Soft decision device, soft decision method, and program

Abstract

A control unit executes bit likelihood estimation processing for estimating the likelihood that a k-th bit in an (n+1)-th symbol of a transmission signal is a predetermined bit, using a path metric of each candidate for the (n+1)-th symbol of the transmission signal obtained by path metric estimation processing, and without using path metrics other than the path metric of each candidate for the (n+1)-th symbol of the transmission signal. The control unit changes the likelihood estimated in the bit likelihood estimation processing if the decision result of the bit of the n-th symbol obtained by calculation in order from the (n+1)-th to the n-th symbol of the transmission signal and the decision result of the bit of the n-th symbol by calculation in order from the n-th to the (n+1)-th symbol of the transmission signal are different.

Description

Soft decision device, soft decision method and program

[0001] The present invention relates to a soft decision device, a soft decision method, and a program.

[0002] In order to cope with the recent increase in network traffic, studies are underway to increase the speed and distance of optical transmission systems.

[0003] Here, a receiver in an optical transmission system may perform maximum likelihood sequence estimation (MLSE). Non-Patent Document 1 discloses a signal processing technique for maximum likelihood sequence estimation. The receiver estimates the transfer function of the transmission path of the optical signal. The receiver compares the output of the estimated transfer function with the received signal. Based on the comparison result, the receiver determines the most likely candidate sequence as the decision result for the sequence of the received signal. The output of a general Viterbi decoder used in maximum likelihood sequence estimation is the decided symbol itself (hard decision output). For this reason, hard decision forward error correction (HD-FEC) is used for maximum likelihood sequence estimation.

[0004] The performance of soft-decision forward error correction (SD-FEC) is higher than that of hard-decision forward error correction. In order for soft-decision forward error correction to be used in maximum likelihood sequence estimation, a symbol decision algorithm capable of outputting soft decisions expressed using log-likelihood ratios must be used. Therefore, the soft-output Viterbi algorithm has been proposed (see Non-Patent Document 2).

[0005] 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)J. Hagenauer et al., 'A Viterbi Algorithm with Soft-Decision Outputs and its Applications,' 1989 IEEE Global Telecommunications Conference and Exhibition 'Communications Technology for the 1990s and Beyond', pp.1680-1686 (1989)

[0006] However, in optical transmission systems, signal distortion and noise increase as the speed and distance increase. Therefore, a technology to estimate the symbols of the transmitted signal, which is the optical signal sent by the transmitter, is needed. One method to estimate the symbols of the transmitted signal using the inverse function of the transfer function of the transmission path has been proposed. However, the estimation accuracy using the proposed technology was sometimes low.

[0007] In view of the above circumstances, an object of the present invention is to provide a technique for estimating symbols of a transmitted signal with higher accuracy.

[0008] One aspect of the present invention is a soft decision device that performs soft decision on a main symbol that is the (n+1)th (n is an integer between 1 and N, N is an integer greater than or equal to 1) symbol of a transmission signal with a symbol multilevel degree of m (m is an integer greater than or equal to 2), the soft decision device comprising: a branch metric estimation process that estimates a branch metric, which is a distance indicating the likelihood of transition from the nth symbol of the transmission signal to each candidate for the (n+1)th symbol, based on an estimated transfer function that is a previously obtained estimation result of a transfer function of a transmission path through which the transmission signal propagates, and a received signal that is a result of receiving the transmission signal; and a path metric that is the sum of a distance indicating the likelihood that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal, and a distance from the first to nth surviving paths of the transmission signal, based on the result of the branch metric estimation process. and a control unit that executes a path metric estimation process in which the kth bit (k is an integer between 1 and m) in the (n+1)th symbol of the transmission signal is a predetermined bit, using path metrics of each candidate for the (n+1)th symbol of the transmission signal obtained by the path metric estimation process, without using any path metrics other than the path metrics of each candidate for the (n+1)th symbol of the transmission signal, wherein the control unit changes the likelihood estimated in the bit likelihood estimation process when a decision result for the bit of the nth symbol obtained by performing calculations in order from the (n+1)th to the nth symbol of the transmission signal differs from a decision result for the bit of the nth symbol obtained by performing calculations in order from the nth to the (n+1)th symbol of the transmission signal.

[0009] One aspect of the present invention is a soft decision method executed by a soft decision device that performs soft decision on a primary symbol that is the (n+1)th (n is an integer between 1 and N, N is an integer greater than or equal to 1) symbol of a transmission signal with a symbol multilevel degree of m (m is an integer greater than or equal to 2), the method comprising: a branch metric estimation process that estimates a branch metric, which is a distance indicating the likelihood of transition from the nth symbol of the transmission signal to each candidate for the (n+1)th symbol, based on an estimated transfer function that is a previously estimated result of a transfer function of a transmission path through which the transmission signal propagates, and a received signal that is a result of receiving the transmission signal; and a path metric that is the sum of a distance indicating the likelihood that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal, and a distance from the first to nth surviving paths of the transmission signal, based on the result of the branch metric estimation process. and a bit likelihood estimation process for estimating a likelihood that the k-th (k is an integer between 1 and m) bit in the (n+1)th symbol of the transmission signal is a predetermined bit, using path metrics of each candidate for the (n+1)th symbol of the transmission signal obtained by the path metric estimation process, without using any path metrics other than the path metrics of each candidate for the (n+1)th symbol of the transmission signal, wherein the control step includes changing the likelihood estimated in the bit likelihood estimation process when a decision result for the bit of the n-th symbol obtained by performing calculations in order from the (n+1)th to the n-th symbol of the transmission signal differs from a decision result for the bit of the n-th symbol obtained by performing calculations in order from the n-th to the (n+1)th symbol of the transmission signal.

[0010] One aspect of the present invention is a program for causing a computer to function as the soft decision device described above.

[0011] According to the present invention, it is possible to estimate the symbols of a transmitted signal with higher accuracy.

[0012] 1 is an explanatory diagram illustrating an optical transmission system according to an embodiment. 2 is an explanatory diagram illustrating a Viterbi algorithm according to an embodiment. 3 is a diagram illustrating an example of the hardware configuration of a soft decision device according to an embodiment. 4 is a flowchart illustrating a first example of the flow of processing performed by the soft decision device according to an embodiment. 5 is a flowchart illustrating a second example of the flow of processing performed by the soft decision device according to an embodiment. 6 is a first diagram illustrating an example of an experimental result according to an embodiment. 7 is a second diagram illustrating an example of an experimental result according to an embodiment. 8 is a diagram illustrating an example of the configuration of a control unit according to an embodiment. 9 is a flowchart illustrating a third example of the flow of processing performed by the soft decision device according to an embodiment. 10 is a diagram illustrating an example of a bit likelihood histogram according to an embodiment. 11 is a third diagram illustrating an example of an experimental result according to an embodiment. 12 is a diagram illustrating a fourth example of the flow of processing performed by the soft decision device according to an embodiment. 13 is a fourth diagram illustrating an example of an experimental result according to an embodiment. 14 is a fifth diagram illustrating an example of an experimental result according to an embodiment.

[0013] First Embodiment Fig. 1 is an explanatory diagram illustrating an optical transmission system 100 according to an embodiment. The optical transmission system 100 includes a transmitter 1, a transmission path 2, a receiver 3, and a soft decision device 4. The transmitter 1 transmits an optical signal. Hereinafter, the optical signal transmitted by the transmitter 1 will be referred to as a transmission signal. In the optical transmission system 100, the symbol multilevel degree of the transmission signal is m (m is an integer equal to or greater than 1). Hereinafter, the symbol of the transmission signal will be referred to as a primary symbol.

[0014] The transmission path 2 is a path through which an optical signal propagates, such as an optical fiber. The transmission signal sent from the transmitter 1 propagates through the transmission path 2 and reaches the receiver 3. The receiver 3 receives the optical signal that has propagated through the transmission path 2. Hereinafter, the result of the optical signal that has propagated through the transmission path 2 and that is received by the receiver will be referred to as the received signal.

[0015] The transfer function of the transmission line 2 is expressed as a vector H = {h １ , ..., h ｌ}, the received signal y ｎ is x ｎ ・H+W ｎ H is a vector whose elements are weight coefficients. １ , ..., h ｌ are weighting coefficients. l is the memory length, i.e., l is the time spread of the transfer function. xｎ is a symbol string representing a transmitted signal, and is a symbol string having symbols from the (n-l+1)th symbol to the nth symbol. A dot (.) indicates an inner product. W ｎ represents the white noise imparted to the optical signal as it propagates through the transmission line 2.

[0016] The soft decision device 4 makes a soft decision on the (n+1)th symbol (n is an integer between 1 and N, inclusive; N is an integer greater than or equal to 1) of the transmission signal. The soft decision device 4 includes a control unit 40 having a processor 91 such as a CPU (Central Processing Unit) and a memory 92 connected by a bus, and executes a program.

[0017] <Viterbi Algorithm> In the soft decision made by the soft decision device 4, quantities defined in the Viterbi algorithm are used. Therefore, before explaining the soft decision made by the soft decision device 4, the Viterbi algorithm will be explained for completeness. For simplicity of explanation, an example will be given in which the memory length l=3 and the symbol multilevel degree m=2. In addition, an example will be given in which the signal is a sequence of two bits, 0 and 1.

[0018] 2 is an explanatory diagram for explaining the Viterbi algorithm in the embodiment, more specifically, a trellis diagram for explaining the Viterbi algorithm.

[0019] Since the symbol multilevel degree m=2 and the memory length l=3, there are (R+1) possible states of the transmitted signal at each time n. R is the value obtained by subtracting 1 from m raised to the (l-1)th power. In FIG. 2, there are four possible states of the transmitted signal at time n, and R=3. The state of the transmitted signal at time n is specifically the symbol of the transmitted signal at time n. Note that the symbol of the transmitted signal at time n means the nth symbol in the transmitted signal. In FIG. 2, each of the four possible states is represented by S ０ , S １ , S ２ , S ３ It is expressed as follows.

[0020] State S ０ is a symbol represented by an ordered set of "0" bits and "0" bits.１ is a symbol represented by an ordered set of "0" bits and "1" bits. ２ is a symbol represented by an ordered set of "1" bits and "0" bits. ３ is a symbol represented by an ordered set of "1" bits and "1" bits.

[0021] p Ｍ ｎ＋１ (M is an integer between 0 and R) is a quantity called a path metric in the Viterbi algorithm. Ｍ ｎ＋１ is the distance obtained by the Viterbi algorithm, which is the distance indicated by a predetermined distance function, and the symbol at time (n+1) of the transmitted signal is S ｒ The path metric p Ｍ ｎ＋１ is the symbol of the transmitted signal at time (n+1) ｒ and the distances of the first to nth surviving paths of the transmitted signal. Note that the distance of the predetermined distance function may be, for example, a square error or a sum of square errors.

[0022] b ｑ ｎ＋１ (q is an integer between 1 and Q, where Q=(R+1)×m) is a quantity called a branch metric in the Viterbi algorithm. ｑ ｎ＋１ is a distance obtained by the Viterbi algorithm, a distance indicated by a predetermined distance function, and a distance indicating the likelihood of transition from the nth symbol of the transmitted signal to each candidate for the (n+1)th symbol. Since the symbol multilevel degree is m=2, the next bit following each candidate for the nth symbol in the (n+1)th symbol is either 0 or 1. Therefore, the number Q of branch metrics is (R+1)×m.

[0023] The distance indicated by the branch metric may be, for example, a squared error or a sum of squared errors. The distance of a predetermined distance function in the path metric may differ from the distance of a predetermined distance function in the branch metric. Therefore, for example, if the distance indicated by the branch metric is a squared error, the distance indicated by the path metric is the sum of squared errors.

[0024] In the example of FIG. 2, for example, the symbol at time (n-1) is in state S ０ If, at time n, the state S １ The distance indicated by the branch metric when １ ｎ is.

[0025] The branch metric values ​​are calculated based on the received signal and an estimated transfer function, which is a previously estimated result of the transfer function of the transmission path 2. The estimated transfer function is estimated, for example, based on the result of propagating a previously prepared training signal to the receiver 3 via the transmission path 2.

[0026] The process of calculating the branch metric value based on the estimated transfer function and the received signal may be any existing process. For example, the process of calculating the branch metric value based on the estimated transfer function and the received signal is a process of obtaining 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. Note that the symbol sequence indicated by the branch metric refers to a candidate sequence corresponding to the branch corresponding to the branch metric.

[0027] The (n+1)th path metric is the sum of the nth path metric of the transition source and a branch metric indicating the likelihood of a transition from the nth state of the transition source to the (n+1)th state of the transition destination.

[0028] The Viterbi algorithm is a process for sequentially calculating path metrics and branch metrics from time n=1 to n=N in this manner.

[0029] <First Soft Decision Processing> Returning to the explanation of Fig. 1 , the control unit 40 performs, for example, first soft decision processing as processing for making a soft decision on the (n+1)th symbol (n is an integer between 1 and N, and N is an integer greater than or equal to 1) of the transmission signal. The first soft decision processing is processing that includes branch metric estimation processing, path metric estimation processing, and bit likelihood estimation processing.

[0030] The branch metric estimation process is a process of estimating the likelihood of transition from the nth symbol of the transmission signal to each candidate of the (n+1)th symbol, which is obtained by the Viterbi algorithm, based on the received signal and an estimated transfer function, which is a previously obtained estimation result of the transfer function of the transmission path 2. As described above, the likelihood of transition from the nth symbol of the transmission signal to each candidate of the (n+1)th symbol is a quantity called a branch metric in the Viterbi algorithm. Therefore, in the example of FIG. 2, the state S ０ , S １ , S ２ , S ３ is an example of a candidate.

[0031] The path metric estimation process is a process for estimating the likelihood obtained by the Viterbi algorithm that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal, based on the result of the branch metric estimation process. As described above, the likelihood obtained by the Viterbi algorithm that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal is a quantity called a path metric in the Viterbi algorithm.

[0032] The bit likelihood estimation process is a process of estimating the likelihood that the kth (k is an integer between 1 and m) bit in the (n+1)th symbol of the transmission signal is a predetermined bit, using the path metric of each candidate for the (n+1)th symbol of the transmission signal. The path metric of each candidate for the (n+1)th symbol of the transmission signal is the path metric obtained by the path metric estimation process. The bit likelihood estimation process is a process that does not use any path metrics other than the path metric of each candidate for the (n+1)th symbol of the transmission signal.

[0033] The control unit 40 acquires the likelihood estimated in the bit likelihood estimation process as the result of soft decision for the (n+1)th symbol of the transmission signal.

[0034] <First Example of Likelihood in First Soft Decision Process> The likelihood estimated in the bit likelihood estimation process is expressed by, for example, the following equation (1). ｋ、ｎ is the likelihood estimated by the bit likelihood estimation process, and indicates 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, information indicating the likelihood that the bit is 0 is also information indicating the likelihood that the bit is 1.

[0035]

[0036]

[0037] c ｋ , ｎ represents the k-th bit of the n-th symbol of the transmission signal. σ represents the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2. Therefore, when the likelihood estimated in the bit likelihood estimation process is expressed by equation (1), the bit likelihood estimation process also uses information indicating the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2.

[0038] The standard deviation of the distribution of noise imparted to the optical signal in the transmission line 2 is, for example, a predetermined value. Ｍ represents a candidate symbol value, i.e., u Ｍ Ha ０ ~u Ｒ Therefore, for example, when the modulation method is PAM4 (4 Pulse Amplitude Modulation), for example, Ｍ If M=0, then u ０ = [c １，ｎ , c ２，ｎ ] = [0, 0], and if M = 1, then u １ = [c １，ｎ , c ２，ｎ ] = [0, 1], and if M = 2, then u ２ = [c １，ｎ , c ２，ｎ ] = [1, 1], and if M = 3, then u３ = [c １，ｎ , c ２，ｎ ] = [1, 0].

[0039] <Second Example of Likelihood in First Soft Decision Process> The likelihood estimated in the bit likelihood estimation process may be expressed by, for example, the following equation (3). Note that equation (1) is an approximation of equation (3). Specifically, the approximation replaces all symbol likelihoods except the maximum symbol likelihood with 0.

[0040] The left side of equation (3) λ ｋ、ｎ is the likelihood estimated by the bit likelihood estimation process, and indicates 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, information indicating the likelihood that the bit is 0 is also information indicating the likelihood that the bit is 1.

[0041]

[0042]

[0043] Equation (4) includes the value of the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2. Therefore, when the likelihood estimated in the bit likelihood estimation process is expressed by equation (3), information indicating the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2 is also used in the bit likelihood estimation process.

[0044] <Second Soft Decision Processing> The control unit 40 may perform, for example, second soft decision processing as processing for making a soft decision on the (n+1)th symbol (n is an integer between 1 and N, and N is an integer greater than or equal to 1) of the transmission signal. The second soft decision processing includes hard decision processing, likelihood estimation processing, and difference acquisition processing.

[0045] The hard decision process is a process of making a hard decision using the Viterbi algorithm based on the estimated transfer function and the received signal.

[0046] The likelihood estimation process is a process of estimating the likelihood of each candidate for the (n+1)th symbol of the transmitted signal (hereinafter referred to as a "symbol candidate") based on the result of the hard decision process, the estimated transfer function, and the received signal. ０ , S １ , S２ , S ３ is an example of a symbol candidate. The likelihood estimated in the likelihood estimation process is called an estimated likelihood.

[0047] The difference acquisition process is a process for acquiring the difference (hereinafter referred to as "likelihood difference") between the estimated likelihood of a symbol candidate whose kth bit (k is an integer between 1 and K) is a predetermined bit and the estimated likelihood of a symbol candidate whose kth bit is not the predetermined bit.

[0048] The control unit 40 acquires the likelihood difference obtained in the difference acquisition process as the result of soft decision on the (n+1)th symbol of the transmission signal.

[0049] <First Example of Estimated Likelihood in Second Soft-Decision Process> The estimated likelihood is expressed by, for example, the following equation (5).

[0050]

[0051]

[0052] In equation (5), H with a hat accent (^) represents the estimated transfer function. ｎ represents the received signal. C' expressed by equation (6) Ｍ、ｎ is the result of the hard decision process and the symbol u, which is one of the candidates for the n-th symbol of the transmitted signal. Ｍ Hereinafter, we will refer to the ordered set C'. Ｍ、ｎ is called a symmetric ordered set. ｎ represents the n-th symbol of the transmitted signal estimated by hard decision processing, where l is the memory length as described above.

[0053] When the estimated likelihood is expressed by equation (5), the likelihood difference is expressed, for example, by the following equation (7). Note that in the example of equation (7), there are two types of bits, 0 and 1. Therefore, information indicating the likelihood that the bit is 0 is also information indicating the likelihood that the bit is 1.

[0054]

[0055] Equation (7) includes the value of the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2. Therefore, when the likelihood difference estimated in the difference acquisition process is expressed by equation (7), information indicating the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2 is also used in the difference acquisition process.

[0056] <Second Example of Estimated Likelihood in Second Soft-Decision Processing> The estimated likelihood may be expressed, for example, by the following equation (8). Note that equation (5) is obtained by normalizing equation (8) and taking the natural logarithm. Here, coefficients that do not depend on M and n are normalized.

[0057]

[0058] Equation (8) includes the value of the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2. Therefore, when the likelihood estimated in the likelihood estimation process is expressed by equation (8), information indicating the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2 is also used in the likelihood estimation process.

[0059] When the estimated likelihood is expressed by equation (8), the likelihood difference is expressed, for example, by the following equation (9). Note that in the example of equation (9), there are two types of bits: 0 and 1. Therefore, information indicating the likelihood that the bit is 0 is also information indicating the likelihood that the bit is 1.

[0060]

[0061] <Third Example of Estimated Likelihood in Second Soft-Decision Processing> The estimated likelihood may be obtained, for example, based on the difference between the result of applying an estimated transfer function to the result of the hard-decision processing and the received signal. The difference between the result of applying the estimated transfer function to the result of the hard-decision processing and the received signal represents an estimated result of the noise distribution.

[0062] The difference between the result of applying the estimated transfer function to the result of the hard decision process and the received signal is specifically expressed by the following equation (10).

[0063]

[0064] x' in bold in equation (10) ｎ means the ordered set of the following formula (11).

[0065]

[0066] As described above, the distribution of the difference between the result of applying the estimated transfer function to the result of hard decision processing and the received signal is an estimated result of the noise distribution, so W is a quantity that represents the estimated result of the noise.

[0067] Hereinafter, the process of obtaining an estimated likelihood of a candidate for the (n+1)th symbol of a transmitted signal based on the distribution of the difference between the result of applying an estimated transfer function to the result of hard decision processing and the received signal will be referred to as a modified likelihood estimation process. The modified likelihood estimation process is a type of likelihood estimation process, as it is a process of estimating the likelihood of each candidate for the (n+1)th symbol of a transmitted signal based on the result of hard decision processing, the estimated transfer function, and the received signal.

[0068] 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 hard decision process on l symbols before the symbol to be estimated in the modified likelihood estimation process. Therefore, for example, when a candidate for the (n+1)th symbol of a transmission signal is the symbol to be estimated by the modified likelihood estimation process, hard decision is made on l symbols before the nth symbol in the hard decision process.

[0069] In the modified likelihood estimation process, for example, a histogram with a predetermined class width is generated for noise W with a sample count of α. The horizontal axis of the histogram represents the class, and the vertical axis represents the frequency. Note that processing for noise with a sample count of α means processing for a set whose elements are noise W and whose number of elements is α. In such a case, the modified likelihood estimation process then normalizes the number of samples in each class by the number of samples in the class with the largest number of samples.

[0070] In such a case, the next step in the deformation likelihood estimation process is to calculate the target ordered set C'. Ｍ、ｎ The number of samples belonging to a class that includes the difference between the result of applying the estimated transfer function to the received signal and the result of applying the estimated transfer function to the received signal is obtained as the likelihood for each symbol. Ｍ、ｎThe phrase "includes the difference between the result of applying an estimated transfer function to the received signal" specifically means selecting a class corresponding to the likelihood of the symbol M at time index n.

[0071] 3 is a diagram showing an example of the hardware configuration of the soft decision-making device 4 in the embodiment. The soft decision-making device 4 includes a control unit 40 including a processor 91 such as a CPU and a memory 92 connected by a bus, and executes a program. By executing the program, the soft decision-making device 4 functions as a device including the control unit 40, an interface unit 41, and a storage unit 42.

[0072] More specifically, the processor 91 reads out a program stored in the storage unit 42 and stores the read program in the memory 92. The processor 91 executes the program stored in the memory 92, whereby the soft decision device 4 functions as a device including the control unit 40, the interface unit 41, and the storage unit 42.

[0073] The control unit 40 controls the operations of various functional units included in the soft decision device 4. The control unit 40 executes, for example, a first soft decision process. The control unit 40 executes, for example, a second soft decision process instead of the first soft decision process.

[0074] The interface unit 41 includes an interface for connecting the soft decision device 4 to an external device. The interface unit 41 communicates with the external device via wired or wireless communication. The external device is, for example, the receiver 3. In this case, the interface unit 41 acquires, for example, a received signal acquired by the receiver 3.

[0075] The interface unit 41 includes input devices such as a mouse, a keyboard, a touch panel, etc. The interface unit 41 may also include an interface that connects these input devices to the soft decision device 4.

[0076] The interface unit 41 includes a display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, an organic EL (Electro-Luminescence) display, etc. The interface unit 41 may include an interface that connects these display devices to the soft decision device 4.

[0077] The storage unit 42 is configured using a computer-readable storage medium device (non-transitory computer-readable recording medium) such as a magnetic hard disk device or a semiconductor storage device. The storage unit 42 stores various information related to the soft decision device 4. The storage unit 42 may store, for example, various information generated as a result of processing executed by the control unit 40. The storage unit 42 may store, for example, a received signal acquired by the interface unit 41. The storage unit 42 may, for example, have an estimated transfer function stored in advance.

[0078] 4 is a flowchart illustrating a first example of the flow of processing executed by the soft decision-making device 4 in the embodiment. More specifically, FIG. 4 is a flowchart illustrating an example of the flow of processing executed by the soft decision-making device 4 that executes the first soft decision processing.

[0079] The control unit 40 acquires the estimated transfer function stored in the storage unit 42 and the received signal acquired by the interface unit 41 (step S101). Next, the control unit 40 executes branch metric estimation processing (step S102). Next, the control unit 40 executes path metric estimation processing (step S103).

[0080] Next, the control unit 40 executes a bit likelihood estimation process (step S104). The control unit 40 acquires the likelihood estimated in the process of step S104 as a result of soft decision for the (n+1)th symbol of the transmission signal. Next, the control unit 40 controls the operation of the interface unit 41 to cause the interface unit 41 to output the likelihood estimated in step S104 (step S105).

[0081] 5 is a flowchart illustrating a second example of the flow of processing executed by the soft decision-making device 4 in the embodiment. More specifically, FIG. 5 is a flowchart illustrating an example of the flow of processing executed by the soft decision-making device 4 that executes the second soft decision processing.

[0082] The control unit 40 acquires the estimated transfer function stored in the storage unit 42 and the received signal acquired by the interface unit 41 (step S201). Next, the control unit 40 executes hard decision processing (step S202). Next, the control unit 40 executes likelihood estimation processing (step S203).

[0083] Next, the control unit 40 executes a difference acquisition process (step S204). The control unit 40 acquires the likelihood difference acquired in the process of step S204 as a result of soft decision for the (n+1)th symbol of the transmission signal. Next, the control unit 40 controls the operation of the interface unit 41 to cause the interface unit 41 to output the likelihood difference estimated in step S204 (step S205).

[0084] In this way, the soft decision device 4 performing the second soft decision process makes a soft decision on the main symbol, which is the (n+1)th symbol of the transmission signal with a symbol multilevel degree of m. The soft decision device 4 performing the second soft decision process includes a control unit 40. The control unit 40 performs hard decision processing using the Viterbi algorithm based on an estimated transfer function, which is a previously obtained estimate of the transfer function of the transmission path 2 through which the transmission signal propagates, and a received signal, which is a result of receiving the transmission signal. The control unit 40 performs likelihood estimation processing to estimate the likelihood of each candidate for the (n+1)th symbol based on the hard decision processing result, the estimated transfer function, and the received signal. The control unit 40 performs difference acquisition processing to acquire 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 soft decision result.

[0085] <Experimental Results> An example of the results of an experiment using the soft decision device 4 will be described. In the experiment, a comparative experiment was also conducted to evaluate the effect of the experiment using the soft decision device 4. The technology used in the comparative experiment was a technology that does not use the soft decision device 4 (hereinafter referred to as the "comparison technology"). More specifically, the comparison technology is a technology that estimates a primary symbol by applying an inverse function of a transfer function to a received signal.

[0086] First, an example of an optical transmission system 100 used in the experiment will be described.

[0087] In the experiment, transmitter 1 converted a digital signal representing the content the user wanted to transmit into an analog signal. The conversion in the experiment was 128 Gsample / s, 65 GHz. In the experiment, transmitter 1 amplified the analog signal obtained by the conversion.

[0088] In the experiment, transmitter 1 modulated a laser beam with a wavelength of 1310 nm with an amplified analog signal and output the modulated signal as an optical signal. The modulation method was PAM4. The optical signal output from transmitter 1 was incident on transmission line 2 and propagated through transmission line 2.

[0089] In the experiment, the transmission line 2 was a single-mode fiber with a length of 10 km. The chromatic dispersion of the transmission line 2 was −8 ps / nm at a wavelength of 1310 nm.

[0090] In the experiment, receiver 3 was equipped with a variable optical attenuator, and the power of the optical signal output from transmission line 2 was attenuated by the variable optical attenuator in receiver 3. Receiver 3 converted the optical signal after the power attenuation by the variable optical attenuator into an electrical signal using a photodiode. The bandwidth of the photodiode was 50 GHz.

[0091] In the 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 was an example of a received signal in the experiment.

[0092] In the experiment, the soft decision device 4 acquired the received signal obtained in this manner. In the experiment, the control unit 40 included in the soft decision device 4 executed a first soft decision process and acquired the likelihood estimated by the first soft decision process as the soft decision result. More specifically, in the experiment, the control unit 40 estimated the likelihood expressed by equation (1) by executing the first soft decision process.

[0093] Fig. 6 is a first diagram showing an example of experimental results in the embodiment. More specifically, Fig. 6 is a diagram showing an example of experimental results using the comparative technology. The horizontal axis of Fig. 6 represents frequency. The vertical axis of Fig. 6 represents loss. Fig. 6 shows that when the comparative technology is used, loss increases near a frequency of 60 GHz.

[0094] 7 is a second diagram showing an example of experimental results in the embodiment. The horizontal axis of FIG. 7 represents received optical power (ROP). The vertical axis of FIG. 7 represents normalized general mutual information (NGMI).

[0095] "MLSE(NGMI)" shows the results of estimating the likelihood expressed by equation (1) by performing the first soft decision process using the soft decision device 4, as indicated by the NGMI value. "FFE(NGMI)" (Feed-Forward Equalizer) shows the results of using the comparison technology, as indicated by the NGMI value. Figure 7 shows that the NGMI is higher when the first soft decision process is performed using the soft decision device 4 and the likelihood expressed by equation (1) is estimated than when using the comparison technology.

[0096] FIG. 7 shows that by using the soft decision result from the soft decision device 4, the main symbol can be estimated with higher accuracy than with the comparative technology.

[0097] <Explanation of Effects Achieved by the Soft Decision Device 4> As described above, the comparative technology estimates the main symbol by applying the inverse function of the transfer function to the received signal. When applying the inverse function, even the noise added to the signal on the transmission path 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.

[0098] The soft decision device 4 configured in this manner executes the first soft decision process or the second soft decision process, and therefore obtains a soft decision result without using the inverse function of the transfer function, allowing the soft decision device 4 to estimate the symbols of the transmission signal with higher accuracy.

[0099] <Modification of the first embodiment>

[0100] It should be noted that the above-mentioned formulas (1), (4), (7), and (8) include the standard deviation σ of the distribution of noise imparted to the optical signal in the transmission path 2, but the value of the standard deviation σ of the distribution of noise imparted to the optical signal in the transmission path 2 may or may not be a predetermined value.

[0101] For example, the standard deviation σ may be calculated based on the difference between the result of applying an estimated transfer function to the correct data and the received signal. The correct data is data that indicates the correctness of the transmitted signal. Therefore, for example, the standard deviation σ may be calculated by the process expressed by the following equation (12).

[0102]

[0103]

[0104] x in formula (13) ｄindicates the d-th symbol of the transmitted signal indicated by the correct data. In equation (13), l denotes the memory length of the estimated transfer function, while in equation (12), e denotes the start position of the transmitted signal indicated by the correct data. The start position indicates the position along the time axis in the correct data used. D denotes the number of symbols used to calculate the standard deviation σ. d denotes the time index in the correct data used. Therefore, equation (12) represents a process of obtaining the average value of D estimated noises as the standard deviation σ. The estimated noise is the squared error between the result of applying the estimated transfer function to the correct data and the received signal.

[0105] For example, the standard deviation σ may be obtained based on the difference between the result of applying an estimated transfer function to the result of hard decision processing and the received signal. Therefore, for example, the standard deviation σ may be obtained by processing expressed by the following equation (14):

[0106]

[0107]

[0108] x' in formula (15) ｄ indicates the d-th symbol of the transmitted signal indicated by the result of the hard decision process. The l in equation (15) denotes the memory length of the estimated transfer function, while the e in equation (14) denotes the start position of the transmitted signal indicated by the result of the hard decision process. The start position denotes the position along the time axis in the hard decision process result. D denotes the number of symbols used to calculate the standard deviation σ. d denotes the time index in the hard decision result to be used. Therefore, equation (14) represents the process of obtaining the average value of D estimated noises as the standard deviation σ.

[0109] For example, the value of the standard deviation σ may be a value that satisfies the condition of maximizing the NGMI. The NGMI is a quantity defined by, for example, the following equation (16).

[0110]

[0111]

[0112]

[0113] m' represents the number of bits of the transmitted signal. Therefore, when the modulation method is PAM4, m' is log ２ m' = 2. N represents the number of symbols used in calculating CrossEntropy.

[0114] Note that the soft output value (i.e., the result of soft decision) may diverge to the positive or negative side. Some programming languages ​​do not output a value when they diverge. Therefore, to avoid a situation where no value is output, an upper or lower limit of the soft output value may be set in advance in the process of making a soft decision on the (n+1)th symbol of the transmission signal.

[0115] The soft decision-making device 4 may be implemented using a plurality of information processing devices communicably connected via a network. In this case, the functional units of the soft decision-making device 4 may be distributed and implemented in the plurality of information processing devices.

[0116] Note that all or part of the functions of the soft decision device 4 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array). The program may be recorded on a computer-readable recording medium. Examples of computer-readable recording media include portable media such as flexible disks, magneto-optical disks, ROMs, and CD-ROMs, and storage devices such as hard disks built into computer systems. The program may be transmitted via a telecommunications line.

[0117] (Second Embodiment) In the second embodiment, when a symbol decision result (hard decision result) obtained by backward calculation (tracing back survivor paths) in a trellis diagram differs from a symbol decision result obtained by forward calculation (path metric calculation and survivor path selection), the soft decision result obtained by backward calculation for a complex soft decision output that requires path metrics indicated by paths other than survivor paths is replaced with a predetermined soft decision result obtained by simple calculation, which is a major difference from the first embodiment. In the second embodiment, the differences from the first embodiment will be mainly described.

[0118] 8 is a diagram showing an example of the configuration of the control unit 40 in the embodiment. The control unit 40 includes a transfer function estimation unit 401, a branch metric processing unit 402, a path metric processing unit 403, a hard decision output unit 404, and a soft decision output unit 405.

[0119] In the following, symbols placed above letters in mathematical expressions or functions (hereinafter referred to as "mathematical expressions, etc.") are written before the letters. For example, the symbol "^" placed above letters in mathematical expressions, etc. will be written before the letter "H" as "^H" in the following.

[0120] The transfer function estimation unit 401 calculates the estimated transfer function "^H" as shown in equation (19).

[0121]

[0122] The branch metric processing unit 402 calculates the branch metric "b" as shown in equation (20).

[0123]

[0124] The path metric processing unit 403 calculates the path metric "p" as shown in equation (21).

[0125]

[0126] The hard decision 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 decision output unit 404 outputs "m" at the time index "n". ｌThe minimum path metric is selected from the path metrics of the "states s". The path in the time direction made up of the branches used to calculate the selected minimum path metric is called the "survival path".

[0127] Whichever state "s" is selected as the starting point for tracing the remaining paths of the trellis diagram in the direction opposite to the time direction (state transition direction), the same path will be traced back. Traces back the same path is called "merging paths by backward operation." The symbol corresponding to the state at the end of the merged path (hereinafter referred to as "traceback") is output as the symbol decision result. The symbol decision result corresponds to the hard decision result (hard decision output).

[0128] The hard decision output unit 404 outputs the hard decision result "x'" by backward calculation in the trellis diagram. ｎ－ａ The symbol determination result is expressed as in equation (22).

[0129]

[0130] Here, "a" represents the number of times (number of times) to trace back the path in the direction opposite to the state transition direction. ｊ " represents the state at the traceback destination "j".

[0131] Furthermore, the hard decision output unit 404 outputs the hard decision result "x'' by forward calculation in the trellis diagram. ｎ－ａ The state with the smallest path metric at time index "n" is "s ｊ ", the symbol "x'' determined as a result of the forward operation (path metric calculation and survivor path selection) is ｎ " is expressed as in equation (23). Note that the state S ｊ The time index of the state S in Eq. (22) ｊ It should be noted that the left side of equation (23) is not equal to the left side of equation (22).

[0132]

[0133] This determined symbol "x'' ｎ" is the determination result obtained by using only forward calculations (path metric calculation and survivor path selection) without using backward calculations (tracing survivor paths). Here, since only the sequence length of the most likely symbol candidate is estimated, the effect of sequence length estimation including the number of traces back by backward calculations cannot be obtained.

[0134] Therefore, even if the time index is the same "na", the symbol determination result "x'" by the backward calculation is ｎ－ａ " and the symbol determination result "x'' by forward operation ｎ－ａ If they are different, the symbol determination result "x''" by the forward operation is ｎ－ａ ", the symbol determination result "x'" by backward calculation is ｎ－ａ " is likely to be more accurate.

[0135] In the formula (1) exemplified in the first embodiment, the log-likelihood ratio "λ Ｍ，ｎ Therefore, the symbol determination result of the backward operation is "x' ｎ－ａ " and the symbol determination result of the forward operation "x'' ｎ－ａ " is different, the accuracy of the log-likelihood ratio "λ" estimated based on the path metric information obtained by forward calculation may not be high.

[0136] Therefore, in the second embodiment, the soft-decision output unit 405 approximately incorporates the effect of tracing back paths (backward calculations) in a trellis diagram through simple calculations. That is, the soft-decision output unit 405 replaces the soft-decision results of complex backward calculations with soft-decision results of simple calculations. The complexity of this simple calculation is comparable to the complexity of the Viterbi algorithm used in hard-decision maximum likelihood sequence estimation (MLSE), for example.

[0137] Log-likelihood ratio λ' ｋ，ｎ " is expressed as in equation (24) using equation (25). The operation of equation (24) is essentially the same as equation (7).

[0138]

[0139]

[0140] Here, "n" represents a time index (1≦n≦N). "k" represents the bit number (1≦k≦m) of the symbol decision result at time index "n". ｋ，ｎ " is the symbol decision result "x' at time index "n". ｎ " represents the k-th bit (0 or 1) of "c''. ｋ，ｎ " is the symbol decision result "x'' at time index "n". ｎ " represents the k-th bit (0 or 1) of ".

[0141] The soft decision output unit 405 obtains a predetermined positive constant "A" from, for example, the memory 92. This constant "A" is predetermined, for example, so that the normalized generalized mutual information (NGMI) is maximized as a result of changing the positive variable at a predetermined interval. For example, a variable that takes a value from 0.001 to 1.000 is changed at intervals of 0.001, and a log-likelihood ratio "λ" is calculated for each value of the variable. The value of the variable that maximizes the normalized generalized mutual information is predetermined as the positive constant "A."

[0142] The soft decision output unit 405 outputs the symbol decision result "x' ｎ－ａ " and the symbol determination result of the forward operation "x'' ｎ－ａ The soft decision output unit 405 compares the symbol decision result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ " are the same, the soft decision output unit 405 outputs the soft decision result "λ ｋ，ｎ－ａ " and the log-likelihood ratio "λ' ｋ，ｎ－ａ " is output.

[0143] The soft decision output unit 405 outputs the symbol decision result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ " is different from the log-likelihood ratio "λ'" in equation (24) using the sign function "sgn". ｋ，ｎ The soft decision output unit 405 obtains the sign of the log likelihood ratio "λ' ｋ，ｎ Instead of taking the sign of , the log-likelihood ratio , λ , in Eq.ｋ，ｎ The soft decision output unit 405 may obtain the sign of the log-likelihood ratio "λ' ｋ，ｎ ” and a predetermined constant “A” and a standard deviation “σ” of the noise distribution. ｋ，ｎ－ａ " is calculated.

[0144] Symbol determination result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ ” and the soft decision result “λ ｋ，ｎ－ａ (log likelihood ratio) and the symbol decision result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ ” and the new soft decision result “λ ｋ，ｎ－ａ ” (modified log-likelihood ratio) and are expressed as in equation (26).

[0145]

[0146] 9 is a flowchart showing a third example of the flow of processing executed by the soft decision device 4 in the embodiment. The control unit 40 acquires the estimated transfer function stored in the storage unit 42 and the received signal acquired by the interface unit 41 (step S301). Next, the control unit 40 executes branch metric estimation processing (step S302). Next, the control unit 40 executes path metric estimation processing (step S303).

[0147] The control unit 40 executes hard decision processing to generate a symbol decision result of the backward calculation and a symbol decision result of the forward calculation (step S304). The control unit 40 executes bit likelihood estimation processing based on the symbol decision result of the backward calculation, the symbol decision result of the forward calculation, and a predetermined constant "A" (step S305). The control unit 40 acquires the likelihood estimated in the processing of step S305 as a result of soft decision. The control unit 40 controls the operation of the interface unit 41 to acquire the likelihood "λ" estimated in step S305. ｋ，ｎ－ａ " is output to the interface unit 41 (step S306).

[0148] As described above, the control unit 40 calculates the decision result "x'" of the nth symbol by performing calculations in order from the (n+a)th (for example, a=1) to the nth symbol of the transmission signal. ｎ " and the decision result "x'' of the nth symbol obtained by performing calculations in order from the nth to the (n+a)th symbol of the transmitted signal. ｎ " is different, the sign of the estimated likelihood (sgn(λ' ｋ，ｎ )) is the opposite sign "-", a predetermined constant "A", and a standard deviation "σ", and the likelihood "λ ｋ，ｎ The predetermined constant "A" is determined by "2σ" based on the likelihood "P" of the distribution indicating a positive peak and the standard deviation "σ". ２ It is defined as "P".

[0149] In this way, in the second embodiment, the symbol determination result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ " and the symbol determination result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ " and " are different, the logarithmic likelihood ratio (bit likelihood) for each bit "λ ｋ，ｎ－ａ This makes it possible to further improve the standard generalized mutual information (NGMI).

[0150] Furthermore, compared to the first embodiment, it is possible to estimate the symbols of the transmission signal with higher accuracy.

[0151] <First Modification of 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 exemplified in equation (26), the absolute value of the soft decision result is "A / 2σ ２ " is expressed as:

[0152] The variance of the bit likelihood histogram, σ ２ Regardless of the bit likelihood histogram, the optimum value of the positive constant "A" tends to be constant for each transmission system and demodulation method. In addition, the optimum value of the positive constant "A" is determined by the positive likelihood "P(=A / 2σ)" that indicates the peak of the bit likelihood histogram. ２ ) is close to the likelihood "P (= A / 2σ２ )), a positive constant "A" may be predetermined.

[0153] <Experimental Results> An example of the results of an experiment using the soft decision device 4 will be described. Fig. 11 is a third diagram showing an example of the experimental results in the embodiment. In Fig. 11, the symbol multilevel degree "M" is 4, for example. The memory length "d" is 5, for example. The number of traces "T" is 20, for example. The predetermined positive constant "A" in the second embodiment is 0.018, for example.

[0154] The number of path metrics required to calculate the log-likelihood ratio “λ” in the first embodiment is “M ｄ " is, for example, 1024. The number of path metrics "2M ｄ " is, for example, 1024. The number of path metrics "M" required to calculate the log-likelihood ratio "λ" of the FFE method is ｄ＋１ "T" is 81920 as an example.

[0155] The graph on the left side of Figure 11 shows the relationship between received optical power (ROP) and standard 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.

[0156] In both the NL-MLSE method in the first embodiment and the NL-MLSE method in the second embodiment, a standard generalized mutual information (MMI) higher than that of the FFE method is achieved. When the ROP is 3 dBm, the standard generalized MMI is improved by approximately 18% in the first embodiment. In addition, the standard generalized MMI is improved by approximately 22% in the second embodiment.

[0157] The graph on the right side of Figure 11 shows the relationship between the bit error rate (BER) and the standard generalized mutual information (NGMI) for the FFE scheme, the NL-MLSE scheme in the first embodiment, and the NL-MLSE scheme in the second embodiment. In the graph on the right side, the dashed line overlapping the results for the FFE scheme represents a theoretical curve for an additive white Gaussian noise (AWGN) channel. The performance represented by the theoretical curve corresponds to the performance of a soft output Viterbi algorithm (SOVA), which requires a very high computational load, when the same BER as the NL-MLSE scheme is obtained.

[0158] The FFE method cannot achieve a bit error rate of "0.8". In contrast, the NL-MLSE method in the first embodiment can achieve a bit error rate of "0.931". Furthermore, the NL-MLSE method in the second embodiment can achieve a bit error rate of "0.962". In this way, the optical transmission system 100 in the second embodiment can achieve performance close to the standard generalized mutual information of "0.985" achieved by the soft-output Viterbi algorithm, with a smaller amount of calculation.

[0159] <Second Variation of Second Embodiment> In the above-described second embodiment, even if the determination result for each bit of a symbol is correct, if the determination result for each symbol is incorrect, the log-likelihood ratio “λ” may be changed, and therefore the standard generalized mutual information may not be improved.

[0160] In the second modification of the second embodiment, a determination is made for each bit of a symbol. The second modification of the second embodiment differs from the second embodiment in that, when the kth bit of the first symbol and the kth bit of the second symbol are different, a predetermined fixed value is set as a new log-likelihood ratio for the kth bit. The second modification of the second embodiment will be described mainly focusing on the differences from the first and second embodiments.

[0161] Even if the decision result of a symbol is overturned by backward calculation in the trellis diagram (tracing back the survivor path), the bit of the symbol before the decision result was overturned and the bit of the symbol after the decision result was overturned may be the same for corresponding bits. Therefore, the hard decision output unit 404 outputs the symbol decision result "x' ｎ－ａ " bit "c' ｋ，ｎ－ａ " and the symbol determination result "x'' ｎ－ａ " bit "c'' ｋ，ｎ－ａ " to the soft decision output unit 405. The soft decision output unit 405 outputs the symbol decision result "x' ｎ－ａ " and the symbol result is "x'' ｎ－ａ " is judged for each bit of the symbol judgment result.

[0162] For example, in the trellis diagram illustrated in FIG. 2, the provisional symbol decision result "x' ｎ " status "S ０ " is the symbol judgment result "x'' ｎ " status "S １ Even if it is covered by "c' １，ｎ " value "0" and bit "c'' １，ｎ " is the same as the value "0". ２，ｎ " value "0" and bit "c'' ２，ｎ " is different from the value "1." In this case, the soft decision output unit 405 changes the log-likelihood ratio (soft decision result) only for bits with different values.

[0163] Symbol determination result "x' ｎ－ａ " bit "c' ｋ，ｎ－ａ " and the symbol result is "x'' ｎ－ａ " bit "c'' ｋ，ｎ－ａ ” is the same as the log likelihood ratio “λ ｋ，ｎ－ａ (soft decision result) and symbol decision result "x' ｎ－ａ " bit "c' ｋ，ｎ－ａ " and the symbol result is "x'' ｎ－ａ " bit "c'' ｋ，ｎ－ａ ” and the modified log-likelihood ratio ”λ ｋ，ｎ－ａ " (new soft decision result) and are expressed as in equation (27).

[0164]

[0165] As described above, when the determination result of bit "c'" of nth symbol "x'" obtained by performing calculations on the (n+1)th to nth symbols of the transmission signal differs from the determination result of bit "c"" of nth symbol "x"" obtained by performing calculations on the nth to (n+1)th symbols of the transmission signal (c'≠c"), the control unit 40 changes the likelihood "λ'" estimated in the bit likelihood estimation process to a new likelihood "λ". Here, the control unit 40 changes the likelihood "λ'" to a new likelihood "λ" based on the sign "-sgn" that is the opposite of the sign of the estimated likelihood, a predetermined constant "A", and a standard deviation "σ".

[0166] This makes it possible to improve the standard generalized mutual information (NGMI) while increasing the possibility of obtaining an improvement effect on the standard generalized mutual information compared to the second embodiment. Also, it makes it possible to estimate the symbols of a transmission signal with higher accuracy while increasing the possibility of obtaining an improvement effect on the standard generalized mutual information compared to the second embodiment.

[0167] (Third Embodiment) In the third embodiment, a decision is made for each bit of a symbol. The third embodiment is mainly different from the first and second embodiments in that a final log-likelihood ratio for the k-th bit is calculated based on a provisional log-likelihood ratio depending on whether the k-th bit of the first symbol is the same as the k-th bit of the second symbol and whether the provisional log-likelihood ratio (soft decision result) is positive or negative. The third embodiment will be described mainly focusing on the differences from the first and second embodiments.

[0168] In the soft-output Viterbi algorithm, soft-output calculations are performed based on the path metric "p" at the state traced back in the backward calculations. Therefore, the amount of information held and the amount of calculations in the soft-output Viterbi algorithm increase compared to the hard-output Viterbi algorithm. Therefore, it is necessary to suppress the increase in the amount of calculations.

[0169] 12 is a diagram showing a fourth example of the flow of processing executed by the soft decision device in the embodiment. "α" shown in FIG. 12 is the bit likelihood histogram (log likelihood ratio "λ' ｋ，ｎ "). The compression rate (fixed value) is a constant equal to or greater than 1. When "α" is 1, the result of the backward calculation is not reflected at all in the change of the log-likelihood ratio.

[0170] In addition, the larger "α" is, the more the result of the backward calculation is reflected in the change of the log-likelihood ratio. ｋ，ｎ " is 0 or more (0 or positive value)), and a histogram showing bit "1" (log likelihood ratio "λ' ｋ，ｎ When "α" is less than 0 (negative value), the larger "α" is, the thinner the histogram becomes in the direction of the log-likelihood ratio. As a result, both the histogram representing the bit "0" and the histogram representing the bit "1" move away from the log-likelihood ratio of "0".

[0171] However, the further each histogram is from the log-likelihood ratio "0," the greater the adverse effect of an incorrect bit decision result. For this reason, "α" should not be too large. Therefore, the optimal value of "α" is efficiently estimated by a search process so that the tails of histograms do not overlap near the log-likelihood ratio "0."

[0172] 12 is a parameter that determines the median of the histogram compressed in the direction of the log-likelihood ratio in the bit likelihood histogram. ｋ，ｎ The median of the histogram in the region where β is greater than or equal to 0 is ＋ / 2σ ２ ". Also, the log-likelihood ratio "λ' ｋ，ｎ The median of the histogram in the region where β is less than 0 is － / 2σ ２ "

[0173] The log-likelihood ratio (peak position) that indicates the peak of the histogram and "β / 2σ ２The soft decision output unit 405 estimates the value of the parameter "β" based on the shape of the histogram so that "α" and "β" are equal. Furthermore, since the log-likelihood ratio is normalized by dividing the log-likelihood ratio by the square of the standard deviation, the soft decision output unit 405 estimates the optimal value (constant) of the parameter "β" regardless of the degree of spread of the histogram (the amount of white noise). In this way, the optimal values ​​of "α" and "β" are estimated so that the normalized generalized mutual information (NGMI) is maximized. The soft decision output unit 405 does not need to obtain a predetermined constant "A".

[0174] The soft decision output unit 405 generates a bit likelihood histogram. That is, the soft decision output unit 405 calculates the log likelihood ratio (peak position) indicating the peak of the bit likelihood histogram and the β / 2σ ２ " and " are equal to each other, so the parameter "β ＋ " and parameter "β － " and the standard deviation "σ", the log-likelihood ratio "λ' ｋ，ｎ " is calculated (step S401).

[0175] The soft decision output unit 405 outputs a bit likelihood histogram (log likelihood ratio "λ' ｋ，ｎ " distribution), the log likelihood ratio "λ'" is greater than or equal to 0. ｋ，ｎ－ａ " and the log-likelihood ratio "λ' ｋ，ｎ－ａ " (step S402). The soft-decision output unit 405 compresses the distribution of the bit likelihood histogram in the direction of the log-likelihood ratio for each histogram having a peak based on the compression rate "α" (step S403). The soft-decision output unit 405 identifies the log-likelihood ratio "λ" based on the distribution of the compressed bit likelihood histogram. ｋ，ｎ " is calculated (step S404).

[0176] Log-likelihood ratio λ' ｋ，ｎ－ａ ” is greater than or equal to 0, the new soft decision result “λ ｋ，ｎ－ａ " is expressed as in equation (28).

[0177]

[0178] Log-likelihood ratio λ' ｋ，ｎ－ａ ” is less than 0, the new soft decision result “λｋ，ｎ－ａ " is expressed as in equation (29).

[0179]

[0180] As described above, when the determination result of bit "c'" of nth symbol "x'" obtained by performing calculations on the (n+1)th to nth symbols of the transmission signal differs from the determination result of bit "c"" of nth symbol "x"" obtained by performing calculations on the nth to (n+1)th symbols of the transmission signal (c' ≠ c"), the control unit 40 changes the likelihood "λ'" estimated in the bit likelihood estimation process to a new likelihood "λ". Here, the control unit 40 changes the likelihood "λ'" to the new likelihood "λ" based on the peak position "β" of the likelihood distribution, the compression rate "α", and the standard deviation "σ".

[0181] As a result, the amount of information taken into consideration is greater than in the second embodiment, making it possible to further improve the standard generalized mutual information (NGMI) while suppressing an increase in the amount of calculations.Furthermore, compared to the second embodiment, it becomes possible to estimate the symbols of the transmitted signal with higher accuracy while suppressing an increase in the amount of calculations.

[0182] <Experimental Results> An example of the results of an experiment (128 GBaud PAM4 O-band 10 km transmission experiment) using the soft decision device 4 will be described. FIG. 13 is a fourth diagram showing an example of the experimental results in the embodiments. FIG. 13 shows the relationship between received optical power (ROP) and standard generalized mutual information (NGMI) for the NL-MLSE method in the first embodiment, the NL-MLSE method in the second modified example of the second embodiment, and the NL-MLSE method in the third embodiment. In the second modified example of the second embodiment, the predetermined positive constant "A" is, for example, 0.018. In the third embodiment, "β" is ＋ " is, for example, +0.04. － " is, for example, -0.04.

[0183] The dashed line superimposed on the FFE results represents a theoretical curve for an additive white Gaussian noise (AWGN) channel, whose performance corresponds to that of the computationally intensive soft-output Viterbi algorithm (SOVA) when achieving the same BER as the NL-MLSE method.

[0184] In both the second modification of the second embodiment and the third embodiment, the standard generalized mutual information is improved compared to the first embodiment. That is, in both the second modification of the second embodiment and the third embodiment, it is possible to achieve performance close to that of the soft-output Viterbi algorithm in terms of the standard generalized mutual information while suppressing an increase in the amount of calculation.

[0185] FIG. 14 is a fifth diagram showing an example of experimental results in the embodiment. On the right side of FIG. 14, a bit likelihood histogram (distribution of log-likelihood ratios) in the first embodiment is shown. The area where the soft decision result "λ" is 0 or more corresponds to bit "0". Also, the area where the soft decision result "λ" is less than 0 corresponds to bit "1". "α" in the third embodiment is 1.005. "β" in the third embodiment is ＋ " is, for example, +0.04. － " is, for example, -0.04.

[0186] In the third embodiment, the area where the histogram representing the bit "0" and the histogram representing the bit "1" overlap is small, and therefore the symbol decision performance is improved compared to the first embodiment. In this way, in the third embodiment, natural distribution separation of the log-likelihood ratios and more accurate soft decision output are realized based on the results of the backward calculation and the distribution information of the log-likelihood ratios.

[0187] The device of the present invention can also be realized by a computer and a program, and the program can be recorded on a recording medium or provided via a network.

[0188] Although an embodiment of the present invention has been described above in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and includes designs within the scope of the gist of the present invention.

[0189] 100...optical transmission system, 1...transmitter, 2...transmission path, 3...receiver, 4...soft decision device, 40...control unit, 41...interface unit, 42...storage unit, 91...processor, 92...memory, 401...transfer function estimating unit, 402...branch metric processing unit, 403...path metric processing unit, 404...hard decision output unit, 405...soft decision output unit

Claims

1. A soft decision device that performs soft decision on a main symbol that is the (n+1)th (n is an integer between 1 and N, N is an integer greater than or equal to 1) symbol of a transmission signal with a symbol multilevel degree of m (m is an integer greater than or equal to 2), comprising: a branch metric estimation process that estimates a branch metric, which is a distance indicating the likelihood of transition from the nth symbol of the transmission signal to each candidate for the (n+1)th symbol, based on an estimated transfer function that is a previously obtained estimation result of a transfer function of a transmission path through which the transmission signal propagates, and a received signal that is a result of receiving the transmission signal; and a path metric estimation process that estimates a path metric, which is the sum of a distance indicating the likelihood that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal, and a distance of a surviving path from the 1st to the nth of the transmission signal, based on a result of the branch metric estimation process. a control unit that executes a bit likelihood estimation process that estimates a likelihood that a k-th (k is an integer greater than or equal to 1 and less than or equal to m) bit in the (n+1)-th symbol of the transmission signal is a predetermined bit, using path metrics of each candidate for the (n+1)-th symbol of the transmission signal obtained by the path metric estimation process, and without using any path metrics other than the path metrics of each candidate for the (n+1)-th symbol of the transmission signal, wherein the control unit changes the likelihood estimated in the bit likelihood estimation process when a determination result of the bit of the n-th symbol obtained by performing calculations in order from the (n+1)-th to the n-th symbol of the transmission signal differs from a determination result of the bit of the n-th symbol obtained by performing calculations in order from the n-th to the (n+1)-th symbol of the transmission signal.

2. The soft decision device according to claim 1, wherein the control unit changes the likelihood based on a sign opposite to a sign of the estimated likelihood, a predetermined constant, and a standard deviation.

3. The soft decision device according to claim 1, wherein the control unit changes the likelihood based on a peak position of the distribution of the likelihood, a compression rate, and a standard deviation.

4. A soft decision method executed by a soft decision device that performs soft decision on a main symbol that is the (n+1)th (n is an integer between 1 and N, N is an integer greater than or equal to 1) symbol of a transmission signal with a symbol multilevel degree of m (m is an integer greater than or equal to 2), comprising: a branch metric estimation process that estimates a branch metric, which is a distance indicating the likelihood of transition from the nth symbol of the transmission signal to each candidate for the (n+1)th symbol, based on an estimated transfer function that is a previously obtained estimation result of a transfer function of a transmission path through which the transmission signal propagates, and a received signal that is a result of receiving the transmission signal; and a path metric estimation process that estimates a path metric, which is the sum of a distance indicating the likelihood that each candidate for the (n+1)th symbol of the transmission signal is a symbol of the transmission signal, and a distance of a surviving path from the 1st to the nth of the transmission signal, based on a result of the branch metric estimation process. a control step of executing a bit likelihood estimation process for estimating a likelihood that a k-th bit (k is an integer greater than or equal to 1 and less than or equal to m) in the (n+1)th symbol of the transmission signal is a predetermined bit, using path metrics of each candidate for the (n+1)th symbol of the transmission signal obtained by the path metric estimation process, and without using any path metrics other than the path metrics of each candidate for the (n+1)th symbol of the transmission signal; and a control step of executing the bit likelihood estimation process when a decision result of the bit of the n-th symbol obtained by performing calculations in order from the (n+1)th to the nth symbol of the transmission signal differs from a decision result of the bit of the n-th symbol obtained by performing calculations in order from the nth to the (n+1)th symbol of the transmission signal.

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

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