1)th path metric is the sum of the nth path metric of the source state and the branch metric, which indicates the likelihood of the transition from the nth state of the source state to the (n+1)th state of the destination state.

[0026] The Viterbi algorithm is a process that sequentially calculates path metrics and branch metrics from time n=1 to n=N in this manner.

[0027] <First softness determination process> Returning to the explanation of Figure 1, the control unit 40 performs a soft decision process for the (n+1)th symbol of the transmitted signal (where n is an integer between 1 and N, and N is an integer greater than or equal to 1). For example, it performs a first soft decision process. The first soft decision process includes branch metric estimation, path metric estimation, and bit likelihood estimation.

[0028] The branch metric estimation process estimates the likelihood obtained by the Viterbi algorithm for transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal, based on the estimated transfer function, which is a previously obtained estimation result of the transfer function of transmission path 2, and the received signal. As described above, the likelihood for transitioning from the nth symbol to each candidate symbol (n+1) of the transmitted signal is a quantity called the branch metric in the Viterbi algorithm. Therefore, states S0, S1, S2, and S3 in the example in Figure 2 are examples of candidates.

[0029] The path metric estimation process estimates the likelihood obtained by the Viterbi algorithm that each candidate for the (n+1)th symbol of the transmitted signal is the symbol of the transmitted signal, based on the results of the branch metric estimation process. As mentioned above, the likelihood obtained by the Viterbi algorithm that each candidate for the (n+1)th symbol of the transmitted signal is the symbol of the transmitted signal is a quantity called the path metric in the Viterbi algorithm.

[0030] The bit likelihood estimation process estimates the likelihood that the k-th bit (where k is an integer between 1 and m) of the (n+1)th symbol of the transmitted signal is a predetermined bit, using the path metric of each candidate symbol of the (n+1)th symbol of the transmitted signal. The path metric of each candidate symbol of the (n+1)th symbol of the transmitted signal is the path metric obtained through the path metric estimation process. The bit likelihood estimation process does not use any path metrics other than the path metric of each candidate symbol of the (n+1)th symbol of the transmitted signal.

[0031] The control unit 40 obtains the likelihood estimated in the bit likelihood estimation process as the result of a soft decision on the (n+1)th symbol of the transmitted signal.

[0032] <First example of likelihood in the first soft decision process> The likelihood estimated by the bit likelihood estimation process can be expressed, for example, by the following equation (1). The left side of equation (1) is λ k、n This is the likelihood estimated by the bit likelihood estimation process, and it represents the likelihood that the k-th bit of the n-th symbol of the transmitted signal is 0. Note that in the example of equation (1), there are two types of bits: 0 and 1. Therefore, the information that represents the likelihood of a bit being 0 is also the information that represents the likelihood of a bit being 1.

[0033]

number

[0034]

number

[0035] c k , n σ represents the k-th bit of the n-th symbol of the transmitted signal. σ represents the standard deviation of the noise distribution added to the optical signal in transmission path 2. Therefore, when the likelihood estimated by the bit likelihood estimation process is expressed by equation (1), the bit likelihood estimation process also uses information indicating the standard deviation of the noise distribution added to the optical signal in transmission path 2.

[0036] The standard deviation of the noise distribution added to the optical signal in transmission path 2 is, for example, a predetermined value. M represents a candidate symbol value. That is, u M is u0~u R This represents the symbol value of each symbol. Therefore, for example, if the modulation scheme is PAM4, for example u M If M=0, then u0=[c 1,n , c 2,n ]=[0,0], and if M=1 then u1=[c 1,n , c 2,n ] = [0, 1], and if M = 2, then u2 = [c 1,n , c 2,n ]=[1,1], and if M=3 then u3=[c 1,n , c 2,n ] represents [1, 0].

[0037] <Second example of likelihood in the first soft decision process> The likelihood estimated by the bit likelihood estimation process may be expressed, for example, by equation (3) below. Note that equation (1) is an approximation of equation (3). Specifically, the approximation involves replacing all symbols except the largest symbol likelihood with 0.

[0038] The left side of equation (3) λ k、n This is the likelihood estimated by the bit likelihood estimation process, and it represents the likelihood that the k-th bit of the n-th symbol of the transmitted signal is 0. Note that in the example of equation (3), there are two types of bits: 0 and 1. Therefore, the information that represents the likelihood of a bit being 0 is also the information that represents the likelihood of a bit being 1.

[0039]

number

[0040]

number

[0041] Equation (4) includes the standard deviation of the noise distribution added to the optical signal in transmission path 2. Therefore, when the likelihood estimated by the bit likelihood estimation process is expressed by equation (3), the bit likelihood estimation process also uses information indicating the standard deviation of the noise distribution added to the optical signal in transmission path 2.

[0042] <Second soft judgment process> The control unit 40 may perform a soft determination process for the (n+1)th symbol of the transmitted signal (where n is an integer between 1 and N, and N is an integer greater than or equal to 1), for example, a second soft determination process. The second soft determination process includes a hard determination process, a likelihood estimation process, and a difference acquisition process.

[0043] The hardness determination process is a process that performs hardness determination using the Viterbi algorithm based on the estimated transfer function and the received signal.

[0044] The likelihood estimation process estimates the likelihood of each candidate symbol (hereinafter referred to as "symbol candidate") for the (n+1)th symbol of the transmitted signal, based on the result of the hard decision process, the estimated transfer function, and the received signal. In the example in Figure 2, states S0, S1, S2, and S3 are examples of symbol candidates. The likelihood estimated by the likelihood estimation process is called the estimated likelihood.

[0045] The difference acquisition process is a process that acquires the difference (hereinafter referred to as "likelihood difference") between the estimated likelihood of a symbol candidate whose k-th bit (k is an integer between 1 and K) is a predetermined bit and the estimated likelihood of a symbol candidate whose k-th bit is not a predetermined bit.

[0046] The control unit 40 obtains the likelihood difference obtained in the difference acquisition process as the result of a soft decision on the (n+1)th symbol of the transmitted signal.

[0047] <First example of estimated likelihood in the second soft decision processing> The estimated likelihood can be expressed, for example, by the following equation (5).

[0048]

number

[0049]

number

[0050] In equation (5), the H with a hat (^) as an accent mark represents the estimated transfer function. n This represents the received signal. C' is represented by equation (6). M、n This is the result of the hard determination process and the symbol u, which is one of the candidates for the nth symbol of the transmitted signal. M This represents the ordered set of and . Below, the ordered set C' M、n This is called an ordered set. n This represents the nth symbol of the transmitted signal estimated by the hard judgment process. Note that l is the memory length, as mentioned above.

[0051] When the estimated likelihood is expressed by equation (5), the difference in likelihood can be expressed, for example, by equation (7). Note that in the example of equation (7), there are two types of bits: 0 and 1. Therefore, the information indicating the likelihood when the bit is 0 is also the information indicating the likelihood when the bit is 1.

[0052]

number

[0053] Equation (7) includes the standard deviation of the noise distribution added to the optical signal in transmission path 2. Therefore, when the likelihood difference estimated by the difference acquisition process is expressed by equation (7), the difference acquisition process also uses information indicating the standard deviation of the noise distribution added to the optical signal in transmission path 2.

[0054] <Second example of estimated likelihood in the second soft decision processing> The estimated likelihood may also be expressed by, for example, equation (8) below. Note that equation (5) is obtained by normalizing equation (8) and taking the natural logarithm. Here, the coefficients that do not depend on M and n are normalized.

[0055]

number

[0056] Equation (8) includes the standard deviation of the noise distribution added to the optical signal in transmission path 2. Therefore, when the likelihood estimated in the likelihood estimation process is expressed by equation (8), the likelihood estimation process also uses information indicating the standard deviation of the noise distribution added to the optical signal in transmission path 2.

[0057] When the estimated likelihood is expressed by equation (8), the difference in likelihood can be expressed, for example, by equation (9). Note that in the example of equation (9), there are two types of bits: 0 and 1. Therefore, the information indicating the likelihood when the bit is 0 is also the information indicating the likelihood when the bit is 1.

[0058]

number

[0059] <Third example of estimated likelihood in the second soft decision processing> The estimated likelihood may be obtained, for example, based on the difference between the result obtained by applying the estimated transfer function to the result of the hard decision process and the received signal. The difference between the result obtained by applying the estimated transfer function to the result of the hard decision process and the received signal represents the estimated result of the noise distribution.

[0060] The difference between the result obtained by applying the estimated transfer function to the hard decision processing result and the received signal is specifically expressed by the following equation (10).

[0061]

number

[0062] x', which is shown in bold in equation (10) n This represents the ordered set of equation (11) below.

[0063]

number

[0064] As described above, the distribution of the difference between the result obtained by applying the estimated transfer function to the result of the hard decision processing and the received signal is the estimated result of the noise distribution, so W is a quantity that represents the estimated result of the noise.

[0065] The process of obtaining the estimated likelihood of the (n+1)th symbol candidate of the transmitted signal based on the distribution of the difference between the result obtained by applying the estimated transfer function to the result of the hard decision process and the received signal is called the modified likelihood estimation process. Since the modified likelihood estimation process estimates the likelihood of each candidate for the (n+1)th symbol of the transmitted signal based on the result of the hard decision process, the estimated transfer function, and the received signal, it is a type of likelihood estimation process.

[0066] As can be seen from equation (11), the result of the hard decision process used in the modified likelihood estimation process is the result of the hard decision process on the l symbols preceding the target of estimation in the modified likelihood estimation process. Therefore, for example, if the candidate for the (n+1)th symbol of the transmitted signal is the target of estimation by the modified likelihood estimation process, the hard decision process will perform a hard decision on the l symbols prior to the nth symbol.

[0067] In the modified likelihood estimation process, for example, a histogram with a predetermined class width is generated for noise W with a sample size α. The horizontal axis of the histogram represents the class, and the vertical axis represents the frequency. Note that processing noise with a sample size α means processing a set of elements where the elements are noise W and the number of elements is α. In such a case, the modified likelihood estimation process then normalizes the sample size in each class by the sample size of the class with the largest sample size.

[0068] In such cases, the deformed likelihood estimation process then proceeds to the ordered set C'. M、n The number of samples belonging to the class containing the difference between the result obtained by applying the estimated transfer function to the received signal and the normalized number of samples is obtained as the likelihood for each symbol. Note that this is obtained for the ordered set C'. M、nThe statement that the result of applying the estimated transfer function to the signal includes the difference between that signal and the received signal specifically means selecting a class corresponding to the likelihood of symbol M at time index n.

[0069] <Hardware Description> Figure 3 shows an example of the hardware configuration of the soft judgment device 4 in the embodiment. The soft judgment device 4 includes a control unit 40 which has a processor 91 such as a CPU and memory 92 connected by a bus, and executes a program. The soft judgment device 4 functions as a device comprising the control unit 40, interface unit 41 and storage unit 42 by executing the program.

[0070] More specifically, the processor 91 reads the program stored in the storage unit 42 and stores the read program in the memory 92. By executing the program stored in the memory 92, the processor 91 functions as a device comprising a control unit 40, an interface unit 41, and a storage unit 42.

[0071] The control unit 40 controls the operation of various functional units of the soft judgment device 4. For example, the control unit 40 executes a first soft judgment process. For example, the control unit 40 executes a second soft judgment process instead of the first soft judgment process.

[0072] The interface unit 41 is configured to include an interface for connecting the soft judgment device 4 to an external device. The interface unit 41 communicates with the external device via wired or wireless means. The external device is, for example, a receiver 3. In such a case, the interface unit 41, for example, acquires the received signal acquired by the receiver 3.

[0073] The interface unit 41 is configured to include, for example, input devices such as a mouse, keyboard, or touch panel. The interface unit 41 may also be configured to include an interface for connecting these input devices to the soft judgment device 4.

[0074] The interface unit 41 is configured to include a display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, or an organic EL (Electro-Luminescence) display. The interface unit 41 may also be configured to include an interface for connecting these display devices to the soft judgment device 4.

[0075] The storage unit 42 is configured using a computer-readable storage medium (non-transitory computer-readable recording medium) such as a magnetic hard disk drive or a semiconductor storage device. The storage unit 42 stores various information related to the soft judgment device 4. The storage unit 42 may also store various information resulting from processing performed by the control unit 40, for example. The storage unit 42 may also store received signals acquired by the interface unit 41, for example. The storage unit 42 may have, for example, an estimated transfer function pre-stored.

[0076] Figure 4 is a flowchart showing a first example of the processing flow performed by the soft determination device 4 in the embodiment. More specifically, Figure 4 is a flowchart showing an example of the processing flow performed by the soft determination device 4 when it performs the first soft determination process.

[0077] The control unit 40 obtains the estimated transfer function stored in the memory unit 42 and the received signal acquired by the interface unit 41 (step S101). Next, the control unit 40 performs branch metric estimation processing (step S102). Next, the control unit 40 performs path metric estimation processing (step S103).

[0078] Next, the control unit 40 performs bit likelihood estimation processing (step S104). The control unit 40 obtains the likelihood estimated in step S104 as the result of a soft decision for the (n+1)th symbol of the transmitted signal. Next, the control unit 40 controls the operation of the interface unit 41 to output the likelihood estimated in step S104 to the interface unit 41 (step S105).

[0079] Figure 5 is a flowchart showing a second example of the processing flow performed by the soft determination device 4 in the embodiment. More specifically, Figure 5 is a flowchart showing an example of the processing flow performed by the soft determination device 4 when it performs the second soft determination process.

[0080] The control unit 40 obtains the estimated transfer function stored in the memory unit 42 and the received signal acquired by the interface unit 41 (step S201). Next, the control unit 40 performs a hard determination process (step S202). Next, the control unit 40 performs a likelihood estimation process (step S203).

[0081] Next, the control unit 40 performs the difference acquisition process (step S204). The control unit 40 acquires the likelihood difference acquired in the process of step S204 as the result of a soft decision for the (n+1)th symbol of the transmitted signal. Next, the control unit 40 controls the operation of the interface unit 41 to output the likelihood difference estimated in step S204 to the interface unit 41 (step S205).

[0082] Thus, the soft determination device 4, which performs the second soft determination process, performs a soft determination on the main symbol, which is the (n+1)th symbol of the transmitted signal with a symbol multi-level index of m. The soft determination device 4, which performs the second soft determination process, includes a control unit 40. The control unit 40 performs a hard determination process that performs a hard determination using the Viterbi algorithm based on the estimated transfer function, which is a previously obtained estimated result of the transfer function of the transmission path 2 through which the transmitted signal propagates, and the received signal, which is the result of receiving the transmitted signal. The control unit 40 performs a likelihood estimation process that estimates the likelihood of each candidate for the (n+1)th symbol based on the result of the hard determination process, the estimated transfer function, and the received signal. The control unit 40 performs a difference acquisition process that acquires the difference between the likelihood of a candidate whose kth bit (k is an integer between 1 and m) is a predetermined bit and the likelihood of a candidate whose kth bit is not the predetermined bit. The control unit 40 outputs the acquired difference as the result of the soft determination.

[0083] <Experimental Results> An example of the results of an experiment using the soft judgment device 4 is described below. In the experiment, a comparative experiment was also conducted to evaluate the effectiveness of the experiment using the soft judgment device 4. The technique used in the comparative experiment was a technique that did not use the soft judgment device 4 (hereinafter referred to as the "comparative technique"). More specifically, the comparative technique is a technique that estimates the principal symbol by applying the inverse function of the transfer function to the received signal.

[0084] First, let's describe an example of the optical transmission system 100 used in the experiment.

[0085] In the experiment, transmitter 1 converted a digital signal indicating the content the user wanted to transmit into an analog signal. The conversion in the experiment was performed at 128 Gsample / s and 65 GHz. In the experiment, the analog signal obtained by the conversion was amplified by an amplifier in transmitter 1.

[0086] In the experiment, transmitter 1 output an optical signal obtained by modulating a laser beam with a wavelength of 1310 nm with an amplified analog signal. The modulation scheme was PAM4. The optical signal output by transmitter 1 was incident on transmission line 2 and propagated through transmission line 2.

[0087] In the experiment, transmission line 2 was a 10 km long single-mode fiber. The chromatic dispersion of transmission line 2 was -8 ps / nm at a wavelength of 1310 nm.

[0088] In the experiment, receiver 3 was equipped with a variable optical attenuator. The power of the optical signal emitted from transmission path 2 was attenuated by the variable optical attenuator. Receiver 3 then converted the attenuated optical signal into an electrical signal using a photodiode. The photodiode had a bandwidth of 50 GHz.

[0089] In receiver 3, the electrical signal obtained by the photodiode was amplified and then converted into a digital signal. The conversion to a digital signal was performed at 160 Gsample / s and 63 GHz. The converted signal is an example of a received signal and represents an example of a received signal in the experiment.

[0090] In the experiment, the soft-determination device 4 acquired the received signal obtained in this manner. In the experiment, the control unit 40 of the soft-determination device 4 performed a first soft-determination process and obtained the likelihood estimated by the first soft-determination process as the result of the soft-determination. More specifically, in the experiment, the control unit 40 estimated the likelihood represented by equation (1) by performing the first soft-determination process.

[0091] Figure 6 is the first figure showing an example of experimental results in the embodiment. More specifically, Figure 6 shows an example of experimental results using the comparative technology. The horizontal axis in Figure 6 represents frequency. The vertical axis in Figure 6 represents loss. Figure 6 shows that when using the comparative technology, the loss becomes large around a frequency of 60 GHz.

[0092] Figure 7 is the second figure showing an example of experimental results in the embodiment. The horizontal axis of Figure 7 represents ROP (Received Optical Power). The vertical axis of Figure 7 represents Normalized General Mutual Information (NGMI).

[0093] Figure 7 shows the NGMI value obtained by “MLSE(NGMI)” (Maximum Likelihood Sequence Estimation) after performing the first soft determination process using the soft determination device 4 and estimating the likelihood expressed by equation (1). Figure 7 shows the NGMI value obtained by using the comparison technology and performing the first soft determination process using the soft determination device 4 and estimating the likelihood expressed by equation (1) compared to the comparison technology.

[0094] Figure 7 shows that the main symbol can be estimated with higher accuracy than the comparison technology by using the results of the soft determination device 4.

[0095] <Explanation of the effects of the soft judgment device 4> As mentioned above, the comparative technology estimates the main symbol by applying the inverse function of the transfer function to the received signal. When the inverse function is applied, even the noise added to the signal in transmission line 2 is amplified. On the other hand, the soft decision device 4 does not use the inverse function of the transfer function, so the noise is not amplified. Therefore, the soft decision device 4 can estimate the main symbol with higher accuracy than the comparative technology.

[0096] The soft determination device 4 configured in this way performs either the first soft determination process or the second soft determination process. Therefore, since the result of the soft determination is obtained without using the inverse function of the transfer function, the soft determination device 4 can estimate the symbol of the transmitted signal with higher accuracy.

[0097] <Modified form of the first embodiment>

[0098] In addition, equations (1), (4), (7), and (8) above include the standard deviation σ of the noise distribution added to the optical signal in transmission path 2. However, the value of the standard deviation σ of the noise distribution added to the optical signal in transmission path 2 may be a predetermined value, or it may not be a predetermined value.

[0099] For example, the value of the standard deviation σ may be obtained based on the difference between the result obtained by applying the estimated transfer function to the ground truth data and the received signal. The ground truth data is data that indicates the correct transmission signal. Therefore, for example, the standard deviation σ may be obtained by the process represented by the following equation (12).

[0100]

number

[0101]

number

[0102] x in equation (13) dd represents the d-th symbol of the transmitted signal as shown by the ground truth data. In equation (13), l represents the memory length of the estimated transfer function, while in equation (12), e represents the starting position of the transmitted signal as shown by the ground truth data. The starting position refers to the position in the time axis direction in the ground truth data used. D represents the number of symbols used to calculate the standard deviation σ. d represents the time index in the ground truth data used. Therefore, equation (12) represents the process of obtaining the average of D estimated noises as the standard deviation σ. Estimated noise is the squared error between the result of applying the estimated transfer function to the ground truth data and the received signal.

[0103] For example, the value of the standard deviation σ may be obtained based on the difference between the result obtained by applying the estimated transfer function to the result of the hard judgment process and the received signal. Therefore, for example, the standard deviation σ may be obtained by the process represented by the following equation (14).

[0104]

number

[0105]

number

[0106] x' in equation (15) d d represents the d-th symbol of the transmitted signal indicated by the hard decision processing result. In equation (15), l represents the memory length of the estimated transfer function, while in equation (14), e represents the starting position of the transmitted signal indicated by the hard decision processing result. The starting position refers to the position in the time axis direction in the hard decision processing result. D represents the number of symbols used to calculate the standard deviation σ. d represents the time index in the hard decision result used. Therefore, equation (14) represents the process of obtaining the average of D estimated noises as the standard deviation σ.

[0107] For example, the value of the standard deviation σ may be a value that satisfies the condition of maximizing NGMI. NGMI is a quantity defined, for example, by the following equation (16).

[0108]

number

[0109]

number

[0110]

number

[0111] m' represents the number of bits in the transmitted signal. Therefore, for example, if the modulation scheme is PAM4, log2m' = 2. N represents the number of symbols used to calculate the CrossEntropy.

[0112] Note that the soft output value (i.e., the result of the soft judgment) may diverge to the positive or negative side. Some programming languages ​​do not output a value when it diverges. Therefore, to avoid situations where no value is output, an upper or lower limit to the soft output value may be predetermined in the process of performing a soft judgment on the (n+1)th symbol of the transmitted signal.

[0113] The soft judgment device 4 may be implemented using multiple information processing devices connected to each other via a network. In this case, each functional unit of the soft judgment device 4 may be distributed and implemented across multiple information processing devices.

[0114] Furthermore, all or part of the functions of the soft judgment device 4 may be implemented using hardware such as ASICs (Application Specific Integrated Circuits), PLDs (Programmable Logic Devices), or FPGAs (Field Programmable Gate Arrays). The program may be recorded on a computer-readable recording medium. Computer-readable recording media include, for example, portable media such as flexible disks, magneto-optical disks, ROMs, and CD-ROMs, as well as storage devices such as hard disks built into computer systems. The program may also be transmitted via a telecommunications line.

[0115] (Second Embodiment) In the second embodiment, the main difference from the first embodiment is that, if the symbol determination result (hard determination result) obtained by backward calculation (tracing back the remaining paths) in the trellis diagram differs from the symbol determination result obtained by forward calculation (calculation of path metrics and selection of remaining paths), the soft determination result obtained by backward calculation, which is necessary for a complex soft determination output that also requires path metrics indicated by paths other than the remaining paths, is replaced with a predetermined soft determination result obtained by a simpler calculation. The second embodiment will be explained focusing on the differences from the first embodiment.

[0116] Figure 8 shows an example of the configuration of the control unit 40 in the embodiment. The control unit 40 comprises a transfer function estimation unit 401, a branch metric processing unit 402, a path metric processing unit 403, a hardness determination output unit 404, and a softness determination output unit 405.

[0117] In the following, symbols that are placed above letters in mathematical formulas or functions (hereinafter referred to as "formulas, etc.") will be written before the letters. For example, the symbol "^" that is placed above letters in mathematical formulas, etc. will be written as "^H" before the letter "H" in the following.

[0118] The transfer function estimation unit 401 calculates the estimated transfer function "^H" as shown in equation (19).

[0119]

number

[0120] The branch metric processing unit 402 calculates the branch metric "b" as shown in equation (20).

[0121]

number

[0122] The path metric processing unit 403 calculates the path metric "p" as shown in equation (21).

[0123]

number

[0124] The hard judgment output unit 404 compares the path metric "p" of each state "s" for each time index. Based on the comparison result of the path metric "p", the hard judgment output unit 404 determines "m" at time index "n". l From among the path metrics of state "s", select the minimum path metric. The time-direction path composed of the branches used to calculate the selected minimum path metric is called the "residual path".

[0125] Regardless of which state "s" is selected as the starting point for tracing back the remaining paths in the trellis diagram in the opposite direction to the time direction (state transition direction), the same path will be traced back. Tracing back the same path is called "path merging by backward operation." The symbol corresponding to the state at the end of the traced path (hereinafter referred to as "the destination") is output as the symbol judgment result. The symbol judgment result corresponds to the hard judgment result (hard judgment output).

[0126] The hardness determination output unit 404 displays the hardness determination result "x'" in the trellis diagram, calculated backward. n-a This generates ". The result of the symbol determination is expressed as shown in equation (22).

[0127]

number

[0128] Here, "a" represents the number of times the path is traced back in the opposite direction to the state transition (the number of traces). j " represents the state at the previous destination "j".

[0129] Furthermore, the hardness determination output unit 404 displays the hardness determination result "x''" in the trellis diagram, which is calculated using forward calculation. n-a This generates "". The state with the minimum path metric at time index "n" is "s j If this is the case, the symbol "x''" is determined as the result of the forward operation (calculation of path metrics and selection of remaining paths). n This can be expressed as shown in equation (23). Note that the state S in equation (23) j The time index is the state S in equation (22). j This is different from the time index. Therefore, it should be noted that the left side of equation (23) and the left side of equation (22) are not equal.

[0130]

number

[0131] This determined symbol "x'' n This result is obtained because only forward operations (calculation of path metrics and selection of remaining paths) were used, without backward operations (tracing back through remaining paths). Here, only the sequence length of the most likely symbol candidate has been estimated, so the effect of sequence length estimation including the number of traversals by backward operations is not obtained.

[0132] Therefore, even with the same time index "na", the symbol determination result "x'" from the backward operation is different. n-a " and the symbol determination result from forward operation "x'' n-aThis may differ from the symbol determination result "x''" obtained by forward arithmetic. n-a The symbol determination result "x'" is obtained by backward operation rather than " n-a " is more likely to be accurate.

[0133] In equation (1) illustrated in the first embodiment, the log-likelihood ratio "λ" is calculated based on the path metric information obtained by forward calculation. M,n The result of the backward operation symbol check "x' n-a " and the symbol determination result of forward operation "x'' n-a If this differs from the previous case, the accuracy of the log-likelihood ratio "λ" estimated based on the path metric information obtained through forward calculation may not be high.

[0134] Therefore, in the second embodiment, the soft decision output unit 405 approximates the effect of tracing back the path in the trellis diagram (backward operation) through a simplified calculation. That is, the soft decision output unit 405 replaces the soft decision result of a complex backward operation with the soft decision result of a simplified calculation. The complexity of this simplified calculation is comparable to, for example, the complexity of the Viterbi algorithm used in hard decision maximum likelihood sequence estimation (MLSE).

[0135] Log-likelihood ratio "λ' k,n This can be expressed as equation (24) using equation (25). The operation in equation (24) is essentially the same as in equation (7).

[0136]

number

[0137]

number

[0138] Here, "n" represents the time index (1 ≤ n ≤ N). "k" represents the bit number (1 ≤ k ≤ m) of the symbol determination result at time index "n".k,n " is the symbol determination result "x' at time index "n". n This represents the k-th bit (0 or 1) of "". Note that "c'' k,n " is the symbol determination result "x'' at time index "n". n This represents the k-th bit (0 or 1) of ''.

[0139] The soft judgment output unit 405 obtains a predetermined positive constant "A" from, for example, memory 92. This constant "A" is predetermined such that the Generalized Mutual Information Value (NGMI) is maximized depending on the result of changing a positive variable at predetermined intervals. For example, by changing a variable that takes values ​​from 0.001 to 1.000 at intervals of 0.001, the log-likelihood ratio "λ" is calculated for each value of the variable. The value of the variable that maximizes the Generalized Mutual Information Value is predetermined as the positive constant "A".

[0140] The soft judgment output unit 405 outputs the symbol judgment result of the backward operation "x' n-a " and the symbol determination result of the forward operation "x'' n-a The soft judgment output unit 405 outputs the symbol judgment result "x' n-a " and the symbol determination result "x'' n-a If the result is the same as the result, the soft judgment output unit 405 outputs the soft judgment result "λ k,n-a The log-likelihood ratio "λ'" is used as the log-likelihood ratio. k,n-a It outputs "".

[0141] The soft judgment output unit 405 outputs the symbol judgment result "x' n-a " and the symbol determination result "x'' n-a If these are different, use the sign function "sgn" to calculate the log-likelihood ratio "λ'" in equation (24). k,n The sign of " is obtained. The soft decision output unit 405 obtains the log-likelihood ratio "λ'" of equation (24). k,n Instead of obtaining the sign of ", the log-likelihood ratio "λ" of equation (1) k,n The sign of "" may be obtained. The soft decision output unit 405 outputs the log-likelihood ratio "λ' k,nBased on the sign opposite to that of ", a predetermined constant "A", and the standard deviation of the noise distribution "σ", a new soft judgment result "λ" is generated. k,n-a Calculate ".

[0142] Symbol determination result "x' n-a " and the symbol determination result "x'' n-a The soft judgment result when " and are the same "λ k,n-a (log-likelihood ratio) and symbol determination result "x' n-a " and the symbol determination result "x'' n-a When this differs from the new soft judgment result "λ k,n-a The two (modified log-likelihood ratio) are expressed as shown in equation (26).

[0143]

number

[0144] Figure 9 is a flowchart showing a third example of the processing flow performed by the soft determination device 4 in the embodiment. The control unit 40 obtains the estimated transfer function stored in the memory unit 42 and the received signal acquired by the interface unit 41 (step S301). Next, the control unit 40 performs branch metric estimation processing (step S302). Next, the control unit 40 performs path metric estimation processing (step S303).

[0145] The control unit 40 generates a symbol determination result for backward operation and a symbol determination result for forward operation by executing a hard determination process (step S304). The control unit 40 performs bit likelihood estimation processing based on the symbol determination result for backward operation, the symbol determination result for forward operation, and a predetermined constant "A" (step S305). The control unit 40 obtains the likelihood estimated in the process of step S305 as the result of soft determination. The control unit 40 controls the operation of the interface unit 41 to obtain the likelihood "λ" estimated in step S305. k,n-a The following is output to the interface unit 41 (step S306).

[0146] As described above, the control unit 40 determines the determination result "x'" of the n-th symbol obtained by calculating the (n + a)-th (for example, a = 1) to the n-th of the transmission signal in order. n ", and when the determination result "x'' n " of the n-th symbol obtained by calculating the n-th to the (n + a)-th of the transmission signal in order is different, based on the sign "-" opposite to the sign of the estimated likelihood (sgn(λ' k,n )), the predetermined constant "A", and the standard deviation "σ", the likelihood "λ k,n " is changed. The predetermined constant "A" is determined as "2σ 2 P" based on the likelihood "P" indicating the positive peak of the distribution and the standard deviation "σ".

[0147] Thus, in the second embodiment, when the symbol determination result "x' n-a " and the symbol determination result "x'' n-a " are the same, and when the symbol determination result "x' n-a " and the symbol determination result "x'' n-a " are different, the bit-by-bit log-likelihood ratio (bit likelihood) "λ k,n-a " is made different. As a result, it is possible to further improve the normalized generalized mutual information (NGMI).

[0148] Also, compared with the first embodiment, it becomes possible to estimate the symbol of the transmission signal with higher accuracy.

[0149] <Modification Example of the Second Embodiment> FIG. 10 is a diagram showing an example of a bit likelihood histogram in the embodiment. The soft decision output unit 405 acquires a predetermined positive constant "A" from, for example, the memory 92. As illustrated in Equation (26), the absolute value of the soft decision result is expressed as "A / 2σ 2 ".

[0150] The variance "σ 2Regardless of the above, the optimal value of the positive constant "A" tends to be constant for each transmission system and demodulation method. Furthermore, the optimal value of the positive constant "A" is the positive likelihood "P(=A / 2σ)" that shows the peak of the bit likelihood histogram. 2 It is close to "). Therefore, its likelihood "P(=A / 2σ)". 2 A positive constant "A" may be predetermined based on the following.

[0151] <Experimental Results> An example of the results of an experiment using the soft judgment device 4 is described below. Figure 11 is the third figure showing an example of experimental results in the embodiment. In Figure 11, the symbol multi-level "M" is 4 as an example. The memory length "d" is 5 as an example. The number of steps back "T" is 20 as an example. The predetermined positive constant "A" in the second embodiment is 0.018 as an example.

[0152] The number of path metrics required to calculate the log-likelihood ratio "λ" in the first embodiment is "M". d For example, this is 1024. The number of path metrics required to calculate the log-likelihood ratio "λ" in the second embodiment is "2M d For example, this is 1024. The number of path metrics required to calculate the log-likelihood ratio "λ" in the FFE method is "M d+1 For example, "T" is 81920.

[0153] The graph on the left in Figure 11 shows the relationship between received optical intensity (ROP) and standardized mutual information (NGMI) for the FFE method, the NL-MLSE method in the first embodiment, and the NL-MLSE method in the second embodiment.

[0154] In both the NL-MLSE method in the first embodiment and the NL-MLSE method in the second embodiment, a higher standard generalized mutual information (SIM) is achieved compared to the FFE method. When the ROP is 3 dBm, the SIM generalized mutual information is improved by approximately 18% in the first embodiment. In the second embodiment, the SIM generalized mutual information is improved by approximately 22%.

[0155] The graph on the right in Figure 11 shows the relationship between the bit error rate (BER) and the generalized mutual information (NGMI) for the FFE method, the NL-MLSE method in the first embodiment, and the NL-MLSE method in the second embodiment. In the graph on the right, the dashed line overlapping with the results for the FFE method represents the theoretical curve for an additive white Gaussian noise (AWGN) channel. The performance represented by the theoretical curve corresponds to the performance of a very computationally intensive soft output Viterbi algorithm (SOVA) when the same BER as the NL-MLSE method is obtained.

[0156] In the FFE method, a code error rate of "0.8" cannot be achieved. In contrast, the NL-MLSE method in the first embodiment can achieve a code error rate of "0.931". Furthermore, the NL-MLSE method in the second embodiment can achieve a code error rate of "0.962". Thus, the optical transmission system 100 in the second embodiment can achieve performance close to the standard generalized mutual information quantity of "0.985" using the soft output Viterbi algorithm with less computation.

[0157] While embodiments of this invention have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments and includes designs and the like that do not depart from the spirit of this invention. [Explanation of Symbols]

[0158] 100…Optical transmission system, 1…Transmitter, 2…Transmission path, 3…Receiver, 4…Soft judgment device, 40…Control unit, 41…Interface unit, 42…Storage unit, 91…Processor, 92…Memory, 401…Transfer function estimation unit, 402…Branch metric processing unit, 403…Path metric processing unit, 404…Hard judgment output unit, 405…Soft judgment output unit

Claims

1. A soft determination device that performs a soft determination on the main symbol which is the (n+1)th symbol (n is an integer between 1 and N, N is an integer between 1 and N) of a transmitted signal with a symbol multi-level index of m (where m is an integer of 2 or more), A branch metric estimation process estimates a branch metric, which is a distance obtained by the Viterbi algorithm, is a distance represented by a predetermined distance function, and represents the likelihood of transitioning from the nth symbol to the (n+1)th symbol of the transmitted signal, based on an estimated transfer function, which is a previously obtained estimated result of the transfer function of the transmission path through which the transmitted signal propagates, and a received signal, which is the result of receiving the transmitted signal. Based on the results of the branch metric estimation process, a path metric estimation process is performed to estimate a path metric which is the sum of the distance obtained by the Viterbi algorithm, which is the distance indicated by a predetermined distance function and represents the likelihood that each candidate for the (n+1)th symbol of the transmitted signal is a symbol of the transmitted signal, and the distance of the remaining path consisting of the first to nth symbols of the transmitted signal. A bit likelihood estimation process is performed to estimate the likelihood that the k-th bit (where k is an integer between 1 and m) in the (n+1)-th symbol of the transmitted signal is a predetermined bit, using the path metrics of each candidate symbol of the transmitted signal obtained by the path metric estimation process, and without using any path metrics other than those of each candidate symbol of the transmitted signal. A control unit that executes Equipped with, The control unit obtains the likelihood estimated in the bit likelihood estimation process as the result of the soft decision, The control unit also estimates the likelihood using the standard deviation of the noise distribution applied to the transmitted signal in the transmission path. If the determination result of the nth symbol obtained by calculating the transmission signal in order from the (n+1)th to the nth symbol differs from the determination result of the transmission signal in order from the nth to the (n+1)th symbol, the control unit changes the likelihood based on the sign opposite to the estimated likelihood, a predetermined constant, and the standard deviation. Soft decision device.

2. The standard deviation is obtained based on the difference between the result obtained by applying the estimated transfer function to the ground truth data representing the correct transmission signal and the received signal. The softness determination device according to claim 1.

3. The predetermined constant is determined based on the likelihood that shows the positive peak of the distribution and the standard deviation. The softness determination device according to claim 1.

4. A soft determination method for performing a soft determination on the main symbol which is the (n+1)th symbol (n is an integer between 1 and N, N being an integer of 1 or more) of a transmitted signal with a symbol multi-level index of m (where m is an integer of 2 or more), A branch metric estimation process that estimates a branch metric, which is a distance obtained by the Viterbi algorithm, is a distance in a predetermined distance function, and represents the likelihood of transitioning from the nth symbol to the (n+1)th symbol of the transmitted signal, based on an estimated transfer function, which is a previously obtained estimated result of the transfer function of the transmission path through which the transmitted signal propagates, and a received signal, which is the result of receiving the transmitted signal. Based on the results of the branch metric estimation process, a path metric estimation process is performed to estimate a path metric which is the sum of the distance obtained by the Viterbi algorithm, which is the distance in a predetermined distance function and represents the likelihood that each candidate for the (n+1)th symbol of the transmitted signal is a symbol of the transmitted signal, and the distance of the remaining path consisting of the first to nth symbols of the transmitted signal. A bit likelihood estimation process is performed to estimate the likelihood that the k-th bit (where k is an integer between 1 and m) in the (n+1)-th symbol of the transmitted signal is a predetermined bit, using the path metrics of each candidate symbol of the transmitted signal obtained by the path metric estimation process, and without using any path metrics other than those of each candidate symbol of the transmitted signal. A control step that executes It has, The control step obtains the likelihood estimated in the bit likelihood estimation process as the result of the soft decision, The control step estimates the likelihood using the standard deviation of the noise distribution applied to the transmitted signal in the transmission path, The control step, if the determination result of the nth symbol obtained by calculating the transmission signal in order from the (n+1)th to the nth symbol differs from the determination result of the transmission signal in order from the nth to the (n+1)th symbol, modifies the likelihood based on the opposite sign of the estimated likelihood, a predetermined constant, and the standard deviation. Soft decision method.

5. A program for causing a computer to function as a soft determination device according to any one of claims 1 to 3.

Images