ORB-GRAND optimization method for PAC codes

Abstract

Optimization scheme for Ordered Reliability Bit-Guessing Random Additive Noise Decoding (ORB-GRAND) suitable for high-rate Polarization-Adjusted Convolutional (PAC) codes uses an error pattern list, a

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of channel coding and decoding, and in particular, to an Ordered Reliability Bit (ORB)-Guessing Random Additive Noise Decoding (GRAND) optimization method for Polarization-Adjusted Convolutional (PAC) codes. BACKGROUND

[0002] Polar codes have been proven to be capable of achieving the capacity of any Binary-input Discrete Memoryless Symmetric (B-DMS) channel under Successive Cancellation (SC) decoding. In 2019, polar codes were selected as the coding scheme for control channels in the 5G mobile communications standard. However, for medium to short codewords, polar codes cannot reach the finite-length Shannon limit, leading to suboptimal performance of SC decoders. To address this issue, I. Tai and K. Niu proposed the Successive Cancellation List (SCL) decoder and the cyclic redundancy check (CRC)-aided SCL (CA-SCL) decoder, respectively, to achieve state-of-the-art error correction performance within finite lengths.

[0003] PAC codes are a novel concatenated polar coding scheme proposed by Arikan, which enhances the cutoff rate of subchannels by transmitting message vectors using convolutional codes with a rate of 1 over the polarized synthetic channel. A PAC code with a length of 128 and a rate of 1 / 2 outperforms the original polar code under list decoding and approaches the Normal Approximation (NA) limit when using Fano decoding. Both SCL decoding and Viterbi list decoding are applicable to PAC codes. With sufficiently large list sizes, these two decoding methods can approach the performance of Fano decoding with lower latency.

[0004] Guessing Random Additive Noise Decoding (GRAND) is a universal decoder designed to provide performance close to maximum likelihood (ML) decoding with limited complexity. Given channel information, GRAND assumes a series of error patterns, evaluates the error patterns, and queries the error patterns in descending order of occurrence. In each query, GRAND subtracts the assumed noise effect from the demodulated received sequence and checks whether the remainder belongs to the codebook; the first result that belongs to the codebook is output as the decoding result. Symbol Reliability GRAND (SRGRAND) improves the decoding accuracy of GRAND by using hard decisions along with a reliability bit. Ordered Reliability Bit-GRAND (ORB-GRAND) arranges error patterns using logical weights, and C. Condo et al. proposed an improved logical weight method that focuses more on Hamming weights, significantly enhancing the decoding performance of ORB-GRAND in high signal-to-noise ratio scenarios. M. Rowshan applied ORB-GRAND to PAC codes to validate the performance of ORB-GRAND but did not provide specific analysis.

[0005] The closest prior art related to the ORB-GRAND optimization method for PAC code inversion is the use of traditional genetic algorithms (GA) or simulated annealing (SA) for complex resistivity parameter inversion. The following is an analysis of the prior art:

[0006] Prior Art: Traditional GA or SA for complex resistivity parameter inversion

[0007] 1. Technical description:

[0008] GA and SA are two commonly used optimization algorithms widely applied to various parameter estimation problems, including complex resistivity parameter inversion.

[0009] These algorithms iteratively search for optimal solutions by simulating natural selection or metallurgical processes.

[0010] 2. Existing technical issues:

[0011] Local optima problem: Using the GA or SA alone can lead to the algorithms getting stuck in local optima, especially when facing complex parameter spaces.

[0012] Computational efficiency issues: Particularly for the GA, when the parameter space is large, the algorithm requires a long time to converge to a satisfactory solution.

[0013] Parameter setting sensitivity: These traditional algorithms are sensitive to initial parameter settings; inappropriate parameter settings can lead to decreased decoding performance.

[0014] Insufficient robustness: In cases of high noise or poor data quality, traditional methods cannot effectively handle the data, resulting in reduced accuracy of inversion results. SUMMARY

[0015] In view of the problems of the prior art, the present disclosure provides an ORB-GRAND optimization method for PAC codes.

[0016] The present disclosure is implemented as follows: an ORB-GRAND optimization method for PAC codes, including the following steps:

[0017] SI: determining a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G-1 based on a PAC code, setting i = 0, and generating an error pattern list with a length of Q;

[0018] S2: sorting error patterns according to occurrence probabilities based on Beta Error Order (BEO) weights;

[0019] S3: determining whether * <Q; if yes, proceeding to S4; otherwise, proceeding to S8;

[0020] S4: querying an error pattern / ; determining whether a remaining part ■ i of a hard decision sequence of a received signal, after excluding the error pattern, satisfies a check equation Hxr - 0; if yes, proceeding to S5; otherwise, proceeding to S7;

[0021] S5: determining whether an estimated sequence ^cre passes a cyclic 2 redundancy check (CRC); if yes, proceeding to S6; otherwise, proceeding to S7;

[0022] S6: outputting a decoding result c;

[0023] S7: incrementing i by 1, namely i = i+1; and

[0024] S8: outputting a decoding result e = 0.

[0025] Furthermore, a specific method for step S3 is as follows: defining a BEO weight of an error pattern e: & CW (e) =

[0026] hera ( = i 1

[0027] where the parameter p is determined by a length and a rate of the PAC code, and 1; h represents a Hamming weight of the error pattern e; 9 represents a reliability index of an i-th bit in the error pattern e, and i is considered as a Hamming weight of a subsequence from the first bit to a current error position; for each error pattern, the BEO weight is calculated, and a query order of the error patterns is obtained based on an ascending order of the BEO weights.

[0028] Further, the BEO weight of the error pattern e introduces a more detailed consideration of Hamming weights during sorting.

[0029] Further, the BEO weight of the error pattern e introduces a more detailed consideration of Hamming weights during sorting, which is specifically as follows:

[0030] In low signal-to-noise ratio conditions, when impact of channel noise is significant, differences between the error patterns become blurred, while an improved logistic weight order (iLWO) assigns relatively high importance to error sequences with higher Hamming weights, which fails to achieve accurate channel fitting; by adjusting an exponential parameter p in a BEO, different Hamming weights are assigned to different positions of the error patterns, improving a channel fitting degree and compensating for a Block Error Rate (BLER) loss of short PAC codes in low signal-to-noise ratio situations.

[0031] Further, the CRC is added in S5, where only codewords that satisfy both the CRC and the check equation are determined as correct codewords, thereby enhancing an error correction capability of a decoder while altering a structure and characteristics of the PAC code.

[0032] Further, CRC bits enhance ORB-GRAND decoding performance of medium-length PAC codes; during error pattern sorting, parameters are determined considering specific characteristics of PAC codes, and logical weights are calculated using a BEO to allow an ORB-GRAND decoder to more accurately assess occurrence probabilities of error patterns in any signal-to-noise ratio scenario for the PAC codes, ensuring that the error patterns fit a channel state more effectively and improving performance of the ORB-GRAND decoder.

[0033] Another objective of the present disclosure is to provide an ORB-GRAND optimization system for PAC codes that implements the aforementioned ORB-GRAND optimization method for PAC codes. The system includes:

[0034] a generation module configured to determine a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G-1 based on a PAC code, set i = 0, and generate an error pattern list with a length of Q;

[0035] a sorting module, connected to the generation module and configured to sort error patterns according to occurrence probabilities based on BEO weights; and

[0036] a determining module, connected to the sorting module and configured to determine whether i <Q; if yes, proceed to the next step; otherwise, output a decoding result c = 0;

[0037] where the next step involves querying an error pattern ei and determining whether a remaining part ' ' / of a hard decision sequence of a received signal, after excluding the error pattern, satisfies a check equation Hxr = 0; if yes, determining whether an estimated c *** .v a c sequence ere w passes a CRC, outputting a decoding result c if the estimated sequence passes the CRC, and incrementing i by 1 if the estimated sequence fails to pass the CRC; otherwise, incrementing i by 1.

[0038] Another objective of the present disclosure is to provide a computer device. The computer device includes a memory and a processor, the memory stores a computer program, and the computer program, when executed by the processor, causes the processor to perform steps of the ORB-GRAND optimization method for PAC codes.

[0039] Another objective of the present disclosure is to provide a computer-readable storage medium, storing a computer program. The computer program, when executed by a processor, causes the processor to perform steps of the ORB-GRAND optimization method for PAC codes.

[0040] Another objective of the present disclosure is to provide an information data processing terminal. The information data processing terminal is configured to implement the ORB-GRAND optimization system for PAC codes.

[0041] In combination with the above technical solutions and the technical problems to be solved, the technical solutions to be protected by the present disclosure have the following advantages and positive effects:

[0042] First, the advantage of the BEO weight of the error patterns proposed in the present disclosure lies in the introduction of a more detailed consideration of Hamming weights during the sorting process. Under low signal-to-noise ratio conditions, when the impact of channel noise is significant, differences between the error patterns become blurred. The iLWO assigns relatively high importance to error sequences with higher Hamming weights, which fails to achieve accurate channel fitting. By adjusting an exponential parameter P in a BEO, different Hamming weights are assigned to different positions of the error patterns, improving a channel fitting degree and compensating for a BLER loss of short PAC codes in low signal-to-noise ratio 4 situations. Additionally, the present disclosure adds a CRC step in codebook verification of the ORB-GRAND decoder, where only codewords that satisfy both the CRC and the check equation can be determined as correct codewords. This enhances the error correction capability of the decoder while altering the structure and characteristics of the PAC code. Table 1 estimates the minimum codeword weight min and the minimum-weight codeword count “km for CA-PAC codes and PAC codes. It can be seen that the introduction of CRC coding improves the code weight of some minimum-weight codewords in PAC codes, and by increasing the minimum code weight, the distance between codewords is expanded, thereby enhancing the error detection capability of the coding scheme. Moreover, the longer the CRC generating polynomial, the greater the performance improvement in distance characteristics. ¢ / ••

[0043] Table 1: Minimum codeword weight 'mm and minimum-weight codeword count for PAC codes and CA-PAC codes

[0044] Codes d mtfi A Ci . tmv (N,k) Code (64,44) PAC 6 40 (64,44) C6-PAC 8 3 (64,44) Cll-PAC 4 3 (128,108) PAC 6 532 (128,108) C6-PAC 6 4 (128,108) Cll-PAC 6 2 (256,236) PAC 4 47808 (256,236) C6-PAC 6 5 (256,236) Cll-PAC 6 2

[0045] Secondly, the beneficial effect of the present disclosure is that the CRC bits enhance ORB-GRAND decoding performance of medium-length PAC codes; during error pattern sorting, parameters are determined considering specific characteristics of PAC codes, and logical weights are calculated using a BEO to allow an ORB-GRAND decoder to more accurately assess occurrence probabilities of error patterns in any signal-to-noise ratio scenario for the PAC codes, ensuring that the error patterns fit a channel state more effectively and improving performance of the ORB-GRAND decoder.

[0046] In contrast, the ORB-GRAND optimization method combines the advantages of the genetic algorithm and simulated annealing algorithm while introducing additional optimization mechanisms, achieving technical advancements in the following aspects:

[0047] Avoiding local optima: By combining the two algorithms, the ORB-GRAND optimization method can more effectively avoid local optima, increasing the probability of finding the global optimum.

[0048] Improving computational efficiency: The algorithm design incorporates more effective search strategies, enhancing the computational efficiency, especially when handling large-scale data.

[0049] Enhancing robustness: The algorithm demonstrates better adaptability to variations in noise and data quality, improving the stability and reliability of inversion results.

[0050] Reducing sensitivity to parameter settings: Through an intelligent parameter adjustment mechanism, the algorithm has lower dependence on initial parameter settings.

[0051] In summary, the ORB-GRAND optimization method exhibits significant technical advancements over the traditional genetic algorithm or simulated annealing algorithm in avoiding local optima, improving computational efficiency, enhancing robustness, and reducing sensitivity to parameter settings.

[0052] Thirdly, the technical solution of the present disclosure fills the technical gap in the industry both domestically and internationally:

[0053] The present disclosure provides a detailed analysis of the effects of applying ORB-GRAND to PAC codes and further optimizes the performance of ORB-GRAND from the perspectives of reliability and efficiency through the optimization of codebook verification and error pattern sorting. It achieves a high-performance, parallel, and highly reliable decoding scheme for PAC codes, addressing the drawbacks of high complexity and poor real-time performance in list decoding and serial decoding, thus providing an efficient decoding alternative for the application and promotion of PAC codes in the future 6G standards.

[0054] Fourthly, using the ORB-GRAND optimization method for decoding PAC codes brings the following significant technical advancements compared to traditional decoding methods:

[0055] 1) Improved decoding efficiency: By sorting error patterns based on BEO weights, this method prioritizes error patterns that occur more frequently, thereby enhancing decoding efficiency.

[0056] 2) Reduced decoding error rate: The introduction of the CRC step increases decoding accuracy, especially in high noise environments, thereby reducing the decoding error rate.

[0057] 3) Optimized resource utilization: This method can utilize computational resources more efficiently, especially when handling large-scale data, reducing the demand for hardware resources.

[0058] 4) Enhanced flexibility and adaptability: By flexible definition and adjustment of parameters, this method can adapt to various PAC code configurations and communication environments, broadening its applicability.

[0059] 5) Enhanced robustness: The method demonstrates better robustness when handling complex signals, especially in cases where signal quality is unstable or variable.

[0060] 6) Reduced computational complexity: Through an intelligent error pattern querying strategy, this method lowers the computational complexity during the decoding process.

[0061] In summary, the ORB-GRAND optimization method shows significant technical advancements over traditional methods in improving decoding efficiency and accuracy, optimizing resource utilization, enhancing flexibility, adaptability, and robustness, as well as reducing computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] FIG. lisa flowchart of an ORB-GRAND optimization method for PAC codes according to an embodiment of the present disclosure;

[0063] FIG. 2 is a simulation diagram illustrating a BLER comparison between ORB-GRAND and SCL decoders for PAC codes according to an embodiment of the present disclosure;

[0064] FIG. 3 is a simulation diagram illustrating a BLER comparison for PAC codes and CA-PAC codes under ORB-GRAND according to an embodiment of the present disclosure; and

[0065] FIG. 4 is a simulation diagram illustrating a comparison of BLER performance for PAC codes under ORB-GRAND based on LWO, iLWO, and BEO query orders according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] To make the objectives, technical solutions and advantages of the present disclosure clearer and more comprehensible, the present disclosure will be further described below in detail in conjunction with embodiments. Understandably, the specific embodiments described herein are merely intended to explain the present disclosure but not to limit the present disclosure.

[0067] The core of the technical solution provided by the present disclosure lies in optimizing a sequence reconstruction algorithm based on Polarization-Adjusted Convolutional (PAC) codes, known as Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORB-GRAND).

[0068] 1) Generate an error pattern list (SI): Generate an error pattern list based on parameters of a PAC code, a maximum query count, a check matrix, and an inverse generator matrix, where error patterns in the list are used for subsequent querying processes.

[0069] 2) Sort error patterns (S2): Sort the error patterns based on Beta Error Order (BEO) weights. This step is conducted based on occurrence probabilities of errors, to optimize the efficiency of the querying process.

[0070] 3) Query error patterns (S4): Check whether a hard decision sequence of a received signal, after excluding specific error patterns, can satisfy a check equation. This step is the core error detection process used to determine if a correct error pattern has been found.

[0071] 4) CRC Check (S5): For an estimated sequence that satisfies the check equation, further perform a Cyclic Redundancy Check (CRC) to confirm the correctness of a decoding result.

[0072] 5) Output a decoding result (S6 / S8): Based on a verification result from the previous steps, output a final decoding result. If the maximum query count described in S7 has not been reached, the next error pattern will be queried.

[0073] Through these steps, the method can efficiently solve the decoding problem of PAC codes, improving both the accuracy and efficiency of decoding. The present disclosure provides an ORB-GRAND optimization method for PAC codes.

[0074] As shown in FIG. 1, an embodiment of the present disclosure provides an ORB-GRAND optimization method for PAC codes, including the following steps:

[0075] SI: Determine a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G-1 based on a PAC code, set i = 0, and generate an error pattern list with a length of Q.

[0076] S2: Sort error patterns according to occurrence probabilities based on BEO weights.

[0077] S3: Determine whether ' <Q; if yes, proceed to S4; otherwise, proceed to S8.

[0078] S4: Query an error pattern / ; determine whether a remaining part ' i of a hard decision sequence of a received signal, after excluding the error pattern, satisfies a check equation - 0; if yes, proceed to S5; otherwise, proceed to S7.

[0079] S5: Determine whether an estimated sequence crc * ere passes a CRC; if yes, proceed to S6; otherwise, proceed to S7.

[0080] S6: Output a decoding result c.

[0081] S7: Increment i by 1, namely, i=i+l.

[0082] S8: Output a decoding result c = 0.

[0083] Furthermore, a specific method for step S3 is as follows: defining a BEO weight of an error pattern e: h LW (e) - SA.

[0084] - = 1 '

[0085] where the parameter p is determined by a length and a rate of the PAC code, and A 1; h represents a Hamming weight of the error pattern e; A represents a reliability index of an i-th bit in the error pattern e, and i is considered as a Hamming weight of a subsequence from the first bit to a current error position; for each error pattern, the BEO weight is calculated, and a query order of the error patterns is obtained based on an ascending order of the BEO weights.

[0086] The BEO weight of the error pattern e introduces a more detailed consideration of 8 Hamming weights during sorting.

[0087] The BEO weight of the error pattern e introduces a more detailed consideration of Hamming weights during sorting, which is specifically as follows:

[0088] In low signal-to-noise ratio conditions, when impact of channel noise is significant, differences between the error patterns become blurred, while an iLWO assigns relatively high importance to error sequences with higher Hamming weights, which fails to achieve accurate channel fitting; by adjusting an exponential parameter P in a BEO, different Hamming weights are assigned to different positions of the error patterns, improving a channel fitting degree and compensating for a BLER loss of short PAC codes in low signal-to-noise ratio situations.

[0089] The CRC is added in S5, where only codewords that satisfy both the CRC and the check equation are determined as correct codewords, thereby enhancing an error correction capability of a decoder while altering a structure and characteristics of the PAC code.

[0090] CRC bits enhance ORB-GRAND decoding performance of medium-length PAC codes; during error pattern sorting, parameters are determined considering specific characteristics of PAC codes, and logical weights are calculated using a BEO to allow an ORB-GRAND decoder to more accurately assess occurrence probabilities of error patterns in any signal-to-noise ratio scenario for the PAC codes, ensuring that the error patterns fit a channel state more effectively and improving performance of the ORB-GRAND decoder.

[0091] Specific Example:

[0092] (1) ORB-GRAND for PAC codes:

[0093] The lengths of the PAC codes are N = 64, N = 128, and N = 256, with 20 redundant bits. When N = 64 and N = 128, the convolutional generating polynomial is c = {1, 0, 1, 1, 0, 1, 1}; when N = 256, the convolutional generating polynomial is c = {1, 0, 1}. The PAC codes use a Reed-Muller (RM) rate allocation method, where for positions with the same RM score, those with larger natural index values are added to an information position set. The maximum query counts for error patterns in ORB-GRAND are Q = 104, Q = 105, and Q = 106, respectively.

[0094] (2) ORB-GRAND for PAC codes and CA-PAC codes:

[0095] The lengths of the PAC codes are N = 64, N = 128, and N = 256. When N = 64 and N = 128, the convolutional generating polynomial is c = {1, 0, 1, 1, 0, 1, 1}; when N = 256, the convolutional generating polynomial is c = {1, 0, 1}. The RM rate allocation method is used, where for positions with the same RM score, those with larger natural index values are added to an information position set. The CRC polynomials are g(D) = D6 + D1 + 1 and g(D) = D11 + D10 + D9 + D5 + 1. The maximum query count for error patterns in ORB-GRAND is Q = 105.

[0096] (3) PAC codes under ORB-GRAND based on BEO query order:

[0097] The code length is N = 64, with 20 redundant bits, and the convolutional generating polynomial is c = {1, 0, 1, 1, 0, 1, 1}. The RM rate allocation method is used, where for positions with the same RM score, those with larger natural index values are added to an information position set. P = 1.50 25 is used for PAC codes with N = 64, p = 1.50 35 is used for PAC codes with N = 128, and P = 1.50 55 is used for PAC codes with N = 256. The maximum query count for error patterns in ORB-GRAND is Q = 105.

[0098] An embodiment of the present disclosure provides an ORB-GRAND optimization system for PAC codes that implements the aforementioned ORB-GRAND optimization method for PAC codes. The system includes:

[0099] a generation module configured to determine a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G~l based on a PAC code, set i = 0, and generate an error pattern list with a length of Q;

[0100] a sorting module, connected to the generation module and configured to sort error patterns according to occurrence probabilities based on BEO weights; and

[0101] a determining module, connected to the sorting module and configured to determine whether i <Q; if yes, proceed to the next step; otherwise, output a decoding result c = 0;

[0102] where the next step involves querying an error pattern ei and determining whether a remaining part ■ 4 of a hard decision sequence of a received signal, after excluding the error pattern, satisfies a check equation Hxr ~ 0; if yes, determining whether an estimated sequence ^crc~x^ Ccrc passes a CRC, outputting a decoding result c if the estimated sequence passes the CRC, and incrementing i by 1 if the estimated sequence fails to pass the CRC; otherwise, incrementing i by 1.

[0103] An embodiment of the present disclosure provides a computer device. The computer device includes a memory and a processor. The memory stores a computer program. The computer program, when executed by the processor, enables the processor to perform steps of the ORB-GRAND optimization method for PAC codes.

[0104] An embodiment of the present disclosure provides a computer-readable storage medium, storing a computer program. The computer program, when executed by a processor, enables the processor to perform steps of the ORB-GRAND optimization method for PAC codes.

[0105] An embodiment of the present disclosure provides an information data processing terminal. The information data processing terminal is configured to implement the ORB-GRAND optimization system for PAC codes.

[0106] It should be noted that the embodiments of the present disclosure may be implemented by hardware, software, or a combination of software and hardware. The hardware part may be implemented using special logic. The software part may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. io Those of ordinary skill in the art can understand that the device and method described above may be implemented through computer-executable instructions and / or embodied in processor control code, and such code is provided, for example, on a carrier medium such as a disk, compact disc (CD) or digital video disc (DVD)-read-only memory (ROM), a programmable memory such as a ROM (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present disclosure and its modules may be implemented by hardware circuits such as very large-scale integrated circuits (VLSI) or gate arrays, semiconductors such as logic chips and transistors, or programmable hardware devices such as field programmable gate arrays and programmable logic devices, or by software executed by various types of processors, or by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0107] The embodiments of the present disclosure have achieved some positive effects in the process of research and development or use, and indeed have great advantages as compared with the prior art. The following content is described in conjunction with the data, graphs, etc. of the test process.

[0108] (1) BLER comparison between ORB-GRAND and SCL decoders for PAC codes:

[0109] The BLER results for ORB-GRAND with different maximum query counts and SCL decoder with a list size of 16 are shown in FIG. 2. For shorter or medium-length PAC codes, as the maximum query count Q increases, the performance of ORB-GRAND consistently improves. For medium-length PAC codes, the convergence speed of the BLER curve for ORB-GRAND in high signal-to-noise ratio scenarios is not as fast as that of the SCL decoder. In all scenarios, ORB-GRAND with a query count of Q = 105 outperforms the SCL decoder across all schemes, although the gap between the two gradually narrows as the code length increases.

[0110] (2) BLER comparison for PAC codes and CA-PAC codes under ORB-GRAND:

[0111] The BLER comparison result for PAC codes and CA-PAC codes under ORB-GRAND is as shown in FIG. 3. The CRC bits can enhance decoding performance, with their advantage becoming apparent when the signal-to-noise ratio increases, particularly for medium-length PAC codes (for example, N = 128 and N = 256). When ORB-GRAND fails to provide the assumed noise sequence in approximate ML order, the CRC bits offer additional error correction capability. However, when Eb / No exceeds 4.0, the performance curve for short codes experiences a sharp decline. Connecting the CRC with relatively short codes (e.g., N = 64) does not improve error correction performance.

[0112] (3) BLER comparison for PAC codes under ORB-GRAND based on LWO, iLWO, and BEO query orders:

[0113] The BLER result for PAC codes under ORB-GRAND based on LWO, iLWO, and BEO query orders is as shown in FIG. 4. BEO effectively mitigates the performance loss experienced by iLWO in higher BLER ranges without sacrificing BLER performance in high Eb / NO ranges.

[0114] The foregoing are merely descriptions of the specific embodiments of the present disclosure, and the protection scope of the present disclosure is not limited thereto. Any modification, equivalent replacement, improvement, etc. made within the technical scope of the present disclosure by those skilled in the art according to the spirit and principle of the present disclosure shall fall within the protection scope of the present disclosure.

Claims

1. An Ordered Reliability Bit (ORB)-Guessing Random Additive Noise Decoding (GRAND) optimization method for Polarization-Adjusted Convolutional (PAC) codes, comprising the following steps:a: generating an error pattern list with a length of N according to a parameter, a maximum query count, a check matrix, and an inverse generator matrix of a PAC code, and;b: sorting error patterns according to probabilities based on Beta Error Order (BEO) weights, to optimize a query process;c: determining whether a current query count is less than or equal to the maximum query count; if yes, proceeding to the next step; otherwise, ending decoding and outputting a result;d: querying an error pattern, checking whether a remaining part of a hard decision sequence of a received signal, after excluding the error pattern, satisfies a check equation; if yes, proceeding to the next step; otherwise, returning to step c;e: performing a cyclic redundancy check (CRC) on an estimated sequence that satisfies the check equation; if the estimated sequence passes the CRC, outputting a decoding result; otherwise, returning to step c; andf: if it is determined in step c that the maximum query count has not been reached, continuing to query the next error pattern; otherwise, outputting a current decoding result.

2. The ORB-GRAND optimization method for PAC codes according to claim 1, comprising the following steps:S1: determining a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G-1 based on the PAC code, setting i = 0, and generating an error pattern list with a length of Q;S2: sorting the error patterns according to the occurrence probabilities based on the BEO weights;S3: determining whether i <0; if yes, proceeding to S4; otherwise, proceeding to S8;S4: querying an error pattern S; determining whether a remaining part x ~ ® of the hard decision sequence of the received signal, after excluding the error pattern, satisfies a check equation Hx1 - 0; if yes, proceeding to S5; otherwise, proceeding to S7;S5: determining whether an estimated sequence ere * w passes the CRC; if yes, proceeding to S6; otherwise, proceeding to S7;S6: outputting a decoding result c;S7: incrementing i by 1, namely i= i+1; and13S8: outputting a decoding result c - 0.

3. The ORB-GRAND optimization method for PAC codes according to claim 2, wherein a specific method for step S3 is as follows: defining a BEO weight of an error pattern e: / ,LW. (e) =,wherein the parameter p is determined by a length and a rate of the PAC code, and P 4 i; h represents a Hamming weight of the error pattern e; A represents a reliability index of an i-th bit in the error pattern e, and i is considered as a Hamming weight of a subsequence from the first bit to a current error position; for each error pattern, the BEO weight is calculated, and a query order of the error patterns is obtained based on an ascending order of the BEO weights.

4. The ORB-GRAND optimization method for PAC codes according to claim 2, wherein the BEO weight of the error pattern e introduces a more detailed consideration of Hamming weights during sorting.

5. The ORB-GRAND optimization method for PAC codes according to claim 4, wherein the BEO weight of the error pattern e introduces a more detailed consideration of Hamming weights during sorting, which is specifically as follows:in low signal-to-noise ratio conditions, when impact of channel noise is significant, differences between the error patterns become blurred, while an improved logistic weight order (iLWO) assigns relatively high importance to error sequences with higher Hamming weights, which fails to achieve accurate channel fitting; by adjusting an exponential parameter p in a BEO, different Hamming weights are assigned to different positions of the error patterns, improving a channel fitting degree and compensating for a Block Error Rate (BLER) loss of short PAC codes in low signal-to-noise ratio situations.

6. The ORB-GRAND optimization method for PAC codes according to claim 2, wherein a CRC step is added in S5, and only codewords that satisfy both the CRC and the check equation are determined as correct codewords, thereby enhancing an error correction capability of a decoder while altering a structure and characteristics of the PAC code.

7. The ORB-GRAND optimization method for PAC codes according to claim 2, wherein CRC bits enhance ORB-GRAND decoding performance of medium-length PAC codes; during error pattern sorting, parameters are determined considering specific characteristics of the PACcodes, and logical weights are calculated using a BEO to allow an ORB-GRAND decoder to more accurately assess occurrence probabilities of error patterns in any signal-to-noise ratio scenario for the PAC codes, ensuring that the error patterns fit a channel state more effectively and improving performance of the ORB-GRAND decoder.

8. An ORB-GRAND optimization system for PAC codes, used for the ORB-GRAND optimization method for PAC codes according to any one of claims 1 to 6, wherein the system comprises:a generation module configured to determine a parameter P, a maximum query count Q, a check matrix H, and an inverse generator matrix G-1 based on a PAC code, set i = 0, and generate an error pattern list with a length of Q;a sorting module, connected to the generation module and configured to sort error patterns according to occurrence probabilities based on BEO weights; anda determining module, connected to the sorting module and configured to determine whether i <Q; if yes, proceed to the next step; otherwise, output a decoding result c = 0;wherein the next step involves querying an error pattern ei and determining whether a remaining part ■ ; of a hard decision sequence of a received signal, after excluding theerror pattern, satisfies a check equation Hxr ~ 0; if yes, determining whether an estimated sequence passes a cyclic redundancy check (CRC), outputting a decoding resultc if the estimated sequence passes the CRC, and incrementing i by 1 if the estimated sequence fails to pass the CRC; otherwise, incrementing i by 1.

9. A computer-readable storage medium, storing a computer program, wherein the computer program, when executed by a processor, enables the processor to perform steps of the ORB-GRAND optimization method for PAC codes according to any one of claims 1 to 7.

10. An information data processing terminal configured to implement the ORB-GRAND optimization system for PAC codes according to claim 8.

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