Iterative decoding method and system of VT code without prior information in DNA storage and storage medium

Abstract

The application discloses a kind of DNA storage in prior information VT code iterative decoding method, system and storage medium, it is related to DNA storage technical field.The method is first obtained systematic code word sequence by VT code, generates noisy reception sequence by ID model simulation channel transmission;Again, joint grid chart is constructed and initialized, and soft information and bit decision information are obtained by completing SISO decoding calculation, and channel parameters are updated based on MAP drift tracking;After convergence by iterative control, multiple independent estimated code words are obtained, and finally original information sequence is recovered by multi-sequence majority voting fusion.The application constructs decoding-estimation closed-loop iteration framework, does not need prior channel parameters, can adaptively learn channel characteristics, capture error hot spot, improve decoding robustness by combining multi-sequence fusion, realize original data high reliability recovery, and promote DNA storage practicality.

Description

Technical Field

[0001] This application relates to the field of DNA storage technology, specifically to a method, system, and storage medium for iterative decoding of VT codes without prior information in DNA storage. Background Technology

[0002] Faced with the exponential growth of global data, existing silicon-based storage media (such as hard drives and flash memory) and magnetic tape storage are gradually approaching their physical limits and are facing bottlenecks such as short storage life, high maintenance costs, and huge energy consumption. Against this backdrop, deoxyribonucleic acid (DNA) molecules, as carriers of biological genetic information, are regarded as a revolutionary storage medium to cope with the future "data tsunami" due to their extraordinary storage density (theoretically reaching EB / gram), extremely long data retention period (up to thousands of years), and extremely low maintenance energy consumption.

[0003] A typical workflow for a DNA storage system encompasses a closed loop of digital-to-biological information conversion: First, the binary digital information is mapped and encoded into an A, T, C, G base sequence (encoding). Next, DNA molecular chains are artificially synthesized using chemical methods (synthesis). These molecules are then physically preserved (stored). When reading is needed, a high-throughput sequencer is used to obtain base sequence information (sequencing). Finally, the original binary data is recovered (decoded) using an algorithm.

[0004] However, unlike the relatively simple bit-flipping errors in electronic storage systems, DNA storage involves complex biochemical reactions during synthesis and sequencing, posing a significant challenge to reliable data recovery. In particular, due to the instability of enzymatic reactions, random insertions, deletions, and substitutions of bases are highly susceptible to occur in DNA sequences, collectively known as IDS errors. Insertion and deletion errors not only alter the base content but also cause changes in sequence length, resulting in severe synchronization loss at the receiving end. Even in mainstream second-generation sequencing technologies, the incidence of such synchronization errors remains significant, and in emerging third-generation sequencing technologies (such as nanopore sequencing), this rate reaches as high as 10%-25%.

[0005] To combat the complex synchronization errors mentioned above, error-correcting codes play a crucial role in DNA storage. Among them, Varshamov-Tenengolts (VT) codes have become the preferred coding scheme in this field due to their excellent insertion / deletion error correction capabilities and extremely low redundancy (asymptotically optimal). Currently, for the application of VT codes in DNA storage, a soft-input soft-output (SISO) decoding algorithm based on Trellis graphs can be used. This scheme uses the BCJR algorithm to perform forward and backward recursive calculations on the Trellis graph of the VT code for multiple noisy copies (reads) of the same original DNA strand, thereby obtaining the log-likelihood ratio (LLR) of each bit. The LLR values ​​from multiple copies are then directly summed to utilize diversity gain to improve the decoding success rate.

[0006] Although the SISO decoding scheme described above offers significant performance improvements over traditional hard-decision or majority-voting methods, it still has significant limitations in practical engineering applications. First, this scheme relies heavily on prior channel parameters, making it a "non-adaptive" system. It requires precise pre-input channel parameters (i.e., insertion and deletion probabilities) to construct the correct grid transition probabilities. However, in real DNA storage experiments, channel parameters are dynamically affected by the state of the synthesis instrument, reagent activity, and sequencing environment, making them unknown and fluctuating. If the preset parameters do not match the actual channels, the decoder's performance will deteriorate drastically. Second, this scheme struggles to handle non-uniform error distributions, typically assuming a uniform error rate across the entire DNA strand. However, in reality, due to the influence of specific sequence motifs on enzyme activity, unknown "error hotspots" often exist on the DNA strand—that is, insertion or deletion probabilities at certain specific sites are much higher than the average. Existing fixed-parameter decoders cannot detect and handle such position-specific non-uniform errors, leading to decoding failures at these critical sites. Finally, existing solutions lack self-learning capabilities and cannot use the received data itself to correct the channel model in reverse. This results in a waste of a large amount of statistical information (such as drift path distribution) contained in the noisy replicas, and fails to form a virtuous cycle of "decoding assists estimation, and estimation feeds back into decoding".

[0007] In summary, existing technologies struggle to guarantee reliable data recovery when precise prior channel information is lacking or when dealing with complex, non-uniform channels. Therefore, developing an iterative decoding method that requires no prior parameters and can adaptively learn channel characteristics is crucial for advancing the practical application of DNA storage. Summary of the Invention

[0008] To address the problem that existing DNA data storage and decoding technologies rely heavily on precise prior channel parameters (such as insertion and deletion probabilities) in soft-input soft-output SISO decoding algorithms, which are often unknown and non-uniformly distributed (e.g., error hotspots) in practical applications, leading to degraded decoding performance or even failure, this invention provides a VT code iterative decoding method, system, and storage medium for DNA storage without prior information. This scheme is a VT code iterative learning decoding method based on the expectation-maximization (EM) algorithm that does not require prior channel information. It can adaptively estimate channel parameters during the decoding process, breaking the circular dependency between parameter estimation and data decoding. Thus, it can achieve highly reliable recovery of the original data even when the channel parameters are unknown or there is a complex non-uniform error distribution.

[0009] To achieve the objectives of this invention, the technical solution provided by this invention is as follows: First aspect This invention provides an iterative decoding method for VT codes in DNA storage without prior information, comprising the following: Step 1: Channel coding based on VT codes: Based on the original binary information sequence u of length k, obtain the systematic VT codeword sequence v of length n; Step 2: Channel transmission simulation based on the ID model: based on the encoded codeword sequence v and the preset channel insertion probability p i And the deletion probability p d This yields a noisy received sequence r of length N; Step 3: Joint Mesh Graph Construction and Initialization: Based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d] min , d max This yields the initialized joint mesh graph structure; Step 4: Soft-input soft-output SISO decoding calculation: based on the received sequence r and the current channel parameter estimate. By combining the mesh graph structure, we obtain the intermediate soft information statistics α, β, γ and the bit decision information of the current iteration round; Step 5: Parameter estimation based on MAP drift tracking: based on intermediate soft information statistics α, β, γ The updated channel parameter estimates are obtained. , ; Step 6: Iterative control and convergence decision: Through iterative optimization, the parameter estimates are made to approximate the true values, resulting in C estimated codewords after independent decoding; Step 7: Multi-sequence majority voting fusion: Based on the estimated codeword set after C independent decodings This yields the final recovered sequence of original information.

[0010] Further, step 1 includes the following: Step 1.1: Determine the codeword length: Based on the input length k, calculate the length n of the encoded codeword, which must satisfy the relationship n = k + ... log2n +1; Step 1.2: Position Allocation: Generate an empty sequence of length n, mark the positions with indices that are powers of 2 and the last position as check bits, and fill the remaining positions with the input information sequence u in order; Step 1.3: Constraint Calculation: Calculate the specific value of the check bit such that the final generated codeword sequence v = (v1, v2, …, v n It satisfies the following congruence equation: , where a is a preset check constant.

[0011] Further, step 2 includes the following: For each symbol x to be transmitted in the codeword sequence v k The channel undergoes state transitions according to the following mutually exclusive probabilities: Insertion event, based on probability p i : Add a randomly generated base symbol to the end of the output sequence at the receiving end. The original symbol x k The pointer remains stationary and does not move; the next moment, the transmission of x will continue. k ; Deletion event, based on probability p d : Current original symbol x k If lost and unable to reach the receiver, the channel pointer moves directly to the next symbol x. k+1 ; Correctly transmitted events, based on probability 1 - p i - p d Original symbol x k Transmitted to the receiving end, the channel pointer moves to the next symbol x. k+1 .

[0012] A noisy received sequence r of length N is obtained.

[0013] Further, step 3 includes the following: Based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d] min , d max ].

[0014] Define the state at time t as σ t = (d t , s t ),in: d tIn drift state: cumulative insertions - cumulative deletions; s t For the accompanying state: the current VT checksum; Initialization: Fix the initial state of the mesh graph to σ0 = (0, 0); The initialized joint mesh graph structure is obtained.

[0015] Further, step 4 includes the following: Based on the received sequence r and the current channel parameter estimate Calculations are performed using the combined mesh graph structure: (1) Calculate the branching metric γ t Calculate the probability based on the drift change Δd during state transition: Δd = -1 (delete) → ; Δd = 0 (normal) → 1 - - ; Δd = 1 (insertion) → ; (2) Forward and backward recursion: Using the BCJR algorithm, calculate the forward metric α. t (σ) and backward metric β t (σ); (3) Calculate LLR: Calculate the t-th bit v using α, γ, and β. t The log-likelihood ratio is less than that of LLR; We obtain the intermediate soft information statistics α, β, γ, and the bit decision information for the current iteration round.

[0016] Further, step 5 includes the following: based on the soft information statistics α, β, γ, the following processing is performed: E-step maximum a posteriori drift estimation: Marginalize the adjoint state s and calculate the most likely drift state at each time t. Restore the MAP drift path; Statistical error: Observing drift path differences ; →Delete event, delete count Add 1; → Insertion event, insertion count Add 1; M-step parameter update: using a damped update strategy. (Observation frequency for this study), where λ is the preset learning rate; Obtain the updated channel parameter estimates , .

[0017] Further, step 6 includes the following: through iterative optimization, the parameter estimate is made to approximate the true value; Determine whether the maximum number of iterations has been reached, or whether the parameter change is less than the convergence threshold; If convergence fails, feed the new parameters back to step 4 and perform SISO decoding again. Convergence achieved → Output the final estimated codeword of the current sequence.

[0018] Further, step 7 includes the following: Based on the estimated codeword set after C independent decodings ; Perform a bit-by-bit vertical comparison of all estimated codewords; For the t-th bit position: count the number of times that position is 1 in C codewords; If the quantity is greater than C / 2, the final decision is 1. Otherwise → the final decision is 0; The original information sequence is finally recovered.

[0019] Second aspect This invention provides an iterative decoding system for VT codes in DNA storage without prior information, comprising: a channel coding unit, an information transmission simulation unit, a joint mesh graph initialization unit, a decoding calculation unit, a parameter estimation unit, an iteration unit, and a fusion unit; The channel coding unit is used for channel coding based on VT codes: based on the original binary information sequence u of length k, a systematic VT codeword sequence v of length n is obtained; The information transmission simulation unit is used for channel transmission simulation based on the ID model: based on the encoded codeword sequence v and the preset channel insertion probability p. i And the deletion probability p d This yields a noisy received sequence r of length N; The joint mesh graph initialization unit is used for joint mesh graph construction and initialization: based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d]. min , d max This yields the initialized joint mesh graph structure; The decoding calculation unit is used for soft-input soft-output SISO decoding calculation: based on the received sequence r and the current channel parameter estimate. By combining the mesh graph structure, we obtain the intermediate soft information statistics α, β, γ and the bit decision information of the current iteration round; The parameter estimation value is obtained as a unit for parameter estimation based on MAP drift tracking: based on intermediate soft information statistics α, β, γ. The updated channel parameter estimates are obtained. , ; The iterative unit is used for iterative control and convergence decision: through iterative optimization, the parameter estimate is made close to the true value, and C estimated codewords after independent decoding are obtained; The fusion unit is used for multi-sequence majority voting fusion: based on the estimated codeword set after C independent decodings. This yields the final recovered sequence of original information.

[0020] Third aspect This invention provides a storage medium storing at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the aforementioned method for iterative decoding of VT codes without prior information in DNA storage.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: To achieve a balance between high storage density, compliance with biochemical constraints, and low decoding complexity, this invention proposes a quaternary biochemical constraint coding method based on entropy coding and rotation coding. Unlike Goldman's ternary tree structure, this scheme innovatively constructs a joint coding mechanism of quaternary entropy coding and dynamic rotation coding. In the entropy coding stage, quaternary tANS coding is introduced, utilizing a state transition mechanism to overcome the Shannon limit and achieve efficient arithmetic compression for long symbol sequences. The input data stream is mapped to a quaternary sequence of 0, 1, 2, 3 numbers, and tANS coding achieves higher compression density through continuous approximation of the probability distribution. Next, a mapping is established between the quaternary sequence and the biochemically compliant DNA sequence, ensuring that the generated DNA sequence meets CG content constraints and homopolymer length constraints, and can avoid specific sequences. Attached Figure Description

[0022] Figure 1 This is a graph showing the change in bit error rate in the test examples of this invention; Figure 1 In Chinese, "Iterative" means iterative; "Oracle" means known parameters. Figure 2 This is a parameter estimation graph from a test example of the present invention; Figure 2 In the middle, est. pd : Estimate the probability of deletion; true pd : Actual deletion probability; est. pi : Estimate the insertion probability; true pi True insertion probability; Figure 3 This is a graph showing the variation of bit error rate in multi-sequence decoding in the test examples of this invention; Figure 3 In Chinese, "Theoretical" refers to the theoretical value, and "Real" refers to the experimental value. Figure 4 This is a learning graph of non-uniform channel parameters in the test example of this invention; Figure 4 In the code, est.pd: estimated deletion probability; true pd: actual deletion probability; est.pi: estimated insertion probability; true pi: actual insertion probability. Detailed Implementation

[0023] 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 the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0024] To address the shortcomings of existing technologies, such as poor decoding performance under unknown or fluctuating parameter environments due to over-reliance on prior channel parameters and lack of adaptive correction capabilities using the data itself, the present invention aims to provide an adaptive estimation and iterative decoding method for DNA storage channel parameters based on the EM algorithm.

[0025] By introducing the Expectation-Maximization (EM) algorithm framework, the unknown insertion and deletion probabilities are treated as latent variables to be estimated, constructing a closed-loop iterative mechanism of "SISO decoding (E-step)" and "parameter update (M-step)". The soft a posteriori probability of the synchronization drift path output by the SISO decoder is used to backward statistically analyze the channel parameters, thereby breaking the deadlock of dependency between parameter estimation and data decoding. Ultimately, even with completely unknown channel parameters, the system can adaptively learn channel characteristics, gradually reducing the bit error rate with iteration, and achieving decoding performance close to the ideal situation (known parameters).

[0026] This invention provides an encoding and iterative decoding method for insertion / deletion (ID) channels in DNA storage. The overall process includes channel encoding and channel transmission simulation at the transmitting end, and iterative decoding and multi-sequence fusion based on parameter adaptive learning at the receiving end. Specific implementation steps are as follows: Step 1: Channel coding based on VT codes Construct a codeword structure with error detection and correction capabilities to combat synchronization errors (insertion / deletion).

[0027] Based on the original binary information sequence u of length k.

[0028] Processing procedure: (1) Determine the code length: Based on the input length k, calculate the length n of the encoded codeword, which must satisfy the relationship n = k + log2n +1; (2) Position allocation: Generate an empty sequence of length n, mark the positions with index powers of 2 (i.e., 1, 2, 4, 8, ...) and the last position (i.e., position n) as check bits, and fill the remaining positions with the input information sequence u in order.

[0029] (3) Constraint calculation: Calculate the specific value of the check bit so that the final generated codeword v = (v1, v2, ..., v n It satisfies the following congruence equation: ; where a is a preset check constant (e.g., a = 0).

[0030] A systematic VT codeword sequence v of length n is obtained.

[0031] Step 2: Channel transmission simulation based on the ID model Simulate random insertion / deletion errors in a DNA storage environment to generate observation data at the receiving end.

[0032] Based on the encoded codeword sequence v (i.e., the symbol x to be transmitted), the preset channel insertion probability p i And the deletion probability p d .

[0033] Processing procedure: For each symbol x to be transmitted in the sequence k The channel undergoes state transitions according to the following mutually exclusive probabilities: Insertion event (probability p) i ): Add a randomly generated base symbol to the end of the output sequence at the receiving end. The original symbol x k Remain stationary, pointer does not move (the next moment will attempt to transfer x). k ); Deletion event (probability p) d ): Current original symbol x k If lost and unable to reach the receiver, the channel pointer moves directly to the next symbol x. k+1 ; Correct transmission event (probability 1 - p) i - p d ): Original symbol x k Transmitted to the receiving end, the channel pointer moves to the next symbol x. k+1.

[0034] It should be noted that, due to the randomness of insertion and deletion, the length N of the received sequence is not necessarily equal to the length n of the transmitted sequence.

[0035] Obtain a noisy received sequence r of length N (in a multi-replica scenario, repeat this step to generate C received sequences).

[0036] Step 3: Joint Trellis Construction and Initialization A mathematical model for the decoder is established to simultaneously track channel drift and codeword verification status.

[0037] Based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d] min , d max ].

[0038] Processing procedure: Define the state at time t as σ t = (d t , s t ),in: d t This is a drift state (cumulative insertion count - cumulative deletion count); s t For the accompanying state (the current VT checksum); Initialization: Fix the initial state of the mesh graph to σ0 = (0, 0).

[0039] The initialized joint mesh graph structure is obtained.

[0040] Step 4: Soft-Input Soft-Output (SISO) Decoding Calculation Calculate the probability of all paths and bit soft information under the current channel parameter estimates.

[0041] Based on the received sequence r, the current channel parameter estimate is... Based on the combined mesh graph structure, the following processing is performed: (1) Calculate the branching metric γ t Calculate the probability based on the drift change Δd during state transition: Δd = -1 (delete) → ; Δd = 0 (normal) → 1 - - ; Δd = 1 (insertion) → ; (2) Forward and backward recursion: Using the BCJR algorithm, calculate the forward metric α. t (σ) and backward metric βt (σ); (3) Calculate LLR: Calculate the t-th bit v using α, γ, and β. t Log-likelihood ratio (LLR).

[0042] The intermediate soft information statistics (α, β, γ) and the bit decision information of the current iteration round are obtained.

[0043] Step 5: Parameter estimation based on MAP drift tracking (E-step and M-step): Use soft information to infer the number of channel errors and update the channel parameters.

[0044] Based on the soft information statistics and other data output from step 4, the following calculations are performed: E-step (maximum a posteriori drift estimation): Marginalize the adjoint state s and calculate the most likely drift state at each time t. Restore the MAP drift path; Statistical error: Observing drift path differences ; →Delete event, delete count Add 1; → Insertion event, insertion count Add 1; M-step (parameter update): Employing a damped update strategy: (Observation frequency for this study), where λ is the preset learning rate; Obtain the updated channel parameter estimates , .

[0045] Step 6: Iterative control and convergence decision: Through iterative optimization, the parameter estimates are made to approximate the true values.

[0046] The processing procedure is as follows: Determine whether the maximum number of iterations has been reached, or whether the parameter change is less than the convergence threshold.

[0047] If convergence fails, feed the new parameters back to step 4 and perform SISO decoding again. Convergence achieved → Output the final estimated codewords of the current sequence; The independent estimated codewords for this received sequence are obtained.

[0048] Step 7: Multi-sequence majority voting fusion: Utilize the redundancy of multiple replicas to eliminate residual random errors.

[0049] Based on the estimated codeword set after C independent decodings The following processing procedure is performed: all estimated codewords are compared bit-by-bit vertically. For the t-th bit position: count the number of times this position is 1 in the C codewords; if the number > C / 2 → the final decision is 1, otherwise → the final decision is 0, thus obtaining the finally recovered original information sequence.

[0050] In the above steps, steps 1 to 2: data generation and channel distortion process, defining the problem input.

[0051] Steps 3 to 6: The core single-sequence iterative decoder (closed-loop adaptive learning system) decodes → counts errors → updates parameters → decodes again in an iterative process, adaptively learning channel parameters to obtain high-precision single-sequence decoding. Step 7: Multi-sequence fusion stage, based on the absence of systematic bias in the single sequence, utilizes majority voting to efficiently filter out residual random noise, obtaining the final reliable result.

[0052] This invention proposes a priori-information-free iterative learning decoding algorithm for DNA storage, specifically for single-sequence decoding of Varshamov-Tenengolts (VT) codes. Addressing the issue of unknown and dynamically fluctuating channel parameters in practical DNA storage, a closed-loop iterative framework based on the expectation-maximization (EM) algorithm is constructed. This framework utilizes the posterior probability of drift paths generated on a joint trellis graph by a soft-input soft-output (SISO) decoder to infer and update the insertion and deletion probabilities of the channel, thus breaking the dependence of traditional SISO decoding on prior channel parameters. Furthermore, for non-uniform channels, a position-specific learning mechanism is introduced, enabling the algorithm to adaptively capture local error hotspots in the DNA sequence. Additionally, a robust multi-sequence decoding strategy based on "independent learning followed by fusion decision" is proposed. For high-coverage-depth data generated by DNA sequencing, traditional methods such as direct hard voting or fixed-parameter soft merging are abandoned. Instead, each received sequence independently and adaptively learns its specific channel parameters using the aforementioned iterative algorithm. By correcting local parameter mismatches in each sequence, systematic decoding biases are eliminated. Based on this, a position-by-position majority voting is performed, effectively utilizing the diversity gain of multiple sequences and significantly improving the decoding robustness under complex channel conditions. A series of experiments were conducted on simulated datasets with different code lengths, different coverage depths, and error hotspots to verify the convergence and effectiveness of the proposed method without prior information.

[0053] To verify the effectiveness and robustness of the proposed iterative learning decoding method without prior information, a DNA storage simulation platform was constructed, and comprehensive tests were conducted on decoding performance under different code lengths, coverage depths, and non-uniform channel conditions. Unless otherwise specified, all initial channel parameters in the experiments adopted a blind initialization strategy (i.e., assuming no prior knowledge is required), and the initial values ​​were set to... .

[0054] 1. Performance verification of single-sequence adaptive decoding.

[0055] This experiment aims to evaluate the algorithm's parameter learning ability and error correction performance with only one received sequence (C=1). Two different VT codes of varying lengths were used: N=68 (corresponding to K=60 information bits) and N=98 (corresponding to K=90 information bits). The actual channel parameters were set as follows. .

[0056] 1.1 Bit Error Rate (BER) Convergence Performance like Figure 1 As shown, the curves illustrate how the decoding bit error rate (BER) changes as the number of iterations increases.

[0057] Initial stage: Due to the use of initial parameters that deviate significantly from the true values, the BER of the first iteration is relatively high.

[0058] Convergence process: As the iteration proceeds, the EM algorithm of this invention quickly corrects the parameter estimates, and the BER shows a significant downward trend.

[0059] Final result: After only about 7 iterations, the decoding performance converged to a level that essentially coincided with the "oracle-aided" baseline (i.e., the theoretical lower bound assuming perfect channel parameters are known) for both codewords with N=68 and N=98. This strongly demonstrates that the algorithm can adaptively achieve optimal decoding performance in completely unknown channel environments.

[0060] 1.2 Parameter Estimation Trajectory like Figure 2 As shown, the trajectory of the estimated channel parameters (insertion probability and deletion probability) with the number of iterations is illustrated in detail in the scenario of a relatively long codeword N=98.

[0061] Experimental results: Although the initial estimate (0.2) was much higher than the true value, the algorithm was able to quickly capture the drift statistics in the received sequence. After several iterations, the estimate converged precisely to the true channel parameters ( ).

[0062] Technical results: The results confirm that the soft EM estimation algorithm based on MAP drift tracking proposed in this invention has strong robustness, can accurately extract channel statistical information from a single noisy sequence, and is insensitive to code length changes.

[0063] 2. Performance verification of multi-sequence fusion decoding For the common multiple reads scenario in DNA storage, this experiment evaluates the effect of different coverage depths (Cluster Size, C) on decoding performance. The experimental setup uses a coverage depth C ∈ {1, 3, 5}. Assume that each sequence is transmitted through an independent insertion / deletion channel.

[0064] like Figure 3 As shown, this illustrates different total error rates. Decoding BER curves under different coverage depths.

[0065] Experimental results: Compared with single-sequence decoding (C=1), the introduction of a multi-sequence fusion strategy significantly reduces the bit error rate. Specifically, when the coverage depth increases to C=3, the decoder can effectively utilize diversity gain to correct ambiguous synchronization errors in a single sequence, resulting in a significant performance improvement.

[0066] Beneficial effects: Experimental data show that the "independent learning first, then majority voting" strategy proposed in this invention can efficiently utilize the redundancy of DNA sequencing data. Highly reliable data recovery can be achieved with only extremely low coverage depth (e.g., C=3 or 5), which is of great significance for reducing the sequencing cost of DNA storage.

[0067] 3. Robustness verification under non-uniform channels (error hotspots) To verify the algorithm's ability to handle complex channels in real biochemical reactions, this experiment simulated a non-stationary channel environment, which introduced an extremely high insertion / deletion error rate (called "mutation points" or "error hotspots") at specific positions of codewords to simulate local defects or homopolymer regions in DNA sequences.

[0068] like Figure 4 As shown, the decoding performance and the learning results of the location-related parameters under this non-uniform channel condition are presented.

[0069] Experimental Results: The position-dependent SISO decoder proposed in this invention successfully identified high-error-rate regions in the sequence. Unlike traditional methods that assume a uniform error rate, this algorithm automatically increases the error probability estimate of the mutation point location during the iteration process.

[0070] Technical Effects: This adaptive mechanism enables the decoder to appropriately weight metrics near abrupt change points when calculating the grid path, effectively preventing the spread of severe local errors to surrounding areas (i.e., preventing error propagation). Experiments demonstrate that even in the presence of severe local interference, this invention maintains robust decoding capabilities.

[0071] In addition, the present invention provides an iterative decoding system for VT codes without prior information in DNA storage, comprising: a channel coding unit, an information transmission simulation unit, a joint mesh graph initialization unit, a decoding calculation unit, a parameter estimation value acquisition unit, an iteration unit, and a fusion unit; The channel coding unit is used for channel coding based on VT codes: based on the original binary information sequence u of length k, a systematic VT codeword sequence v of length n is obtained; The information transmission simulation unit is used for channel transmission simulation based on the ID model: based on the encoded codeword sequence v and the preset channel insertion probability p. i And the deletion probability p d This yields a noisy received sequence r of length N; The joint mesh graph initialization unit is used for joint mesh graph construction and initialization: based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d]. min , d max This yields the initialized joint mesh graph structure; The decoding calculation unit is used for soft-input soft-output SISO decoding calculation: based on the received sequence r and the current channel parameter estimate. By combining the mesh graph structure, we obtain the intermediate soft information statistics α, β, γ and the bit decision information of the current iteration round; The parameter estimation value is obtained as a unit for parameter estimation based on MAP drift tracking: based on intermediate soft information statistics α, β, γ. The updated channel parameter estimates are obtained. , ; The iterative unit is used for iterative control and convergence decision: through iterative optimization, the parameter estimate is made close to the true value, and C estimated codewords after independent decoding are obtained; The fusion unit is used for multi-sequence majority voting fusion: based on the estimated codeword set after C independent decodings. This yields the final recovered sequence of original information.

[0072] In addition, the present invention provides a storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the aforementioned method for iterative decoding of VT codes without prior information in DNA storage.

[0073] Finally, it should be noted that the above embodiments are merely illustrative and explanatory of the present invention, and are not intended to limit the present invention to the scope of the described embodiments. Furthermore, those skilled in the art will understand that the present invention is not limited to the above embodiments, and many more variations and modifications can be made based on the teachings of the present invention, all of which fall within the scope of protection claimed by the present invention.

Claims

1. A method for iterative decoding of VT codes without prior information in DNA storage, characterized in that, Including the following: Step 1: Channel coding based on VT codes: Based on the original binary information sequence u of length k, obtain the systematic VT codeword sequence v of length n; Step 2: Channel transmission simulation based on the ID model: based on the encoded codeword sequence v and the preset channel insertion probability p i And the deletion probability p d This yields a noisy received sequence r of length N; Step 3: Joint Mesh Graph Construction and Initialization: Based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d] min , d max This yields the initialized joint mesh graph structure; Step 4: Soft-input soft-output SISO decoding calculation: based on the received sequence r and the current channel parameter estimate. By combining the mesh graph structure, we obtain the intermediate soft information statistics α, β, γ and the bit decision information of the current iteration round; Step 5: Parameter estimation based on MAP drift tracking: Based on the intermediate soft information statistics α, β, γ, the updated channel parameter estimates are obtained. , ; Step 6: Iterative control and convergence decision: Through iterative optimization, the parameter estimates are made to approximate the true values, resulting in C estimated codewords after independent decoding; Step 7: Multi-sequence majority voting fusion: Based on the estimated codeword set after C independent decodings This yields the final recovered sequence of original information.

2. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 1, characterized in that, Step 1 includes the following: Step 1.1: Determine the codeword length: Based on the input length k, calculate the length n of the encoded codeword, which must satisfy the relationship n = k + log2 n +1; Step 1.2: Position Allocation: Generate an empty sequence of length n, mark the positions with indices that are powers of 2 and the last position as check bits, and fill the remaining positions with the input information sequence u in order; Step 1.3: Constraint Calculation: Calculate the specific value of the check bit such that the final generated codeword sequence v = (v1, v2, …, v n It satisfies the following congruence equation: , where a is a preset check constant.

3. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 2, characterized in that, Step 2 includes the following: For each symbol x to be transmitted in the codeword sequence v k The channel undergoes state transitions according to the following mutually exclusive probabilities: Insertion event, based on probability p i : Add a randomly generated base symbol to the end of the output sequence at the receiving end. The original symbol x k The pointer remains stationary and does not move; the next moment, the transmission of x will continue. k ; Deletion event, based on probability p d : Current original symbol x k If lost and unable to reach the receiver, the channel pointer moves directly to the next symbol x. k+1 ; Correctly transmitted events, based on probability 1 - p i - p d Original symbol x k Transmitted to the receiving end, the channel pointer moves to the next symbol x. k+1 . A noisy received sequence r of length N is obtained.

4. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 3, characterized in that, Step 3 includes the following: Based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d] min , d max ]. Define the state at time t as σ t = (d t , s t ),in: d t In drift state: cumulative insertions - cumulative deletions; s t For the accompanying state: the current VT checksum; Initialization: Fix the initial state of the mesh graph to σ0 = (0, 0); The initialized joint mesh graph structure is obtained.

5. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 4, characterized in that, Step 4 includes the following: Based on the received sequence r and the current channel parameter estimate Calculations are performed using the combined mesh graph structure: (1) Calculate the branching metric γ t Calculate the probability based on the drift change Δd during state transition: Δd = -1 (delete) → ; Δd = 0 (normal) → 1 - - ; Δd = 1 (insertion) → ; (2) Forward and backward recursion: Using the BCJR algorithm, calculate the forward metric α. t (σ) and backward metric β t (σ); (3) Calculate LLR: Calculate the t-th bit v using α, γ, and β. t The log-likelihood ratio is less than that of LLR; We obtain the intermediate soft information statistics α, β, γ, and the bit decision information for the current iteration round.

6. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 5, characterized in that, Step 5 includes the following: Based on the soft information statistics α, β, γ, the following processing is performed: E-step maximum a posteriori drift estimation: Marginalize the adjoint state s and calculate the most likely drift state at each time t. Restore the MAP drift path; Statistical error: Observing drift path differences ; →Delete event, delete count Add 1; → Insertion event, insertion count Add 1; M-step parameter update: using a damped update strategy. (Observation frequency for this study), where λ is the preset learning rate; Obtain the updated channel parameter estimates , .

7. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 6, characterized in that, Step 6 includes the following: Through iterative optimization, the parameter estimates are made to approximate the true values; Determine whether the maximum number of iterations has been reached, or whether the parameter change is less than the convergence threshold; If convergence fails, feed the new parameters back to step 4 and perform SISO decoding again. Convergence achieved → Output the final estimated codeword of the current sequence.

8. The method for iterative decoding of VT codes without prior information in DNA storage according to claim 7, characterized in that, Step 7 includes the following: Based on the estimated codeword set after C independent decodings ; Perform a bit-by-bit vertical comparison of all estimated codewords; For the t-th bit position: count the number of times that position is 1 in C codewords; If the quantity is greater than C / 2, the final decision is 1. Otherwise → the final decision is 0; The original information sequence is finally recovered.

9. A VT code iterative decoding system for DNA storage without prior information, characterized in that, It includes the following: channel coding unit, information transmission simulation unit, joint mesh graph initialization unit, decoding calculation unit, parameter estimation unit, iteration unit, and fusion unit; The channel coding unit is used for channel coding based on VT codes: based on the original binary information sequence u of length k, a systematic VT codeword sequence v of length n is obtained; The information transmission simulation unit is used for channel transmission simulation based on the ID model: based on the encoded codeword sequence v and the preset channel insertion probability p. i And the deletion probability p d This yields a noisy received sequence r of length N; The joint mesh graph initialization unit is used for joint mesh graph construction and initialization: based on the received sequence length N, the transmitted codeword length n, and the preset drift window range [d]. min , d max This yields the initialized joint mesh graph structure; The decoding calculation unit is used for soft-input soft-output SISO decoding calculation: based on the received sequence r and the current channel parameter estimate. By combining the mesh graph structure, we obtain the intermediate soft information statistics α, β, γ and the bit decision information of the current iteration round; The parameter estimation unit is used for parameter estimation based on MAP drift tracking: based on intermediate soft information statistics α, β, γ, it obtains updated channel parameter estimates. , ; The iterative unit is used for iterative control and convergence decision: through iterative optimization, the parameter estimate is made close to the true value, and C estimated codewords after independent decoding are obtained; The fusion unit is used for multi-sequence majority voting fusion: based on the estimated codeword set after C independent decodings. This yields the final recovered sequence of original information.

10. A storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or instruction set is loaded and executed by a processor to implement a method for iterative decoding of VT codes without prior information in DNA storage as described in any one of claims 1-8.

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