A decoding method of a spatially coupled product code based on random bit flipping

Abstract

The application belongs to the field of digital communication and digital storage, and particularly relates to a decoding method of a space-coupled product code based on random bit flipping, which comprises decoding component codes, in the lth iteration decoding, taking the output of the (l-1)th iteration as the input of a component code decoder Dec, performing Dec decoding, obtaining the output of the ith code word of the decoder Dec in the lth iteration decoding, and obtaining the log-likelihood ratio L of the ith code word according to the output of the decoder Dec in the lth iteration decoding. i and the product coefficient w of the lth iteration (l) , obtaining the reliability of each code word according to the relationship between the absolute value of the reliability of each code word and a threshold T, and obtaining the output of the ith code word in the lth iteration.

Description

Technical Field

[0001] This invention belongs to the field of digital communication and digital storage, and specifically relates to a decoding method for spatially coupled product codes based on random bit flipping. Background Technology

[0002] In recent years, with the rise of applications such as streaming media and cloud computing, internet traffic has reached new heights, placing higher demands on data transmission and storage in optical networks. For example, current optical coherent transceivers have a data rate of 400 Gbps, with the next frontier at 1 Tbps, which imposes extremely high requirements on the complexity of decoding schemes. Furthermore, for fiber optic communication systems, due to the absence of feedback loops, the bit error rate of channel coding must be extremely low. Existing decoding schemes cannot simultaneously meet both requirements. Traditional soft-decision iterative decoding schemes perform well in terms of bit error rate but are too complex. This has spurred extensive research into low-complexity decoding schemes, which can operate at very high throughput while achieving performance close to that of traditional soft-decision iterative decoding schemes.

[0003] Spatial coupled product codes combine the advantages of low implementation complexity of algebraic codes with strong error correction capabilities of spatially coupled codes. Therefore, spatially coupled product codes are highly competitive in high-speed optical fiber communication, and decoding schemes for them have attracted considerable attention. In 2019, Alireza Sheikh et al. proposed a low-complexity hard-decision decoding algorithm utilizing soft information, called iBDD-SR, in their paper "Binary Message Passing Decoding of Product-Like Codes" (IEEE Transactions on Communications, vol. 67, no. 12, December, 2019). To achieve further performance gains, Alireza Sheikh et al. disclosed a higher-performance but more complex decoding algorithm, called iBDD-CR, in their paper "Refined Reliability Combining for Binary Message Passing Decoding of Product Codes" (Journal of Lightwave Technology, vol. 39, no. 15, August. 1, 2021). However, existing decoding algorithms still lag far behind soft-information iterative decision algorithms, and more hard-decision decoding algorithms with lower complexity but better performance are needed. Summary of the Invention

[0004] To achieve lower bit error rate and complexity, this invention provides a decoding method based on spatially coupled product codes with random bit flipping. Under the same encoding scheme and decoding iteration number, the decoding method proposed in this invention has a lower bit error rate and complexity.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A decoding method based on spatially coupled product codes with random bit flipping includes the following steps:

[0007] The component code is decoded. In the l-th iteration of decoding, the output of the (l-1)-th iteration is used as the input of the component code decoder Dec, and Dec decoding is performed to obtain the output of the decoder Dec for the i-th codeword in the l-th iteration.

[0008] Based on the output of the decoder Dec to the i-th codeword in the l-th iteration of decoding... The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained.

[0009] Based on the reliability of each codeword The relationship between the absolute value of the i-th codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration.

[0010] The decoding method based on spatially coupled product codes with random bit flipping, as described above, further involves performing Dec decoding to obtain the output of the decoder Dec for the i-th codeword in the l-th iteration of decoding. Specifically, it includes:

[0011] If the Dec decoding fails, then

[0012] If the decoding of Dec is successful, and the decoded output of the i-th codeword is 0, then

[0013] If the decoding of Dec is successful, and the decoded output of the i-th codeword is 1, then

[0014] The decoding method for spatially coupled product codes based on random bit flipping, as described above, further includes the following step: the decoder Dec outputs the i-th codeword according to the output of the decoder Dec in the l-th iteration of decoding. The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained. Specifically, it is obtained according to the following preset formula:

[0015]

[0016] The decoding method for spatially coupled product codes based on random bit flipping, as described above, further includes the following step: [The text abruptly ends here, so the translation stops.] The relationship between the absolute value of the codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration, specifically including:

[0017]

[0018] The output of the i-th codeword in the l-th iteration is

[0019]

[0020] Here, sign(x) is the sign function.

[0021] The decoding method based on spatially coupled product codes with random bit flipping, as described above, further includes the product coefficients w. (l) With flip probability It is related to the number of iterations l.

[0022] The decoding method based on spatially coupled product codes with random bit flipping, as described above, further includes a component code that is a linear block code with a code length of n and an information bit length of k.

[0023] Compared with the prior art, the advantages of this invention are as follows:

[0024] 1. This invention has the advantages of simple structure, low complexity and strong applicability.

[0025] 2. Compared with existing low-complexity hard-decision decoding algorithms, the present invention has a lower bit error rate. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a decoding block diagram of the method in an embodiment of the present invention.

[0028] Figure 2 This is a block diagram of the product code encoding in an embodiment of the present invention.

[0029] Figure 3 This is a performance diagram of Embodiment 1 of the present invention.

[0030] Figure 4 This is a block diagram of the ladder code encoding in an embodiment of the present invention.

[0031] Figure 5 This is a performance diagram of Embodiment 2 of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0033] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, in the embodiments of this invention are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0034] Example:

[0035] This embodiment provides a decoding method for spatially coupled product codes, specifically including the following steps:

[0036] Step 100: Decode the codeword. In the l-th iteration of decoding, use the output of the (l-1)-th iteration as the input of the decoder Dec, and perform Dec decoding to obtain the output of the decoder Dec for the i-th codeword in the l-th iteration.

[0037] Step 200: Output the i-th codeword to the decoder Dec in the l-th iteration of the decoding. The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained.

[0038] Step 300: Assess the reliability of each codeword The relationship between the absolute value of the i-th codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration.

[0039] In one embodiment, the Dec decoding is performed to obtain the output of the decoder Dec for the i-th codeword in the l-th iteration of decoding. Specifically, it includes:

[0040] If the Dec decoding fails, then

[0041] If the decoding of Dec is successful, and the decoded output of the i-th codeword is 0, then

[0042] If the decoding of Dec is successful, and the decoded output of the i-th codeword is 1, then

[0043] In one embodiment, the output of the decoder Dec to the i-th codeword in the l-th iteration of decoding... The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained. Specifically, it is obtained by setting it as follows:

[0044]

[0045] In one embodiment, the reliability of each codeword is considered. The relationship between the absolute value of the codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration, specifically including:

[0046]

[0047] The output of the i-th codeword in the l-th iteration is

[0048]

[0049] Here, sign(x) is the sign function.

[0050] In one embodiment, the product coefficient w (l) With flip probability It is related to the number of iterations l.

[0051] In one embodiment, the linear block code has a code length of n and an information bit length of k.

[0052] Example 1:

[0053] The encoding scheme adopts a product code scheme, and the decoding algorithm adopts a limited-distance decoding algorithm. The component code is a BCH code with a code length of 255 and an information bit length of 2^31. Therefore, the received codeword is a 255*255 matrix. The maximum number of iterations is set to 12, of which 10 iterations execute the random bit-flipping algorithm proposed in this invention, and 2 iterations execute only the limited-distance decoding algorithm. In each iteration of decoding, rows are decoded first, followed by columns. The specific decoding algorithm process is as follows:

[0054] Step 1: In the l-th iteration of decoding, decode the codeword in the i-th row. Output the column decoding result from the previous iteration. This is used as input to the distance-bounded decoding algorithm, and the distance-bounded decoding algorithm is executed. If decoding fails, then... If decoding is successful, and the decoded output of the codeword in column j is 0, then If decoding is successful, and the decoded output of the codeword in column j is 1, then Then, based on the row product coefficients of the given current iteration number... The log-likelihood ratio L of each codeword i,j Calculate the reliability of each codeword in

[0055] Step 2: Judgment Is it less than the threshold T? If... but like Then there is random probability have probability Then, the codeword in row i and column j is output as the row decoding output in the l-th iteration.

[0056] Step 3: Repeat Step 1 and Step 2 until all rows have been decoded. Decode the codeword in column j. Output the decoded row for the current iteration number. This serves as the input to the distance-limited decoding algorithm. The operation in step one is performed to obtain... and Then perform the update operation in step two. Finally, the output of the codeword in the i-th row and j-th column in the l-th iteration is:

[0057] Figure 2 The encoding flowchart of the product code is given. Figure 3 Performance graphs of the decoding method based on random bit flipping product codes in this example are presented. For performance comparison, Figure 3The paper also presents a scaled-reliability limited-range decoding algorithm and its performance on a Gaussian white noise channel. The coding scheme and the maximum number of decoding iterations used are the same as in Example 1. Figure 3 As can be seen, the decoding method based on product codes with random bit flipping proposed in this example has a lower bit error rate and performs about 0.16 dB better than the scaled reliability limited distance decoding algorithm.

[0058] Example 2

[0059] The encoding scheme adopts a ladder code scheme, and the decoding algorithm adopts a limited-distance decoding algorithm. The component code is a shortened BCH code with a code length of 254 and an information bit length of 230. Let... For the k-th matrix The codeword in the i-th row and j-th column can be represented by the following mapping relationship according to the ladder code encoding method:

[0060]

[0061] The maximum number of iterations is set to 12, with 10 iterations executing the proposed random bit-flipping algorithm and 2 iterations executing only the distance-limited decoding algorithm. The decoding window size is set to 762, meaning there are 6 matrices within the window. The specific decoding algorithm process is as follows:

[0062] Step 1: In the l-th iteration of decoding, for the k-th matrix... Decode the codeword in the i-th row. Output the decoded code from the previous iteration. It is used as input to the limited-distance decoding algorithm and is then executed. If decoding fails, then... If decoding is successful, and the decoded output of the codeword in column j is 0, then If decoding is successful, and the decoded output of the codeword in column j is 1, then Then, based on the product coefficient w of the k-th matrix in the given current iteration number... k,(l) Log-likelihood ratio with each codeword Calculate the reliability of each codeword in

[0063] Step 2: Judgment Is it less than the threshold T? If... but like Then there is random probability have probability Then, the codeword in the i-th row and j-th column of the k-th matrix is ​​decoded and output in the l-th iteration as follows:

[0064] Step 3: Output the decoded code obtained in Step 2. Update the corresponding codeword in the mapping. That is, update the (i+127th)th column of the (k-1)th matrix and the (i)th column of the (k+1)th matrix.

[0065] Step 4: Repeat steps 1 to 3 until all rows in the decoding window have been decoded, then proceed with the next iteration of decoding.

[0066] Figure 4 The coding block diagram of the ladder code is given, where B k This represents a 127x127 matrix. Representative matrix B k The transpose of . It is a matrix of all zeros, used for initialization.

[0067] Figure 5 Performance graphs of the ladder code decoding method based on random bit flipping in this example are presented. For performance comparison, Figure 5 The paper also presents a scale-reliable limited-range decoding algorithm and its performance on a Gaussian white noise channel. This is achieved through observation... Figure 5 As can be seen, the decoding method based on product codes with random bit flipping proposed in this example performs far better than the other two algorithms in terms of bit error rate, and is about 0.22 dB better than the limited distance decoding algorithm with scaling reliability.

[0068] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0069] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A decoding method for spatially coupled product codes based on random bit flipping, characterized in that, Including the following steps: To decode the block code, in the l-th iteration of decoding, the output of the (l-1)-th iteration is used as the input to the Dec decoding algorithm, and the Dec decoding algorithm is executed to obtain the output of the Dec decoding algorithm for the i-th codeword in the l-th iteration. Based on the output of the Dec decoding algorithm for the i-th codeword in the l-th iteration of decoding... The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained. Based on the reliability of each codeword The relationship between the absolute value of the codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration; Specifically, the execution of the Dec decoding algorithm yields the output of the Dec decoding algorithm for the i-th codeword in the l-th iteration of decoding. Specifically, it includes: If the Dec decoding fails, then If the decoding of Dec is successful, and the decoded output of the i-th codeword is 0, then If the decoding of Dec is successful, and the decoded output of the i-th codeword is 1, then 2. The decoding method for spatially coupled product codes based on random bit flipping according to claim 1, characterized in that, The output of the i-th codeword based on the Dec decoding algorithm in the l-th iteration of decoding. The log-likelihood ratio L of the i-th codeword i The product coefficient w of the l-th iteration (l) The reliability of each codeword is obtained. Specifically, it is obtained according to the following preset formula:

3. The decoding method for spatially coupled product codes based on random bit flipping according to claim 1, characterized in that, The reliability of each codeword The relationship between the absolute value of the codeword and the threshold T is used to obtain the output of the i-th codeword in the l-th iteration, specifically including: The output of the i-th codeword in the l-th iteration is Where sign(x) is the sign function. It is the probability of flipping.

4. The decoding method for spatially coupled product codes based on random bit flipping according to claim 3, characterized in that, Product coefficient w (l) With flip probability It is related to the number of iterations l.

5. The decoding method for spatially coupled product codes based on random bit flipping according to claim 1, characterized in that, The block code is a linear block code with a code length of n and an information bit length of k.

Images