ERROR CORRECTION DECODING DEVICE AND ERROR CORRECTION DECODING METHOD

Abstract

An error correction decoding device includes processing circuitry configured to; acquire each of the pulse amplitude modulation symbols from a communication symbol sequence, calculate a first hard decision bit indicating positive and negative of a log posterior probability ratio of each of M bits, and calculate an absolute value of each of log posterior probability ratios as a first reliability; operate an exclusive OR of D×M first hard decision bits having been calculated; perform comparison of D×M first reliabilities having been calculated with each other, select one first reliability from the D×M first reliabilities on a basis of a result of the comparison, and output the one first reliability as a second reliability; and perform soft decision error correction decoding on an operation result of the exclusive OR and the second reliability.

Description

TECHNICAL FIELD

The present disclosure relates to an error correction decoding device and an error correction decoding method.

BACKGROUND ART

There is an error correction decoding device that decodes a multi-level modulation symbol in which the number of dimensions is D (D is an integer equal to or more than 1) and the number of bits per dimension is M (M is an integer equal to or more than 2) from D pulse amplitude modulation symbols (see, for example, Non Patent Literature 1).

The error correction decoding device includes a soft decision unit that calculates hard decision bits indicating positive and negative of a log posterior probability ratio of each bit included in the multi-level modulation symbol of the number of dimensions D by performing soft decision on the D pulse amplitude modulation symbols.

When the pulse amplitude modulation symbol is Nbit quantized per dimension, the number of coordinates after quantization on the reception side is 2{circumflex over ( )}N{circumflex over ( )}D. For example, if N=6 and D=4, the number of coordinates is 2{circumflex over ( )}6{circumflex over ( )}4=16,777,216.

CITATION LIST

Non Patent Literature

Non Patent Literature 1: T. Kakizaki et al., “Low-complexity Channel-polarized Multilevel Coding for Probabilistic Amplitude Shaping,” Proc. OFC 2022, W3H.4.

SUMMARY OF INVENTION

Technical Problem

In the error correction decoding device disclosed in Non Patent Literature 1, as the number of dimensions D is larger, the calculation processing of each of a hard decision bit and reliability by the soft decision unit increases. As a result, there is a problem that it may take a lot of time for the soft decision unit to decode the multi-level modulation symbol.

If the soft decision unit has 2{circumflex over ( )}N{circumflex over ( )}D address spaces and includes a lookup table capable of storing the hard decision bit and the reliability corresponding to the value of the pulse amplitude modulation symbol of the number of dimensions D, each of the hard decision bit and the reliability corresponding to the value of the pulse amplitude modulation symbol can be obtained, but the address space included in the lookup table becomes larger as the number of dimensions D is larger. Therefore, depending on the number of dimensions D, the soft decision unit may not be able to implement the lookup table.

The present disclosure has been made to solve the above problems, and an object of the present disclosure is to obtain an error correction decoding device that can suppress an increase in calculation processing of each of a first hard decision bit and reliability due to an increase in the number of dimensions more than by the error correction decoding device disclosed in Non Patent Literature 1.

Solution to Problem

An error correction decoding device according to the present disclosure is an error correction decoding device that decodes a multi-level modulation symbol in which the number of dimensions is D (D is an integer equal to or more than 1) and the number of bits per dimension is M (M is an integer equal to or more than 2) from each of D pulse amplitude modulation symbols. The error correction decoding device includes processing circuitry configured to acquire each of the pulse amplitude modulation symbols from a communication symbol sequence in which the D pulse amplitude modulation symbols are arranged, calculate a first hard decision bit indicating positive and negative of a log posterior probability ratio of each of M bits included in the multi-level modulation symbol from each of the pulse amplitude modulation symbols, and calculate an absolute value of each of log posterior probability ratios as a first reliability; operate an exclusive OR of D×M first hard decision bits having been calculated; perform comparison of D×M first reliabilities having been calculated with each other, select one first reliability from the D×M first reliabilities on a basis of a result of the comparison, and output the one first reliability as a second reliability; and perform soft decision error correction decoding on an operation result of the exclusive OR and the second reliability.

Advantageous Effects of Invention

According to the present disclosure, it is possible to suppress an increase in calculation processing of each of a first hard decision bit and reliability due to an increase in the number of dimensions more than by the error correction decoding device disclosed in Non Patent Literature 1.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a configuration diagram illustrating an error correction decoding device according to a first embodiment.

FIG. 2 is a hardware configuration diagram illustrating hardware of the error correction decoding device according to the first embodiment.

FIG. 3 is a hardware configuration diagram of a computer in a case where the error correction decoding device is implemented by software, firmware, or the like.

FIG. 4 is a flowchart illustrating an error correction decoding method which is a processing procedure performed by the error correction decoding device.

FIG. 5 is a configuration diagram illustrating another error correction decoding device according to the first embodiment.

FIG. 6 is a hardware configuration diagram illustrating hardware of another error correction decoding device according to the first embodiment.

FIG. 7 is a configuration diagram illustrating another error correction decoding device according to the first embodiment.

DESCRIPTION OF EMBODIMENTS

Hereinafter, in order to describe the present disclosure in more detail, modes for carrying out the present disclosure will be described with reference to the accompanying drawings.

First Embodiment

FIG. 1 is a configuration diagram illustrating an error correction decoding device according to a first embodiment.

FIG. 2 is a hardware configuration diagram illustrating hardware of the error correction decoding device according to the first embodiment.

The error correction decoding device illustrated in FIG. 1 is implemented in a reception device, not illustrated, for example. The error correction decoding device illustrated in FIG. 1 includes a soft decision unit 1, an exclusive OR operating unit 2, a reliability selecting unit 3, a soft decision error correction decoding unit 4, a pre-correction unit 5, a hard decision error correction decoding unit 6, and a probability shaping decoding unit 7.

The error correction decoding device decodes a multi-level modulation symbol in which the number of dimensions is D (D is an integer equal to or more than 1) and the number of bits per dimension is M (M is an integer equal to or more than 2) from each of D pulse amplitude modulation symbols.

Since the reception device, not illustrated, includes the error correction decoding device illustrated in FIG. 1, it is possible to correct a bit error generated in a communication path with the transmission device, not illustrated.

The soft decision unit 1 is implemented by, for example, a soft decision circuit 11 illustrated in FIG. 2.

The soft decision unit 1 acquires each pulse amplitude modulation symbol Y_j (j=1, . . . , D) from the communication symbol sequence in which the D pulse amplitude modulation symbols Y₁, Y₂, . . . , Y_D are arranged. The pulse amplitude modulation symbol Y_j is a one-dimensional pulse amplitude modulation symbol.

The soft decision unit 1 calculates, from the pulse amplitude modulation symbol Y_j, a first hard decision bit H_k indicating positive and negative of a log posterior probability ratio of each of the M bits included in the multi-level modulation symbol. The soft decision unit 1 performs a process of calculating M first hard decision bits H_k for D dimensions from one pulse amplitude modulation symbol Y_j. Thus, in H_k indicating the first hard decision bits collected for D dimensions, k=1, 2, . . . , D×M.

The soft decision unit 1 calculates the absolute value of each log posterior probability ratio as a first reliability |L_k|.

The soft decision unit 1 outputs the first hard decision bit H_k to each of the exclusive OR operating unit 2 and the pre-correction unit 5, and outputs the first reliability |L_k| to the reliability selecting unit 3.

The exclusive OR operating unit 2 is implemented by, for example, an exclusive OR operating circuit 12 illustrated in FIG. 2.

The exclusive OR operating unit 2 calculates the exclusive OR of the D×M first hard decision bits H₁ to H_D×M calculated by the soft decision unit 1.

The exclusive OR operating unit 2 outputs the operation result of the exclusive OR to each of the soft decision error correction decoding unit 4 and the pre-correction unit 5 as a second hard decision bit H^d.

The reliability selecting unit 3 is implemented by, for example, a reliability selecting circuit 13 illustrated in FIG. 2.

The reliability selecting unit 3 perform comparison of the D×M first reliabilities |L₁| to |L_D×M| calculated by the soft decision unit 1 with each other, and selects one first reliability from the D×M first reliabilities |L₁| to |L_D×M| on the basis of a result of the comparison.

On the basis of the comparison result, the reliability selecting unit 3 selects a minimum first reliability |L_k| among the D×M first reliabilities |L₁| to |L_D×M|, for example.

The reliability selecting unit 3 outputs the selected first reliability |L_k| to the soft decision error correction decoding unit 4 as a second reliability |L^d|.

Further, the reliability selecting unit 3 outputs an index k indicating the minimum first reliability |L_k| to the pre-correction unit 5 as a correction candidate index k′.

The soft decision error correction decoding unit 4 is implemented by, for example, a soft decision error correction decoding circuit 14 illustrated in FIG. 2.

The soft decision error correction decoding unit 4 acquires the second hard decision bit H^d from the exclusive OR operating unit 2 and acquires the second reliability |L^d| from the reliability selecting unit 3.

The soft decision error correction decoding unit 4 generates a third hard decision bit H by performing soft decision error correction decoding on the second hard decision bit H^d and the second reliability |L^d|.

The soft decision error correction decoding unit 4 outputs the third hard decision bit H to the pre-correction unit 5.

The pre-correction unit 5 is implemented by, for example, a pre-correction circuit 15 illustrated in FIG. 2.

The pre-correction unit 5 acquires the second hard decision bit H^d from the exclusive OR operating unit 2 and acquires the third hard decision bit H from the soft decision error correction decoding unit 4.

Further, the pre-correction unit 5 acquires the correction candidate index k′ from the reliability selecting unit 3.

If the second hard decision bit H^d and the third hard decision bit H are the same, the pre-correction unit 5 outputs each of the D×M first hard decision bits H₁ to H_D×M acquired by the soft decision unit 1 to the hard decision error correction decoding unit 6 as a fourth hard decision bit B-hat_k (k=1, 2, . . . , D×M). In the sentences of the specification, the symbol “A” cannot be added on the letter “B” due to the electronic application. Thus, it is expressed as “B-hat”.

If the second hard decision bit H^d and the third hard decision bit H are different, the pre-correction unit 5 inverts the first hard decision bit H_k (k=k′) corresponding to the correction candidate index k′ among the D×M first hard decision bits H₁ to H_D×M. The first hard decision bit H_k (k=k′) corresponding to the correction candidate index k′ is the first hard decision bit H_k corresponding to the second reliability |L^d|.

The pre-correction unit 5 outputs the inverted first hard decision bit H_k′ as a fourth hard decision bit B-hat_k to the hard decision error correction decoding unit 6. The pre-correction unit 5 outputs the first hard decision bit H_k that is not inverted among the D×M first hard decision bits H₁ to H_D×M to the hard decision error correction decoding unit 6 as the fourth hard decision bit B-hat_k as it is.

The hard decision error correction decoding unit 6 is implemented by, for example, a hard decision error correction decoding circuit 16 illustrated in FIG. 2.

The hard decision error correction decoding unit 6 generates a second restoration bit string as a bit string by performing hard decision error correction decoding on the D×M fourth hard decision bits B-hat₁ to B-hat_D×M output from the pre-correction unit 5.

The probability shaping decoding unit 7 is implemented by, for example, a probability shaping decoding circuit 17 illustrated in FIG. 2.

The probability shaping decoding unit 7 obtains a first restoration bit string by performing probability shaping decoding on the second restoration bit string generated by the hard decision error correction decoding unit 6.

Specifically, in the transmission device, in a case where a second bit string constituting the multi-level modulation symbol is obtained by performing probability shaping coding on the first bit string, the probability shaping decoding unit 7 performs probability shaping decoding on the second restoration bit string to obtain the first restoration bit string.

The probability shaping decoding unit 7 outputs the first restoration bit string to, for example, a processing unit of a reception device, not illustrated.

In FIG. 1, it is assumed that each of the soft decision unit 1, the exclusive OR operating unit 2, the reliability selecting unit 3, the soft decision error correction decoding unit 4, the pre-correction unit 5, the hard decision error correction decoding unit 6, and the probability shaping decoding unit 7, which are components of the error correction decoding device, is implemented by dedicated hardware as illustrated in FIG. 2. That is, it is assumed that the error correction decoding device is implemented by the soft decision circuit 11, the exclusive OR operating circuit 12, the reliability selecting circuit 13, the soft decision error correction decoding circuit 14, the pre-correction circuit 15, the hard decision error correction decoding circuit 16, and the probability shaping decoding circuit 17.

Each of the soft decision circuit 11, the exclusive OR operating circuit 12, the reliability selecting circuit 13, the soft decision error correction decoding circuit 14, the pre-correction circuit 15, the hard decision error correction decoding circuit 16, and the probability shaping decoding circuit 17 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination thereof.

The components of the error correction decoding device are not limited to those implemented by dedicated hardware, and the error correction decoding device may be implemented by software, firmware, or a combination of software and firmware.

The software or firmware is stored in a memory of the computer as a program. The computer means hardware that executes a program, and corresponds to, for example, a central processing unit (CPU), a graphics processing unit (GPU), a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a digital signal processor (DSP).

FIG. 3 is a hardware configuration diagram of a computer in a case where the error correction decoding device is implemented by software, firmware, or the like.

In a case where the error correction decoding device is implemented by software, firmware, or the like, a program for causing a computer to execute respective processing procedures performed in the soft decision unit 1, the exclusive OR operating unit 2, the reliability selecting unit 3, the soft decision error correction decoding unit 4, the pre-correction unit 5, the hard decision error correction decoding unit 6, and the probability shaping decoding unit 7 is stored in the memory 21. Then, a processor 22 of the computer executes the program stored in the memory 21.

Furthermore, FIG. 2 illustrates an example in which each of the components of the error correction decoding device is implemented by dedicated hardware, and FIG. 3 illustrates an example in which the error correction decoding device is implemented by software, firmware, or the like. However, this is merely an example, and some components in the error correction decoding device may be implemented by dedicated hardware, and the remaining components may be implemented by software, firmware, or the like.

Next, an operation of the error correction decoding device illustrated in FIG. 1 will be described.

FIG. 4 is a flowchart illustrating an error correction decoding method which is a processing procedure performed by the error correction decoding device.

The soft decision unit 1 acquires each pulse amplitude modulation symbol Y_j (j=1, . . . , D) from the communication symbol sequence in which the D pulse amplitude modulation symbols Y₁, Y₂, . . . , Y_D are arranged.

The soft decision unit 1 calculates a log posterior probability ratio L^c_k of each of the D×M bits included in the multi-level modulation symbol from the one-dimensional pulse amplitude modulation symbol Y_j as expressed in the following Expression (1). i=1, . . . , M, and M is an integer equal to or more than 2. k=D (i−1)+j. The calculation processing of the log posterior probability ratio L^c_k is constant regardless of the number of dimensions D.

$\begin{array}{cc}{L}_k^c=\ln \frac{{\sum }_{x\in \chi :b_i=0}{P}_X\left(x\right)q_{X,Y}\left(x,Y_j\right)}{{\sum }_{x\in \chi :b_i=1}{P}_X\left(x\right)q_{X,Y}\left(x,Y_j\right)}& \left(1\right)\end{array}$ $\begin{array}{cc}{q}_{X,Y}\left(x,y\right)\propto \exp \left(\frac{{❘y-x❘}^2}{2{\sigma }^2}\right)& \left(2\right)\end{array}$

In Expression (1), Y is a random variable representing the pulse amplitude modulation symbol Y_j. y is one of a set Y of D pulse amplitude modulation symbols Y₁, Y₂, . . . , and Y_D. X is a random variable representing a multi-level modulation symbol output from the error correction decoding device illustrated in FIG. 1. P_X(x) is a probability that X=x. x is one of a set X of multi-level modulation symbols.

i is a bit index for identifying a plurality of bits included in a 2^M-value multi-level modulation symbol. When the multi-level modulation symbol is, for example, 8 pulse amplitude modulation (8PAM), M=3.

q_X,Y(x, y) is a decoding metric in a case where X=x and Y=y. In a one-dimensional additive white Gaussian noise (Additive White Gaussian Noise) communication path, it is expressed as Expression (2). σ is a standard deviation of noise.

“x∈X: b_i=0” indicates a target of the sum, and specifically means that only those satisfying a condition that the bit b_i indicated by the bit index i is 0 are targets of the sum when taking the sum for x.

If the soft decision unit 1 includes the lookup table having 2{circumflex over ( )}N address spaces and storing the log posterior probability ratio L^c_k corresponding to the value of the one-dimensional pulse amplitude modulation symbol Y_j, the soft decision unit 1 can obtain the log posterior probability ratio L^c_k corresponding to the value of the pulse amplitude modulation symbol Y_j from the lookup table without performing the operation of Expression (1). N is the number of bits representing the one-dimensional pulse amplitude modulation symbol Y_j quantized after being affected by noise or distortion in the communication path.

For example, when N=6, y is represented by a value of 64. The address space of the LUT in this case is 64.

In the error correction decoding device disclosed in Non Patent Literature 1, when N=6 and D=2, y is represented by a value of 4096. The address space of the LUT in this case is 4096. Further, when N=6 and D=4, y is represented by a value of 16,777,216. The address space of the LUT in this case is 16,777,216.

As is clear from the difference in the address space of the LUT, the calculation amount of Expression (1) by the soft decision unit 1 is extremely smaller than the calculation amount of the log posterior probability ratio by the soft decision unit of the error correction decoding device disclosed in Non Patent Literature 1.

Next, the soft decision unit 1 calculates a first hard decision bit H_k indicating positive and negative of the log posterior probability ratio L^c_k of the bit b_i included in the multi-level modulation symbol (step ST1 in FIG. 4).

For example, the soft decision unit 1 sets the first hard decision bit H_k to 0 when the log posterior probability ratio L^c_k is positive, and sets the first hard decision bit H_k to 1 when the log posterior probability ratio L^c_k is negative.

The soft decision unit 1 outputs the first hard decision bit H_k to each of the exclusive OR operating unit 2 and the pre-correction unit 5.

The soft decision unit 1 calculates the absolute value of each log posterior probability ratio as the first reliability |L_k| (step ST1 in FIG. 4).

Specifically, the soft decision unit 1 calculates the absolute value of the log posterior probability ratio L^c_k as the first reliability |L_k|.

The soft decision unit 1 outputs the first reliability |L_k| to the reliability selecting unit 3.

The exclusive OR operating unit 2 acquires D×M first hard decision bits H₁ to H_D×M from the soft decision unit 1.

The exclusive OR operating unit 2 operates the exclusive OR of the D×M first hard decision bits H₁ to H_D×M as expressed in the following Expression (3) (step ST2 in FIG. 4).

The exclusive OR operating unit 2 outputs the operation result of the exclusive OR to each of the soft decision error correction decoding unit 4 and the pre-correction unit 5 as the second hard decision bit H^d.

In the error correction decoding device illustrated in FIG. 1, the exclusive OR operating unit 2 calculates the second hard decision bit H^d and outputs the second hard decision bit H^d to the pre-correction unit 5. However, this is merely an example, and the pre-correction unit 5 may calculate the second hard decision bit H^d.

$\begin{array}{cc}{H}^d=\left({\sum }_{k=1}^{D\times M}{H}_k\right)\mathrm{mod}2& \left(3\right)\end{array}$

In Expression (3), “mod 2” is a mathematical symbol representing a remainder.

The reliability selecting unit 3 acquires D×M first reliabilities |L₁| to |L_D×M| from the soft decision unit 1, and compares the first reliabilities |L₁| to |L_D×M| with each other.

The reliability selecting unit 3 selects one first reliability from the D×M first reliabilities |L₁| to |L_D×M| on the basis of the comparison result (step ST3 in FIG. 4).

On the basis of the comparison result, the reliability selecting unit 3 selects the minimum first reliability |L_k| among the D×M first reliabilities |L₁| to |L_D×M|, for example.

The reliability selecting unit 3 outputs the selected first reliability |L_k| to the soft decision error correction decoding unit 4 as the second reliability |L^d|.

Here, an example is illustrated in which the reliability selecting unit 3 selects the minimum first reliability |L_k| among the D×M first reliabilities |L₁| to |L_D×M|. However, this is merely an example, and if there is no practical problem, the reliability selecting unit 3 may select, for example, the second smallest first reliability |L_k| among the D×M first reliabilities |L₁| to |L_D×M|.

The reliability selecting unit 3 specifies an index k indicating the selected first reliability |L_k| as the correction candidate index k′ as expressed in the following Expression (4).

The reliability selecting unit 3 outputs the correction candidate index k′ to the pre-correction unit 5.

$\begin{array}{cc}{k}^{\prime }=\underset{k}{\arg \min }❘L_k❘& \left(4\right)\end{array}$

In Expression (4), “arg min” is a mathematical symbol indicating k that gives the minimum value of |L_k|.

The soft decision error correction decoding unit 4 acquires the second hard decision bit H^d from the exclusive OR operating unit 2 and acquires the second reliability |L^d| from the reliability selecting unit 3.

The soft decision error correction decoding unit 4 generates a third hard decision bit H by performing soft decision error correction decoding on the second hard decision bit H^d and the second reliability |L^d| (step ST4 in FIG. 4).

Specifically, the soft decision error correction decoding unit 4 generates a third hard decision bit H by performing soft decision error correction decoding on a plurality of second log posterior probability ratios configured by a combination of the second hard decision bit H^d and the second reliability |L^d|. Since the soft decision error correction decoding processing itself is a known technique, detailed description thereof will be omitted.

The soft decision error correction decoding unit 4 outputs the third hard decision bit H to the pre-correction unit 5.

As a soft decision error correction code, for example, a low density parity check code or a turbo code is used. The code length of the soft decision error correction code is about several 100 bits to several tens of thousands of bits. As the resolution per second log posterior probability ratio, for example, 8 values, 16 values, or 32 values are assumed.

The pre-correction unit 5 acquires the second hard decision bit H^d from the exclusive OR operating unit 2 and acquires the third hard decision bit H from the soft decision error correction decoding unit 4.

Further, the pre-correction unit 5 acquires D×M first hard decision bits H₁ to H_D×M from the soft decision unit 1, and acquires the correction candidate index k′ from the reliability selecting unit 3.

The pre-correction unit 5 compares the second hard decision bit H^d with the third hard decision bit H.

If the second hard decision bit H^d and the third hard decision bit H are the same, the pre-correction unit 5 outputs the first hard decision bit H_k (k=1, 2, . . . , D×M) as the fourth hard decision bit B-hat_k to the hard decision error correction decoding unit 6. In this case, the pre-correction unit 5 outputs the first hard decision bit H_k as it is to the hard decision error correction decoding unit 6 without inverting any of the first hard decision bits H_k.

If the second hard decision bit H^d and the third hard decision bit H are different, the pre-correction unit 5 inverts the first hard decision bit H_k′ corresponding to the correction candidate index k′ among the D×M first hard decision bits H_k to H_D×M (step ST5 in FIG. 4).

The pre-correction unit 5 outputs the inverted first hard decision bit H_k′ as the fourth hard decision bit B-hat_k (k=k′) to the hard decision error correction decoding unit 6.

Further, the pre-correction unit 5 directly outputs the first hard decision bit H_k that is not inverted among the D×M first hard decision bits H₁ to H_D×M to the hard decision error correction decoding unit 6 as the fourth hard decision bit B-hat_k as it is.

The processing of the pre-correction unit 5 is expressed as the following expressions (5) to (6).

$\begin{array}{cc}{\hat{B}}_k=H_k\left(k\ne k^{\prime }\right)& \left(5\right)\end{array}$ $\begin{array}{cc}{\hat{B}}_{k^{\prime }}=\left(H_{k^{\prime }}+H^d+H\right)\mathrm{mod}2& \left(6\right)\end{array}$

The hard decision error correction decoding unit 6 acquires D×M fourth hard decision bits B-hat₁ to B-hat_D×M from the pre-correction unit 5.

The hard decision error correction decoding unit 6 generates a second restoration bit string by performing hard decision error correction decoding on the D×M fourth hard decision bits B-hat₁ to B-hat_D×M (step ST6 in FIG. 4). Since the hard decision error correction decoding processing itself is a known technique, detailed description thereof will be omitted.

The hard decision error correction decoding unit 6 outputs the second restoration bit string to the probability shaping decoding unit 7.

As the hard decision error correction code, for example, a BCH code, a Staircase code, or a Zipper code can be used. The BCH code is disclosed in, for example, “R. Bose and D. Ray-Chaudhuri, “On a class of error correcting binary group codes,” Information and Control, vol. 3, no. 1, pp. 68-79, March 1960”. The Staircase code is disclosed in, for example, “B. P. Smith et al., “Staircase codes: FEC for 100 Gb/s OTN,” J. Lightw. Technol., vol. 30, no. 1, pp. 110-117, January 2012, doi: 10.1109/JLT. 2011.2175479”. The Zipper code is disclosed in, for example, “A. Y. Sukmadji et al., “Zipper codes: Spatially-coupled product-like codes with iterative algebraic decoding,” Canadian Workshop on Information Theory (CWIT), Hamilton, ON, Canada, June 2019, pp. 1-6, doi: 10.1109/CWIT. 2019.8929906”.

The code length of the hard decision error correction code is, for example, several 100 bits to several 100,000 bits.

By rearranging the bit positions before the hard decision error correction decoding unit 6 performs hard decision error correction decoding, it is also possible to reduce the influence of continuous bit errors.

The probability shaping decoding unit 7 acquires the second restoration bit string from the hard decision error correction decoding unit 6.

The probability shaping decoding unit 7 obtains a first restoration bit string by performing probability shaping decoding on the second restoration bit string generated by the hard decision error correction decoding unit 6 (step ST7 in FIG. 4).

The probability shaping decoding unit 7 outputs the first restoration bit string to, for example, a processing unit of a reception device, not illustrated.

Yet, in a case where the second bit string constituting the multi-level modulation symbol is obtained by performing the probability shaping coding on the first bit string in such a manner that the occurrence probability of the plurality of signal points is biased by the transmission device transmitting the communication symbol sequence in which the D pulse amplitude modulation symbols Y₁, Y₂, . . . , and Y_D are arranged, the probability shaping decoding unit 7 performs the probability shaping decoding on the second restoration bit string. Therefore, in the transmission device, if the second bit string is not obtained by performing the probability shaping coding on the first bit string, the probability shaping decoding unit 7 does not perform the probability shaping decoding on the second restoration bit string.

In the transmission device, for example, in a case where probability shaping coding is performed so that the probability distribution P_X(x) of the multi-level modulation symbol can be brought close to the discrete Gaussian distribution, the signal-to-noise ratio necessary to obtain the predetermined communication quality is reduced. Such probability shaping coding processing is disclosed in, for example, Patent Literature (WO 2020/031257 A).

In the first embodiment, an error correction decoding device that decodes a multi-level modulation symbol in which the number of dimensions is D (D is an integer equal to or more than 1) and the number of bits per dimension is M (M is an integer equal to or more than 2) from each of D pulse amplitude modulation symbols is configured. The error correction decoding device includes a soft decision unit 1 to acquire each of the pulse amplitude modulation symbols from a communication symbol sequence in which the D pulse amplitude modulation symbols are arranged, calculate a first hard decision bit indicating positive and negative of a log posterior probability ratio of each of M bits included in the multi-level modulation symbol from each of the pulse amplitude modulation symbols, and calculate an absolute value of each of log posterior probability ratios as a first reliability, and an exclusive OR operating unit 2 to operate an exclusive OR of D×M first hard decision bits calculated by the soft decision unit 1. Further, the error correction decoding device includes a reliability selecting unit 3 to perform comparison of D×M first reliabilities calculated by the soft decision unit 1 with each other, select one first reliability from the D×M first reliabilities on the basis of a result of the comparison, and output the one first reliability as a second reliability, and a soft decision error correction decoding unit 4 to perform soft decision error correction decoding on an operation result of the exclusive OR by the exclusive OR operating unit 2 and the second reliability. Therefore, the error correction decoding device can suppress an increase in calculation processing of each of a first hard decision bit and reliability due to an increase in the number of dimensions more than by the error correction decoding device disclosed in Non Patent Literature 1.

In the error correction decoding device illustrated in FIG. 1, the soft decision unit 1 acquires each of one-dimensional pulse amplitude modulation symbols from a communication symbol sequence in which the D pulse amplitude modulation symbols are arranged. However, the number of bits representing the one-dimensional pulse amplitude modulation symbol may be switched. In addition, the number of dimensions of the pulse amplitude modulation symbols acquired by the soft decision unit 1 may be switched.

In a case where such switching is performed, each processing in the exclusive OR operating unit 2, the reliability selecting unit 3, the soft decision error correction decoding unit 4, the pre-correction unit 5, and the hard decision error correction decoding unit 6 is affected. Yet, the influence on each processing can be handled, for example, by switching each of the bit index i handled in Expression (1) and a variable j for identifying the pulse amplitude modulation symbol.

In a case where the bit b_i that is not related to calculation of the first hard decision bit H_k is present in the soft decision unit 1, the soft decision unit 1 outputs the log posterior probability ratio L^c_k for the bit b_i to the soft decision error correction decoding unit 8 as the first reliability L′ as illustrated in FIG. 5. FIG. 5 is a configuration diagram illustrating another error correction decoding device according to the first embodiment. In FIG. 5, the same reference numerals as those in FIG. 1 denote the same or corresponding parts, and thus description thereof is omitted.

The soft decision error correction decoding unit 8 acquires the second hard decision bit H^d from the exclusive OR operating unit 2 and acquires the second reliability |L^d| from the reliability selecting unit 3.

The soft decision error correction decoding unit 4 generates a third hard decision bit H by performing soft decision error correction decoding on the second hard decision bit H^d, the second reliability |L^d|, and the first reliability L′.

The soft decision error correction decoding unit 8 is implemented by a soft decision error correction decoding circuit 18, for example, as illustrated in FIG. 6.

FIG. 6 is a hardware configuration diagram illustrating hardware of another error correction decoding device according to the first embodiment. In FIG. 6, the same reference numerals as those in FIG. 2 denote the same or corresponding parts, and thus description thereof is omitted.

In the error correction decoding device illustrated in FIG. 1, the hard decision error correction decoding unit 6 generates a second restoration bit string by performing hard decision error correction decoding on the D×M fourth hard decision bits B-hat₁ to B-hat_D×M output from the pre-correction unit 5. However, this is merely an example, and the hard decision error correction decoding unit 6 may exclude some of the fourth hard decision bits B-hat₁ to B-hat_D×M output from the pre-correction unit 5 from the targets of hard decision error correction decoding.

In this case, as illustrated in FIG. 7, the hard decision error correction decoding unit 6 acquires the third hard decision bit H corresponding to the fourth hard decision bit to be excluded from the soft decision error correction decoding unit 4 instead of the fourth hard decision bit to be excluded. FIG. 7 is a configuration diagram illustrating another error correction decoding device according to the first embodiment. In FIG. 7, the same reference numerals as those in FIG. 1 denote the same or corresponding parts.

Then, the hard decision error correction decoding unit 6 generates a second restoration bit string by performing hard decision error correction decoding on the fourth hard decision bits other than the fourth hard decision bits to be excluded and the third hard decision bit H corresponding to the fourth hard decision bits to be excluded among the fourth hard decision bits B-hat₁ to B-hat_D×M.

Note that, in the present disclosure, any component of the embodiment can be modified, or any component of the embodiment can be omitted.

INDUSTRIAL APPLICABILITY

The present disclosure is suitable for an error correction decoding device and an error correction decoding method.

REFERENCE SIGNS LIST

1: soft decision unit, 2: exclusive OR operating unit, 3: reliability selecting unit, 4: soft decision error correction decoding unit, 5: pre-correction unit, 6: hard decision error correction decoding unit, 7: probability shaping decoding unit, 8: soft decision error correction decoding unit, 11: soft decision circuit, 12: exclusive OR operating circuit, 13: reliability selecting circuit, 14: soft decision error correction decoding circuit, 15: pre-correction circuit, 16: hard decision error correction decoding circuit, 17: probability shaping decoding circuit, 18: soft decision error correction decoding circuit, 21: memory, 22: processor

Claims

1. An error correction decoding device that decodes a multi-level modulation symbol in which a number of dimensions is D (D is an integer equal to or more than 1) and a number of bits per dimension is M (M is an integer equal to or more than 2) from each of D pulse amplitude modulation symbols, the error correction decoding device comprising: processing circuitry configured toacquire each of the pulse amplitude modulation symbols from a communication symbol sequence in which the D pulse amplitude modulation symbols are arranged, calculate a first hard decision bit indicating positive and negative of a log posterior probability ratio of each of M bits included in the multi-level modulation symbol from each of the pulse amplitude modulation symbols, and calculate an absolute value of each of log posterior probability ratios as a first reliability;operate an exclusive OR of D×M first hard decision bits having been calculated;perform comparison of D×M first reliabilities having been calculated with each other, select one first reliability from the D×M first reliabilities on a basis of a result of the comparison, and output the one first reliability as a second reliability; andperform soft decision error correction decoding on an operation result of the exclusive OR and the second reliability.

2. The error correction decoding device according to claim 1, wherein the processing circuitry selects a minimum first reliability among the D×M first reliabilities on the basis of the result of the comparison, and outputs the minimum first reliability as a second reliability.

3. The error correction decoding device according to claim 2wherein the processing circuitry is further configured tooutput each of the D×M first hard decision bits having been calculated as a fourth hard decision bit when a second hard decision bit indicating the operation result of the exclusive OR and a third hard decision bit generated by performing soft decision error correction decoding are same, andinvert a first hard decision bit corresponding to the second reliability among the D×M first hard decision bits, output an inverted first hard decision bit as a fourth hard decision bit, and output each of first hard decision bits other than the first hard decision bit corresponding to the second reliability among the D×M first hard decision bits as a fourth hard decision bit when the second hard decision bit and the third hard decision bit are different.

4. The error correction decoding device according to claim 3, wherein the processing circuitry is further configured to generate a bit string by performing hard decision error correction decoding on D×M fourth hard decision bits having been output.

5. The error correction decoding device according to claim 4, wherein the processing circuitry is further configured to perform probability shaping decoding on the generated bit string.

6. An error correction decoding method for decoding a multi-level modulation symbol in which a number of dimensions is D (D is an integer equal to or more than 1) and a number of bits per dimension is M (M is an integer equal to or more than 2) from each of D pulse amplitude modulation symbols, the error correction decoding method comprising: acquiring each of the pulse amplitude modulation symbols from a communication symbol sequence in which the D pulse amplitude modulation symbols are arranged, calculating a first hard decision bit indicating positive and negative of a log posterior probability ratio of each of M bits included in the multi-level modulation symbol from each of the pulse amplitude modulation symbols, and calculating an absolute value of each of log posterior probability ratios as a first reliability;operating an exclusive OR of D×M first hard decision bits having been calculated;performing comparison of D×M first reliabilities having been calculated with each other, selecting one first reliability from the D×M first reliabilities on a basis of a result of the comparison, and outputting the one first reliability as a second reliability; andperforming soft decision error correction decoding on an operation result of the exclusive OR and the second reliability.