Soft decision device, soft decision method, and program

Abstract

According to the present invention, a control unit executes bit likelihood estimation processing that estimates a logarithmic likelihood ratio calculated from the likelihood that a kth (k being an integer from 1 to m, inclusive) bit of an (n+1)th symbol of a transmission signal is a prescribed bit using a path metric for each candidate for the (n+1)th symbol of the transmission signal obtained by path metric estimation processing and decision results for the bits of the nth symbol from forward computation that is computation in the order from the nth to the (n+1)th of the transmission signal but not using a path metric other than the path metric for each candidate for the (n+1)th symbol of the transmission signal. The control unit corrects the estimated logarithmic likelihood ratio on the basis of decision results for the bits of the nth symbol from backward computation that is computation in the order from the (n+1)th to the nth of the transmission signal.

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). MLSE is a signal processing technique used in a receiver, which estimates the transfer function of a signal transmission path, compares the output of the estimated transfer function with the received signal, and determines the most likely candidate sequence as the decision result. The output of a typical Viterbi decoder used in MLSE is the determined 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 1).

[0005] Techniques have been proposed for improving the soft-output Viterbi algorithm to estimate the symbols of transmitted signals with higher accuracy (see Non-Patent Documents 2 and 3).

[0006] 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) S. Yamamoto, H. Taniguchi, A. Masuda, M. Nakamura, and Y. Kisaka, “Evaluation of NGMI in 128-Gbaud PAM4 O-band 10-km transmission using MLSE based on nonlinear channel estimation and decision feedback,” Proc. of ECOC, We5.26 (2022) S. Yamamoto, H. Taniguchi, A. Masuda, M. Nakamura, and Y. Kisaka, “LLR shaping technique for achievement of high NGMI for SD-FEC scheme in 128-Gbaud PAM4 10-km transmission with advanced MLSE,” Proc. of ECOC, Tu.A.7.4 (2023)

[0007] However, in the soft-output calculation method disclosed in Non-Patent Document 2, the LLR is calculated from information only on the path metrics in the forward calculation, so if the symbol decision result of the backward calculation differs from the symbol decision result of the forward calculation, the LLR is likely to be an inaccurate value. Also, Non-Patent Document 3 discloses a soft-output calculation method that partially includes the effect of the backward calculation, but it is difficult to select and optimize hyperparameters that affect the accuracy of the soft-output calculation.

[0008] 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.

[0009] 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 a k-th bit (k is an integer between 1 and m) in the (n+1)th symbol of the transmission signal is estimated to be 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 a decision result for the bit of the n-th symbol obtained by forward calculation, which is calculation performed in order from the n-th to the (n+1)-th symbol of the transmission signal, 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 corrects the estimated likelihood based on the decision result for the bit of the n-th symbol obtained by backward calculation, which is calculation performed in order from the (n+1)-th to the n-th symbol of the transmission signal.

[0010] One aspect of the present invention is a soft decision method for making a 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 method comprising the steps of: a branch metric estimation process for estimating 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, which is a previously obtained estimation result of a transfer function of a transmission path through which the transmission signal propagates, and a received signal, which is a result of receiving the transmission signal; and 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 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 and decision results for the bit of the n-th symbol obtained by performing calculations on the transmission signal in order from the n-th to the (n+1)-th symbol, without using 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 correcting the estimated likelihood based on decision results for the bit of the n-th symbol obtained by performing calculations on the transmission signal in order from the (n+1)-th to the n-th symbol.

[0011] According to the present invention, the symbols of a transmitted signal can be estimated with higher accuracy.

[0012] FIG. 1 is an explanatory diagram illustrating an optical transmission system 100 according to an embodiment. FIG. 2 is an explanatory diagram illustrating a Viterbi algorithm according to an embodiment. FIG. 3 is a diagram illustrating an example of the configuration of a control unit 40 according to an embodiment. FIG. 4 is a flowchart illustrating the flow of processing executed by a soft decision device 4 according to an embodiment. FIG. 5 is a flowchart illustrating the flow of bit likelihood estimation processing according to an embodiment. FIG. 6 is a flowchart illustrating a provisional log-likelihood ratio λ' ｋ，ｎ From the log-likelihood ratio λ ｋ，ｎ10 is a schematic diagram showing how to calculate the log-likelihood ratio λ as an experimental result in the embodiment. ｋ，ｎ 1 is a diagram showing the distribution of the log-likelihood ratio λ. 2 is a diagram showing the transition of the value of the shift parameter d in an experiment in an embodiment. 3 is a graph showing the NGMI in an experiment in an embodiment. 4 is a diagram showing the optimal value of the shift parameter d calculated by equation (8) and equation (9). ｋ，ｎ 1 is a diagram showing the change in NGMI depending on whether or not the minimum and maximum values ​​of λ are set. ｋ，ｎ 10 is a diagram showing the relationship between NGMI and f. FIG.

[0013] 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 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. x ｎ 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. Wｎ 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. ３is a symbol represented by an ordered set of 1 bit and 1 bit.

[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 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] 3 is a diagram showing an example of the configuration of the control unit 40 in this 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.

[0030] 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.

[0031] The transfer function estimation unit 401 calculates the estimated transfer function "^H" as shown in equation (1).

[0032]

[0033] The branch metric processing unit 402 calculates the branch metric "b" as shown in equation (2).

[0034]

[0035] 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.

[0036] The path metric processing unit 403 calculates the path metric "p" as shown in equation (3).

[0037]

[0038] 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.

[0039] 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". ｌ The 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".

[0040] 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).

[0041] 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 (4).

[0042]

[0043] 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".

[0044] 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 (5). Note that the state S ｊ The time index of the state S in Eq. (5) ｊ It should be noted that the left side of equation (5) is not equal to the left side of equation (4).

[0045]

[0046] 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.

[0047] 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.

[0048] The soft decision output unit 405 outputs the log-likelihood ratio (LLR) "λ'" calculated based on the path metric information obtained by forward calculation. ｋ，ｎ " is converted into the symbol determination result "x' ｎ－ａ " and amend it based on the above.

[0049] The soft decision output unit 405 calculates the provisional log-likelihood ratio "λ' ｋ，ｎ " is calculated.

[0050] In equation (6), LM,n is expressed by equation (7).

[0051] The left side λ' of equation (6) ｋ、ｎ is the likelihood estimated by the bit likelihood estimation process, and indicates the likelihood that the kth bit of the nth symbol of the transmitted signal is 0. In the example of equation (6), 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. ｋ、ｎ ,x'' ｎ represents the k-th bit of the symbol of σ. σ represents the standard deviation of the distribution of noise imparted to the optical signal in the transmission path 2.

[0052] 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 u ３ = [c'' １，ｎ , c'' ２，ｎ ] = [1, 0].

[0053] The soft decision output unit 405 calculates the provisional log-likelihood ratio λ′ using equation (8). ｋ，ｎ Based on the log-likelihood ratio λ ｋ，ｎ Calculate.

[0054] c' ｋ、ｎ is x' ｎ d represents the k-th bit of the symbol λ′. ｋ，ｎ The larger the value of d, the ｋ，ｎ The result of the backward operation is strongly reflected in . ｋ，ｎ The result of the backward operation is not reflected at all in λ'. ｋ，ｎ is slid in the positive or negative direction, ｋ，ｎ is calculated, but the amount of sliding is determined by the value of the shift parameter d. ｋ、ｎ The log-likelihood ratio λ ｋ，ｎ is the provisional log-likelihood ratio λ' ｋ，ｎ The difference is whether the value is slid in the positive direction or the negative direction. ｋ、ｎ If is 0, the log-likelihood ratio λｋ，ｎ is the provisional log-likelihood ratio λ' ｋ，ｎ is slid in the negative direction, and c' ｋ、ｎ If is 1, the log-likelihood ratio λ ｋ，ｎ is the provisional log-likelihood ratio λ' ｋ，ｎ is slid in the positive direction.

[0055] The soft decision output unit 405 outputs the log-likelihood ratio λ ｋ，ｎ may be calculated using equation (9).

[0056] According to equation (9), the log-likelihood ratio λ ｋ，ｎ When calculating the log-likelihood ratio λ without calculating the value of σ, ｋ，ｎ can be calculated.

[0057] The soft decision output unit 405 may update the shift parameter d. The soft decision output unit 405 calculates the shift parameter d and the log-likelihood ratio λ corresponding to the shift parameter d using equations (10) and (11). ｋ，ｎ The shift parameter d' is calculated based on (d).

[0058] μ is the step size parameter. N′ is the number of symbols used to optimize d. c ｋ、ｎ is x ｎ represents the k-th bit of the symbol.

[0059] The soft decision output unit 405 substitutes the calculated shift parameter d′ into equation (10) as the shift parameter d, thereby obtaining a new log-likelihood ratio λ ｋ，ｎ The soft decision output unit 405 may calculate the newly calculated shift parameter d and the log-likelihood ratio λ ｋ，ｎ The shift parameter d may be updated by calculating Equation (10) based on the above. By repeating this process, the shift parameter d can be optimized.

[0060] The soft decision output unit 405 calculates, for example, a predetermined number of shift parameters d and a log likelihood ratio λ ｋ，ｎThe shift parameter d is optimized by repeating the calculation of (12). For example, when d becomes smaller than a predetermined value, the soft decision output unit 405 sets the value of d as the final value and ends the update of the shift parameter. For example, the soft decision output unit 405 sets the value of d that satisfies the formula (12) as the final value.

[0061] In equation (12), Δd is the difference between the values ​​of d before and after the update. Δd is, in other words, equation (13).

[0062] ε is an arbitrary positive real number, for example, 0.001.

[0063] The soft decision output unit 405 may combine the two optimization methods described above. That is, the soft decision output unit 405 performs optimization by using a predetermined number of shift parameters d and a log-likelihood ratio λ ｋ，ｎ When the calculation of d is repeated or when d becomes smaller than a predetermined value, the finally calculated d is set as the shift parameter.

[0064] The soft decision output unit 405 outputs the calculated log likelihood ratio λ ｋ，ｎ The soft decision output unit 405 may set the minimum and / or maximum values ​​of the log-likelihood ratio λ by, for example, equation (14). ｋ，ｎ Set the minimum and maximum values ​​of .

[0065] In equation (14), f is an arbitrary positive constant. The soft decision output unit 405 calculates the log-likelihood ratio λ ｋ，ｎ When is greater than f, the log-likelihood ratio λ ｋ，ｎ is set to the maximum value f, and the log-likelihood ratio λ ｋ，ｎ When is smaller than -f, the log-likelihood ratio λ ｋ，ｎ is set to a minimum value −f, where f is, for example, 6.

[0066] 4 is a flowchart showing the flow of processing executed by the soft decision device 4 in this 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).

[0067] 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 and the symbol decision result of the forward calculation (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 " is output to the interface unit 41 (step S306).

[0068] 5 is a flowchart showing the flow of the bit likelihood estimation process in the embodiment. ｋ，ｎ " is calculated (step S3051). ｋ，ｎ is the symbol determination result "x'' by forward operation. ｎ－ａ " the kth bit "c'' ｋ、ｎ The soft decision output unit 405 calculates λ' ｋ，ｎ and the shift parameter d, the log-likelihood ratio λ ｋ，ｎ (step S3052). After that, the soft decision output unit 405 calculates the log-likelihood ratio λ a predetermined number of times. ｋ，ｎ It is determined whether the log likelihood ratio λ has been calculated a predetermined number of times (step S3053). ｋ，ｎ If the soft decision output unit 405 has not calculated the shift parameter d′ (step S3054), the soft decision output unit 405 calculates the shift parameter d′ (step S3054). ｋ，ｎThen, in step S3052, the soft decision output unit 405 uses the shift parameter d′ as a new shift parameter d to newly calculate λ ｋ，ｎ Calculate.

[0069] A predetermined number of times, the log-likelihood ratio λ ｋ，ｎ If the soft decision output unit 405 has calculated the log-likelihood ratio λ ｋ，ｎ is the estimation result (step S3055). ｋ，ｎ is estimated.

[0070] FIG. 6 shows the provisional log-likelihood ratio λ′ ｋ，ｎ From the log-likelihood ratio λ ｋ，ｎ 6A is a schematic diagram showing how λ′ is calculated. ｋ，ｎ The distribution of decision bit c' is shown. ｋ、ｎ Depending on the value of λ' ｋ，ｎ The distribution of λ' is divided into two. ｋ，ｎ Then, λ' is divided into two parts according to the value of the shift parameter d using equation (8) or (9). ｋ，ｎ The decision bit c' is shifted outwards. ｋ、ｎ λ' where the value of ｋ，ｎ The distribution of the decision bit c' is shifted in the negative direction. ｋ、ｎ λ' where the value of ｋ，ｎ The distribution of λ is shifted in the positive direction. ｋ，ｎ The distribution of the shifted λ' is shown. ｋ，ｎ The distribution of λ ｋ，ｎ This reduces the amount of information taken into account and improves the standardized generalized mutual information (NGMI).

[0071] <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. 7 shows the log-likelihood ratio λ ｋ，ｎ 7A is a diagram showing the distribution of the provisional log-likelihood ratio λ′. ｋ，ｎ 7(b) shows the distribution of the shifted log-likelihood ratio λ. ｋ，ｎ7(a) and (b), the distribution of the provisional log-likelihood ratio λ′ is ｋ，ｎ It can be seen that the two distributions that make up the distribution are shifted in the positive and negative directions.

[0072] 8 is a diagram showing the transition of the value of the shift parameter d in an experiment in this embodiment. The horizontal axis represents the number of times the soft decision output unit 405 updated the shift parameter d. The vertical axis represents the value of the shift parameter d. The shift parameter d was updated based on the power (ROP) of the optical signal received by the receiver 3. It can be seen that the shift parameter d converges to an optimal value by updating the shift parameter d about 2000 times, regardless of the ROP value.

[0073] 9 is a graph showing NGMI in an experiment in this embodiment. The vertical axis represents NGMI, and the horizontal axis represents ROP by the receiver 3. In this embodiment, the soft decision output unit 405 outputs a provisional log-likelihood ratio λ′. ｋ，ｎ By modifying the log-likelihood ratio λ ｋ，ｎ In the comparative example, the soft decision output unit 405 calculates the log likelihood ratio λ ｋ，ｎ Without calculating the log-likelihood ratio λ' ｋ，ｎ The NGMI in this embodiment is larger than the NGMI in the comparative example, and it can be seen that the NGMI has been improved.

[0074] In the above experiment, the shift parameter d was calculated using equation (8). Fig. 10 is a diagram showing the optimal value of the shift parameter d calculated using equations (8) and (9). The vertical axis represents the optimal value of the shift parameter d, and the horizontal axis represents the ROP by the receiver 3. The optimal value of the shift parameter d calculated using equation (8) is almost constant regardless of the ROP, but the optimal value of the shift parameter d calculated using equation (9) tends to increase as the ROP value increases.

[0075] FIG. 11 shows the log-likelihood ratio λ ｋ，ｎ11 shows the change in NGMI depending on whether or not the minimum and maximum values ​​of d are set. In the graph shown in FIG. 11, the vertical axis represents NGMI and the horizontal axis represents the shift parameter d. The optimal value of the shift parameter d was 0.0004. The minimum and maximum values ​​were set using equation (14), with f = 6. When the minimum and maximum values ​​were not set, the NGMI significantly decreased when the shift parameter d deviated from the optimal value. On the other hand, when the minimum and maximum values ​​were set, it was possible to prevent a significant decrease in NGMI even when the shift parameter d deviated from the optimal value.

[0076] FIG. 12 shows the log-likelihood ratio λ when the transmission bit transmitted from the transmitter 1 to the receiver 3 is 0. ｋ，ｎ The vertical axis represents the NGMI, and the horizontal axis represents the log-likelihood ratio λ. ｋ，ｎ As shown in FIG. 12, the log-likelihood ratio λ ｋ，ｎ When is smaller than -6, the NGMI is greater than 0.99. ｋ，ｎ Even if the log-likelihood ratio λ is considered to be -6 when it is smaller than -6, the resulting decrease in NGMI is less than 0.01. When the transmission bit transmitted from the transmitter 1 to the receiver 3 is 1, the tendency is opposite to that shown in FIG. 12. That is, ｋ，ｎ When is greater than 6, the NGMI is greater than 0.99. ｋ，ｎ If the value is greater than 6, it is treated as 6, but the resulting decrease in NGMI is less than 0.01.

[0077] 13 is a diagram showing the relationship between NGMI and f. The vertical axis represents NGMI, and the horizontal axis represents f. As shown in FIG. 13, when f is 6 or more, NGMI does not decrease.

[0078] From the above, the log-likelihood ratio λ ｋ，ｎ It can be seen that by setting the minimum and maximum values ​​of f by equation (14) and setting f = 6, it is possible to prevent a decrease in NGMI due to the value of f, while also preventing a large decrease in NGMI due to changes in the shift parameter d.

[0079] 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.

[0080] 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.

[0081] 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 symbol (n is an integer from 1 to N, and N is an integer greater than or equal to 1) of a transmission signal with a symbol multiplicity of m (m is an integer greater than or equal to 2). Based on an estimated transfer function that is a previously obtained estimation result of the transfer function of the transmission path through which the transmission signal propagates, and a received signal that is the result of receiving the transmission signal, a branch metric estimation process that estimates a branch metric, which is a distance indicating the likelihood of transitioning from the n-th symbol to each candidate of the (n + 1)-th symbol of the transmission signal; a path metric estimation process that estimates a path metric, which is the sum of the distance indicating the likelihood that each candidate of the (n + 1)-th symbol of the transmission signal is a symbol of the transmission signal and the distance of the remaining paths from the 1st to the n-th of the transmission signal, based on the result of the branch metric estimation process; and a bit likelihood estimation process that estimates a log-likelihood ratio calculated from the likelihood that the k-th bit (k is an integer from 1 to m) in the (n + 1)-th symbol of the transmission signal is a predetermined bit, using the path metrics of each candidate of the (n + 1)-th symbol of the transmission signal obtained by the path metric estimation process and the determination result of the bits of the n-th symbol by forward operation, which is the operation in the order from the (n + 1)-th to the n-th of the transmission signal, and not using the path metrics other than the path metrics of each candidate of the (n + 1)-th symbol of the transmission signal. A control unit that executes the above processes is provided. The control unit corrects the estimated log-likelihood ratio based on the determination result of the bits of the n-th symbol by backward operation, which is the operation in the order from the (n + 1)-th to the n-th of the transmission signal. Soft decision device.

2. The control unit determines whether to slide the estimated log-likelihood ratio in the positive direction or the negative direction according to the determination result of the bits of the n-th symbol by backward operation. The soft decision device according to claim 1.

3. The amount of sliding is determined by a shift parameter. The control unit updates the shift parameter by calculating the shift parameter based on the corrected log-likelihood ratio. The soft decision device according to claim 2.

4. The soft decision device according to claim 3, wherein the amount of the slide is further determined by a standard deviation of a distribution of noise added in the process of the received signal propagating through the transmission line.

5. The soft decision device according to claim 3 or 4, wherein the control unit ends the update of the shift parameter when an absolute value of the shift parameter before and after the update with respect to the shift parameter is less than a predetermined value.

6. The soft decision device according to claim 1, wherein the control unit sets a minimum value and a maximum value of the log-likelihood ratio.

7. The soft decision device according to claim 6, wherein the minimum value of the log-likelihood ratio is -6, and the maximum value of the log-likelihood ratio is 6.

8. A soft decision method for performing soft decision on a main symbol that is the (n + 1)-th symbol (n is an integer of 1 or more and N or less, and N is an integer of 1 or more) of a transmission signal with a symbol multiplicity of m (m is an integer of 2 or more), including: a branch metric estimation process for estimating a branch metric, which is a distance indicating a likelihood of transitioning from the n-th symbol of the transmission signal to each candidate of 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 line through which the transmission signal propagates and a received signal that is a result of receiving the transmission signal; a path metric estimation process for estimating a path metric, which is a sum of a distance indicating a likelihood that each candidate of the (n + 1)-th symbol of the transmission signal is a symbol of the transmission signal and a distance of remaining paths from the 1st to the n-th of the transmission signal, based on a result of the branch metric estimation process; a bit likelihood estimation process for estimating a log-likelihood ratio calculated from a likelihood that the k-th (k is an integer of 1 or more and m or less) bit in the (n + 1)-th symbol of the transmission signal is a predetermined bit, using the path metric of each candidate of the (n + 1)-th symbol of the transmission signal obtained by the path metric estimation process and a determination result of a bit of the n-th symbol calculated in order from the (n + 1)-th symbol to the n-th symbol of the transmission signal, without using path metrics other than the path metric of each candidate of the (n + 1)-th symbol of the transmission signal; a control step of executing the above, wherein the control step includes correcting the estimated likelihood based on a determination result of a bit of the n-th symbol calculated in order from the (n + 1)-th symbol to the n-th symbol of the transmission signal.

9. A program for causing a computer to function as the soft determination device according to claim 1.

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