A polar code optimization construction method suitable for ReRAM memory

Abstract

The application discloses a Polar code optimization construction method suitable for a ReRAM memory, and comprises the following steps: a channel model based on a problem of a potential path occurring again after a ReRAM selector failure is constructed; through a Monte Carlo experiment, according to a preset initial population size, a code length and a code rate, error rates corresponding to all populations and probabilities of the potential path occurring are obtained; and the NSGA-II algorithm is used to sort the probabilities of the potential path occurring and the error rates. New individuals are obtained by randomly selecting initial populations for cross. Mutation is performed on individuals with poor performance in the sorting, and all the obtained individuals are comprehensively sorted, and the optimal individual is selected as the construction of the polar code. The application is independent of an actual channel, the error rate and the probability of the potential path occurring are comprehensively considered, and the constructed polar code can achieve better performance under the ReRAM channel.

Description

Technical Field

[0001] This invention belongs to the field of optimization construction technology of novel memory, and particularly relates to a Polar code optimization construction method suitable for ReRAM memory. Background Technology

[0002] ReRAM combines the advantages of traditional random access memory and flash memory, featuring simple and fast read / write operations, low power consumption, and high storage density. Its core structure is a cross-array of memristors, where each memristor cell at the intersection of rows and columns can store data, achieving higher storage density within the same chip area. This characteristic makes ReRAM a promising candidate for applications in non-volatile memory, artificial neural networks, chaotic circuits, programmable logic devices, and information processing and pattern recognition circuits. However, the high-density integration of ReRAM also introduces serious data interference problems, the most prominent being the through-path problem. A through-path refers to a closed path formed in a ReRAM cross-array by alternating vertical and horizontal steps when traversing logic 1 cells. This path can cause current leakage during the read process, interfering with the read result of the target cell and reducing data reliability. To solve this problem, memristors are often connected in series with selectors to avoid current interference between different cells. However, during memory manufacturing and maintenance, the nondeterministic failure of the selector can introduce new problems of mutual interference between array resistors. Therefore, a more sophisticated solution is needed to address the storage nondeterminism problem throughout the array.

[0003] The storage process of ReRAM is achieved by changing the resistance values ​​of the memristors in the cross-array: during writing, logic 0 bits are programmed with a high resistance value (R0), and logic 1 bits are programmed with a low resistance value (R1); during reading, the resistance state is detected by applying a specific voltage and measuring the current, thereby determining the stored data bit. The existence of sneak paths can significantly affect the accuracy of the reading process. By modeling ReRAM as a communication channel model with memory, non-ergodicity, and asymmetry, and utilizing relevant theories of signal detection, information theory, and channel coding, problems such as sneak path interference can be solved. This method does not increase the complexity of ReRAM device fabrication; performance can be significantly improved solely through mathematical and signal processing techniques.

[0004] Polar coding technology, based on channel polarization theory, decomposes the original channel into sub-channels of varying reliability and unreliability through a unique recursive construction method. While ensuring lossless transmission of information bits over highly reliable channels, it achieves theoretically rigorous Shannon capacity reachability, making it the only error correction coding scheme mathematically proven to approach the channel capacity limit. Therefore, polar codes are used to solve the ReRAM channel reliability problem. The polar code encoding process is implemented through recursive matrix operations, resulting in significantly lower encoding and decoding complexity than traditional LDPC codes and Turbo codes, making it particularly suitable for resource-constrained communication scenarios. Under finite code length conditions, by combining it with enhanced decoding algorithms such as dynamic frozen bit configuration and Serial Cancellation List-Cyclic Redundancy Check (SCL-CRC), it exhibits excellent bit error rate and block error rate performance in various scenarios. Furthermore, the recursive structure of polar codes inherently possesses resistance to sudden interference and channel memory effects, exhibiting robustness in fading channels. It also supports flexible adaptation to different channel conditions and quality of service requirements through dynamic rate matching techniques such as shortening, puncturing, and repetition, significantly reducing system implementation complexity. This provides core support for high spectral efficiency and low power consumption communication systems, and can be widely applied in mobile communications, satellite transmission, industrial IoT, and high-reliability data transmission. The core of polar codes is channel polarization; therefore, by transmitting frozen bits (known at the receiver) on a purely noisy channel and information bits on a noise-free channel, channel capacity can be achieved. Polar codes have yielded good results in solving reliability issues in array storage, but currently, there is a lack of construction schemes that comprehensively consider the special properties of ReRAM channels and reduce the occurrence of backdoor paths. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a Polar code optimization construction method suitable for ReRAM memory, which can reduce the occurrence of backdoor paths and still correct errors existing in the entire channel even after a backdoor path occurs.

[0006] To achieve the above objectives, the present invention provides a Polar code optimization construction method suitable for ReRAM memory, comprising:

[0007] ReRAM channel cells are represented using data matrices, readback signals of ReRAM channel cells are calculated, and ReRAM channels are constructed.

[0008] Based on the characteristics of the ReRAM channel and the simulation results of full-pass and non-pass-pass paths, partial cell indices are determined for the positions in the entire array that can be correctly decoded every time and the positions that will be incorrectly decoded every time, and the population is initialized.

[0009] Based on the preset initial population size, the bit error rate and the probability of a hidden path occurring for each population are obtained using the code length and code rate.

[0010] The traditional genetic algorithm is improved by introducing a multi-objective optimization algorithm to perform non-dominated sorting and calculate crowding distance;

[0011] Based on the improved genetic algorithm, the optimal information bit selection strategy in the uncertain channel of the ReRAM channel is found through continuous crossover and mutation, and the optimal construction result is obtained.

[0012] Optionally, initializing the population includes:

[0013] A random binary sequence is generated based on the preset polar code length;

[0014] The generated binary sequence is written sequentially to obtain the encoded data;

[0015] The encoded data is detected and decoded through the full-pass ReRAM channel and the non-pass ReRAM channel respectively to obtain the indexes of the correct and incorrect decoded bits of the constructed scheme, and at the same time, the number of experiments is increased by one.

[0016] When the number of experiments reaches the preset number of experiments, the Monte Carlo experiment is considered complete, and the correct decoding index and the incorrect decoding index obtained in each experiment are compared.

[0017] Record the index of the position that was correctly decoded in each experiment and the index of the position that was incorrectly decoded in each experiment.

[0018] Optionally, based on a preset initial population size, code length, and code rate, the bit error rate and the probability of a stealth path occurring for each population can be obtained, including:

[0019] Two optimization objectives are defined: one is to minimize the bit error rate, and the other is to maximize the proportion of 0s in the constrained encoded array.

[0020] Determine the decision variables and obtain the information bit index set of the polar code;

[0021] An initial population is generated. The channel units that are unreliable at the time of initialization are always set as frozen bits, and the channel units that are reliable are always set as information bits. The remaining uncertain units are selected as information bits or frozen bits according to the preset code rate and the reliability of each unit obtained by the original PW construction algorithm.

[0022] For each individual, calculate the minimum bit error rate and the proportion of 0s in the array after constraint coding;

[0023] For each individual in the population, generate random information bits, construct polar code encoding using the current information bits, transmit through the ReRAM channel model, add stealth path interference and Gaussian noise, use joint BP detection and decoding for decoding, and count the number of bit errors.

[0024] The proportion of 0 and 1 in the constrained-encoded array mainly affects the probability of potential conduction paths occurring in the actual array.

[0025] Optionally, improving the traditional genetic algorithm through introducing a multi-objective optimization algorithm for non-dominated sorting and calculating the crowding distance includes:

[0026] Performing non-dominated sorting on the population to determine the dominance level of each individual;

[0027] For each dominance level, sorting the individuals according to the objective values and calculating the crowding distance of the sorted individuals.

[0028] [[ID=1(4]]According to the improved genetic algorithm, continuously searching for the optimal information bit selection strategy in the uncertain channels of the ReRAM channel through crossover and mutation to obtain the optimal construction result includes:

[0029] Adopting a crowding comparison operator for tournament selection. For two randomly selected individuals p and q, the selection rule is: if r(p) < r(q) or r(p) = r(q) and d(p) > d(q), select p, where r(p) and r(q) are the levels of non-dominated sorting, and d(p) and d(q) are the crowding distances;

[0030] Two-point crossover: Randomly select two crossover points and exchange the chromosome segments of the parents to ensure that the offspring meet the code rate constraint;

[0031] Bit-flip mutation: Randomly flip a small number of genes, adjust the information bit index, and keep the code rate unchanged;

[0032] Merging the parents and offspring, merging the current population and the offspring to form a new population of size 2M; ''

[0033] Retaining the top M optimal individuals to enter the next generation;

[0034] Reaching the maximum number of iterations or the Pareto front converges;

[0035] Selecting typical individuals from the Pareto solution set to obtain the optimal construction result.

[0036] Technical Effects of this Invention: This invention discloses a Polar code optimization construction method suitable for ReRAM memory. Based on the ReRAM channel polar code construction system, and using Monte Carlo experiments, the bit error rate and actual coding rate corresponding to each construction scheme are obtained. A multi-objective optimization algorithm is used to sort and select the bit error rate and actual coding rate corresponding to each individual in the population. Individuals with better fitness are preferentially selected for mutation operations, while individuals with poor fitness are crossover operations, maximizing population diversity while converging as quickly as possible. Through iteration, the coding rate and bit error rate of each individual in the population are optimized, selecting a better construction scheme that more accurately adapts to the specific characteristics of the ReRAM channel, maximizing the use of high-capacity channels to transmit information bits, and determining the optimal construction scheme based on the coding rate and bit error rate corresponding to each construction method. This ensures that information bits are transmitted through the most reliable sub-channel while minimizing the bit error rate, thereby improving the efficiency and quality of signal transmission. Attached Figure Description

[0037] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0038] Figure 1 This is a flowchart illustrating a Polar code optimization construction method for ReRAM memory according to an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of the Pareto front in the polar code construction method applicable to ReRAM according to an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of the bit error rate in the polar code construction method applicable to ReRAM according to an embodiment of the present invention; Detailed Implementation

[0041] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0042] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0043] like Figure 1 As shown, this embodiment provides a Polar code optimization construction method suitable for ReRAM memory, including:

[0044] S1. Set basic parameters according to the characteristics of the ReRAM channel;

[0045] S2. Based on the characteristics of the ReRAM channel and the simulation results of full-pass and non-pass-pass paths, determine the partial cell indices for the positions in the entire array that can be correctly decoded every time and the positions that will be incorrectly decoded every time, and initialize the population.

[0046] S3. Implement the fitness function;

[0047] S4. Introduce a multi-objective optimization algorithm to improve the fitness evaluation method in the traditional genetic algorithm;

[0048] S5. Based on S4, improve the genetic algorithm to find the optimal information bit selection strategy in the uncertain channels of the ReRAM array through continuous crossover and mutation.

[0049] Furthermore, initializing the population based on this prior information includes:

[0050] First, a Monte Carlo experiment is conducted based on the preset population size, the code length of the encoded polar code, and the number of simulation frames to obtain the probability of the occurrence of the hidden path and the bit error rate for each individual in the population.

[0051] The fitness of each individual is obtained based on its code rate and the proportion of 0s in the actual encoded form of the corresponding construction scheme.

[0052] Based on the fitness of each individual and the multi-objective optimization algorithm, each individual is sorted to obtain the individual with the best fitness in the initial population.

[0053] By employing crossover and mutation, individuals with poor fitness in the population are evolved, causing the entire system to move towards a more fitness-oriented direction.

[0054] Calculate the fitness of individuals after crossover and mutation, and merge the populations.

[0055] After reaching the maximum number of iterations, the individual with the highest overall fitness is selected as the final construction scheme.

[0056] Specifically, this invention comprehensively considers the characteristics of ReRAM. First, it determines a certain number of reliable cells and a certain number of unreliable cells based on both the case of no hidden path and the case of a fully hidden path. Considering the requirements of actual memory, the simulation sets the initial constraint code construction parameter to 0.3, the maximum parameter to 0.5, and the initial population selection parameter to 0.3. The code length of the polar code is the length of the codeword, usually represented by n, where the code length must be an integer power of 2. In a preferred embodiment of this invention, the preset number of experiments is 1000, and the code length of the polar code is 256. The probability of each cell selector failing is 0.001.

[0057] For a preset code length, simulations were performed on both fully submerged path channels and channels without submerged path interference to obtain prior information. For the fully submerged path case, it was assumed that all cells with high resistance were affected by submerged path interference. In this case, the overall channel performance is worst; errors present in the actual array storage will inevitably occur in this array. Therefore, a subchannel that is sufficiently reliable under the fully submerged path condition must be reliable for the actual ReRAM channel. Similarly, a channel that is unreliable even without a submerged path must be unreliable for the actual ReRAM channel.

[0058] A random binary sequence is generated based on the preset polar code length, denoted as {x1, x2, x3....}. The generated binary sequence is then written sequentially. The encoded data is then passed through both a full-path ReRAM channel and a non-path ReRAM channel. Finally, detection and decoding are performed to obtain the indices of the correctly decoded and incorrectly decoded bits for this experimental scheme. An additional experiment is then conducted.

[0059] When the preset number of experiments is reached, the Monte Carlo experiment is considered complete, and the correct decoding indexes and incorrect decoding indexes obtained from each experiment are compared. The indexes at which each experiment can be correctly decoded and the indexes at which each experiment cannot be correctly decoded are recorded.

[0060] Furthermore, the steps in S3 to complete the genetic algorithm adapted to the ReRAM channel are as follows:

[0061] S31. Problem Definition and Objective Function: As a high-efficiency memory, ReRAM's performance requires consideration of not only storage accuracy but also the number of information bits that a fixed memory array can store. Therefore, two optimization objectives are chosen. Objective 1 is to maximize the number of erroneous bits that the construction scheme can correct, i.e., to minimize the bit error rate (BER). Objective 2 is to maximize the proportion of 0s in the array after constraint encoding.

[0062] S32. Determine the decision variables. The final goal is to obtain the information bit index set of the polar code (i.e., determine which sub-channels are used to transmit information bits).

[0063] S33. Population initialization: Generate an initial population (size M), set the certain unreliable channel units at the time of initialization as frozen bits, set the certain reliable channel units as information bits, and select the remaining uncertain units as information bits or frozen bits according to the preset code rate and the reliability of each unit obtained by the original PW construction algorithm.

[0064] S34. Next, fitness evaluation is performed. Two target values ​​are calculated for each individual (i.e., each set of information bits): Bit Error Rate (BER) and Frame Error Rate (FER).

[0065] S35. BER Calculation: For each individual in the population, generate random information bits and construct a polar code using the current information bits. Transmit through a ReRAM channel model, incorporating stealth path interference and Gaussian noise. Then, use joint BP detection and decoding for decoding. Count the number of bit errors and calculate BER = number of erroneous bits / total number of bits (using Monte Carlo simulation, setting the simulation count to 1000 times).

[0066] S36. Calculation of FER: The proportion of 0s and 1s in the constrained-encoded array mainly affects the probability of a stealth path occurring in the actual array. Under low-noise conditions, the main determining factor for decoding failure is whether a stealth path occurs; therefore, the presence or absence of decoding failure is used to evaluate the quality of this indicator. For each individual in the population, random information bits are generated, and polar code encoding is constructed using the current information bits. Transmission is performed through a ReRAM channel model, incorporating stealth path interference and Gaussian noise. Decoding is then performed using joint BP detection and decoding. The number of erroneous frames is counted, and FER is calculated as: FER = Number of erroneous experiments / Total number of experiments (using Monte Carlo simulation, setting the number of simulations to 1000).

[0067] Furthermore, S4 improves upon the traditional genetic algorithm by introducing a multi-objective optimization algorithm, as follows: Non-dominated sorting and crowding calculation are performed. Non-dominated sorting stratifies individuals in the population according to Pareto dominance relationships. The first layer represents non-dominated solutions, the second layer represents solutions dominated by the first layer, and so on. For individuals in the same layer, crowding is calculated based on their distribution density in the objective space, prioritizing the retention of sparsely distributed individuals. Crowding calculation is based on the standard deviation of each objective function value or the distance between adjacent individuals. The specific implementation is as follows:

[0068] S41. Perform non-dominated ranking of the population to determine the dominance level (front) of each individual: Dominance relation: Solution: xi dominates xj if and only if f k (xi ) ≤ f k (x j ), and there exists at least one k such that f k (x i ) ≤ f k (x j ): According to the domination relationship, it is divided into multiple Pareto fronts {F1, F2,..., F l}, where F1 is the highest level (i.e., the front that is not dominated by any other individual).

[0069] S42. For each front, calculate the crowding distance of individuals to ensure population diversity: For each objective k, sort the individuals according to the objective values. Define the crowding degree of the boundary individuals as infinity. For the sorted individual i, the crowding distance di is:

[0070] The total crowding distance di is the sum of the crowding distances of all objectives:

[0071] Furthermore, in S5, selection, crossover, and mutation are performed, including the following steps:

[0072] S51. Selection operation: Use the crowding comparison operator for tournament selection. For two randomly selected individuals p and q, the selection rule is: If r(p) < r(q) or r(p) = r(q) and d(p) > d(q), select p, where r(p) and r(q) are the levels of non-dominated sorting, and d(p) and d(q) are the crowding distances.

[0073] S52. Crossover operation: Two-point crossover: Randomly select two crossover points and exchange the parental chromosome segments to ensure that the offspring meet the code rate constraint.

[0074] S53. Mutation operation: Bit flip mutation: Randomly flip a small number of genes (such as 1% of the bits), adjust the information bit index, and keep the code rate unchanged.

[0075] S54. Elite retention and iterative update: Merge the parental and offspring, merge the current population and the offspring to form a new population of size 2M.

[0076] S55. Non-dominated sorting and crowding degree screening: Retain the top M optimal individuals to enter the next generation.

[0077] S56. Termination condition: Reach the maximum number of iterations (such as 100 generations) or the Pareto front converges.

[0078] S57. Select typical individuals (the balance points with the lowest BER and the lowest FER) in the Pareto solution set and compare with the traditional polar code construction method.

[0079] S58. Verify the actual error correction capability and anti-interference effect of joint detection decoding through simulation.

[0080] Figure 2 The Pareto front plot of the genetic algorithm is shown when the noise standard deviation is 60. The algorithm selects a set of construction schemes with better performance. The selected set of codes can be applied to the construction of genetic algorithms under different requirements. Figure 3 The probability that the information bits determined by this algorithm will be incorrectly decoded during transmission was verified.

[0081] This invention presents a polar code construction system based on ReRAM channels. Based on Monte Carlo experiments, it obtains the bit error rate (BER) and actual coding rate for each construction scheme. A multi-objective optimization algorithm is used to sort and select the BER and actual coding rate for each individual in the population. Individuals with better fitness are preferentially selected for mutation, while those with poor fitness are crossovered, maximizing population diversity while achieving convergence as quickly as possible. Through iteration, the coding rate and BER of each individual in the population are optimized, selecting a better construction scheme that more accurately adapts to the specific characteristics of the ReRAM channel, maximizing the use of high-capacity channels to transmit information bits, and determining the optimal construction scheme based on the coding rate and BER corresponding to each construction method. This ensures that information bits are transmitted through the most reliable sub-channel while minimizing the BER, thereby improving signal transmission efficiency and quality.

[0082] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A Polar code optimization construction method suitable for ReRAM memory, characterized in that, include: ReRAM channel cells are represented using data matrices, readback signals of ReRAM channel cells are calculated, and ReRAM channels are constructed. Based on the characteristics of the ReRAM channel and the simulation results of full-pass and non-pass-pass paths, partial cell indices are determined for the positions in the entire array that can be correctly decoded every time and the positions that will be incorrectly decoded every time, and the population is initialized. Based on the preset initial population size, the bit error rate and the probability of a hidden path occurring for each population are obtained using the code length and code rate. The traditional genetic algorithm is improved by introducing a multi-objective optimization algorithm to perform non-dominated sorting and calculate crowding distance; Based on the improved genetic algorithm, the optimal information bit selection strategy in the uncertain channel of the ReRAM channel is found through continuous crossover and mutation, and the optimal construction result is obtained. Based on the preset initial population size, the bit error rate and the probability of a stealth path occurring for each population are obtained using the code length and code rate, including: Two optimization objectives are defined: one is to minimize the bit error rate, and the other is to maximize the proportion of 0s in the constrained encoded array. Determine the decision variables and obtain the information bit index set of the polar code; An initial population is generated. The channel units that are unreliable at the time of initialization are always set as frozen bits, and the channel units that are reliable are always set as information bits. The remaining uncertain units are selected as information bits or frozen bits according to the preset code rate and the reliability of each unit obtained by the original PW construction algorithm. For each individual, calculate the minimum bit error rate and the proportion of 0s in the array after constraint coding; For each individual in the population, generate random information bits, construct polar code encoding using the current information bits, transmit through the ReRAM channel model, add stealth path interference and Gaussian noise, decode using joint BP detection and SC decoding, and count the number of bit errors. The proportion of 0s and 1s in the constrained array mainly affects the probability of a hidden path occurring in the actual array.

2. The Polar code optimization construction method for ReRAM memory as described in claim 1, characterized in that, Population initialization includes: A random binary sequence is generated based on the preset polar code length and the constraint code adjustment parameters. The generated binary sequence is written sequentially to obtain the encoded data; The encoded data is detected and decoded through the full-pass ReRAM channel and the non-pass ReRAM channel respectively to obtain the indexes of the correct and incorrect decoded bits of the constructed scheme, and at the same time, the number of experiments is increased by one. When the number of experiments reaches the preset number of experiments, the Monte Carlo experiment is considered complete, and the correct decoding index and the incorrect decoding index obtained in each experiment are compared. Record the index of the position that was correctly decoded in each experiment and the index of the position that was incorrectly decoded in each experiment.

3. The Polar code optimization construction method for ReRAM memory as described in claim 1, characterized in that, Improving the traditional genetic algorithm by introducing a multi-objective optimization algorithm for non-dominated sorting and calculating crowding distance includes: The population is sorted into non-dominated categories to determine the dominance level of each individual. For each dominance level, individuals are ranked according to the target value, and the crowding distance of the ranked individuals is calculated.

4. The Polar code optimization construction method for ReRAM memory as described in claim 1, characterized in that, According to the improved genetic algorithm, by continuously crossing and mutating, find the optimal information bit selection strategy in the uncertain channels of the ReRAM channel, and the optimal construction results include: Use the crowding comparison operator for tournament selection. For two randomly selected individuals p and q, the selection rule is: if r(p) < r(q) or r(p) = r(q) and d(p) > d(q), select p, where r(p) and r(q) are the levels of non-dominated sorting, and d(p) and d(q) are the crowding distances; Two-point crossover: Randomly select two crossover points and exchange the chromosome segments of the parents to ensure that the offspring meet the code rate constraint; Bit-flip mutation: Randomly flip a small number of genes, adjust the information bit index, and keep the code rate unchanged; Merge the parents and offspring, merge the current population and the offspring to form a new population of size 2M; Retain the first M optimal individuals for the next generation; Reach the maximum number of iterations or the Pareto front converges; Select typical individuals from the Pareto solution set to obtain the optimal construction results.

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