Direct transpose coding method for DNA data storage and related device

Abstract

The invention discloses a direct transpose coding method for DNA data storage and a related device. According to the method and the device, a first coding mode is entered under a low-bit-rate coding requirement, and synchronization and replacement errors are effectively corrected based on a matrix transposition frame and by taking a mark sequence as a synchronization reference point; and entering a second coding mode under the requirement of high code rate, realizing a synchronous anchoring function based on a matrix transpose frame and under the condition of not introducing an explicit mark, improving the storage density and the coding efficiency, and realizing conversion and correction from a synchronous error to a replacement error, thereby improving the DNA storage effect.

Description

Technical Field

[0001] This invention relates to the field of information storage technology, and in particular to a direct transposition encoding method and related apparatus for DNA data storage. Background Technology

[0002] With the rapid development of technologies such as big data, artificial intelligence, and the Internet of Things, the global data volume is exploding, posing unprecedented challenges to data storage capacity, durability, and energy consumption. Traditional magnetoelectric storage media (such as hard drives and flash memory) exhibit numerous bottlenecks when faced with storage demands at the zettabyte and even yottabyte levels: these include difficulties in physical expansion, large footprint, data loss due to physical damage or hardware aging, and the enormous environmental pressure brought about by the production of hundreds of millions of storage units annually. DNA, as a natural information storage medium, demonstrates enormous potential in the field of data storage due to its superior physical and chemical properties. Its most significant advantage lies in its extremely high storage density, far exceeding the capacity limits of traditional hard drives or flash memory. Simultaneously, DNA molecules possess remarkable stability, capable of being preserved for hundreds or even thousands of years under appropriate conditions, and consume very little energy, requiring only a basic biochemical environment to maintain data integrity. Furthermore, DNA storage also possesses security characteristics such as resistance to electromagnetic interference, tamper resistance, and natural encryption, making it considered an ideal solution to address the challenges of traditional storage media in terms of scalability, space occupation, and sustainability.

[0003] However, DNA storage systems involve complex biochemical processes such as DNA synthesis, PCR amplification, and high-throughput sequencing during actual storage. These processes introduce various types of errors, severely impacting data integrity and recoverability. Specifically, DNA storage faces three main types of errors: base insertion, deletion, and substitution. Insertion and deletion errors cause changes in sequence length, leading to phase shifts in all subsequent data and preventing accurate correspondence between the original information and the read sequence. Substitution errors directly alter the chemical properties of individual bases, similar to symbol errors in traditional communication, resulting in direct information distortion. These errors originate from chemical side reactions during DNA synthesis, replication errors during PCR amplification, and inherent recognition errors in high-throughput sequencing platforms. Faced with these complex and unavoidable sources of error, specialized error-correcting coding techniques must be introduced to ensure reliable data recovery. Current error-correcting coding schemes for DNA storage, such as Reed-Solomon (RS) codes and low-density parity-check codes (LDPC), can effectively correct substitution errors, but their ability to correct synchronization errors (i.e., insertion and deletion errors) is limited, resulting in poor DNA storage performance. Summary of the Invention

[0004] This invention provides a direct transpose encoding method and related apparatus for DNA data storage, which addresses the technical problem that existing error-correcting code encoding schemes for DNA storage have limited synchronous correction capabilities, resulting in poor DNA storage performance.

[0005] This invention provides a direct transposition encoding method for DNA data storage, the method comprising: Obtain the encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements; In the first encoding mode, multiple input information bit sequences are encoded and transposed to obtain a first transpose matrix; a marker sequence is inserted into the first transpose matrix to obtain a marker enhancement matrix, which is then mapped to a first DNA sequence matrix; the first DNA sequence matrix is ​​passed through a DNA channel to obtain a first received sequence matrix; based on the marker sequence, the first received sequence matrix is ​​synchronously decoded, and the successfully decoded bit sequence is used as a first synchronization anchor; the first synchronization anchor assists other sequences in the first received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences; In the second encoding mode, the multiple input information bit sequences are divided into low-information bit sequence groups and high-information bit sequence groups. The low-information bit sequence groups are encoded at a low code rate, and the high-information bit sequence groups are encoded at a high code rate, respectively, and combined to obtain a combination matrix. The combination matrix is ​​transposed to obtain a second transposed matrix, which is then mapped to a second DNA sequence matrix. The second DNA sequence matrix is ​​passed through a DNA channel to obtain a second received sequence matrix. The second received sequence matrix is ​​decoded at a low code rate, and the successfully decoded low-code-rate bit sequences are used as second synchronization anchors. The second synchronization anchors are used to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

[0006] Optionally, the step of encoding and transposing multiple input information bit sequences to obtain a first transpose matrix; inserting a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and mapping it to a first DNA sequence matrix includes: The multiple input information bit sequences are encoded by an LDPC encoder to obtain multiple codeword sequences and form a codeword matrix; the codeword matrix is ​​then transposed to obtain a first transpose matrix. According to the preset first sequence insertion period, insert each of the first transpose matrix... Insert after the codeword sequence The label sequence is used to obtain a label enhancement matrix; the label enhancement matrix is ​​then mapped to DNA to obtain a first DNA sequence matrix; The formula for calculating the number of columns in the marker enhancement matrix is ​​as follows:

[0007] In the formula: To indicate the number of columns in the augmentation matrix; The sequence number of the input information bit sequence; The number of consecutive codeword sequences within each preset first sequence insertion period in the first transpose matrix; The number of marker sequences inserted for each preset first sequence insertion period.

[0008] Optionally, the step of dividing the multiple input information bit sequences into low-information bit sequence groups and high-information bit sequence groups, performing low-rate encoding on the low-information bit sequence groups and high-rate encoding on the high-information bit sequence groups respectively, and combining them to obtain a combination matrix includes: The multiple input information bit sequences are divided into a low information bit sequence group and a high information bit sequence group; The low-information bit sequence group is encoded at a low code rate using a low-code-rate LDPC encoder to obtain multiple low-code-rate codeword sequences; the high-information bit sequence group is encoded at a high code rate using a high-code-rate LDPC encoder to obtain multiple high-code-rate codeword sequences. According to the preset second sequence insertion period, the low code rate code word sequence is inserted after each high code rate code word sequence in the row direction arrangement to obtain a combination matrix.

[0009] Optionally, the step of synchronously decoding the first received sequence matrix based on the tag sequence and using the successfully decoded bit sequence as the first synchronization anchor point includes: Based on the position and base symbol of the labeled sequence, the transmission symbol probability at the corresponding position in the first received sequence matrix is ​​initialized, and the corresponding transition probability is calculated. Based on the insertion, deletion and replacement error probability model of DNA channel, forward recursion and backward recursion calculations are performed on each received sequence in the first received sequence matrix according to the transition probability to obtain the forward coefficient and backward coefficient of each received sequence respectively. Based on the forward and backward coefficients of the received sequence, calculate the posterior probability of each transmitted symbol; According to the mapping rule, the posterior probability of the transmitted symbol is converted into the corresponding bit-level log-likelihood ratio; Based on the bit-level log-likelihood ratio, the corresponding LDPC codeword is decoded using confidence propagation. If the decoding result passes the parity check, the codeword is determined to be successfully decoded, and the successfully decoded codeword sequence is determined as the first synchronization anchor point.

[0010] Optionally, the step of performing low-rate decoding on the second received sequence matrix and using the successfully decoded low-rate decoded bit sequence as the second synchronization anchor point includes: The transmission symbol probabilities at corresponding positions in the second received sequence matrix are uniformly initialized; Based on the insertion, deletion and replacement error probability model of DNA channel, forward recursion and backward recursion calculations are performed on each received sequence in the second received sequence matrix according to the probability of transmitted symbols, and the forward coefficient and backward coefficient of each received sequence are obtained respectively. Based on the forward and backward coefficients of the received sequence, calculate the posterior probability of each transmitted symbol; According to the mapping rule, the posterior probability of the transmitted symbol is converted into the corresponding bit-level log-likelihood ratio; From the bit-level log-likelihood ratio, the soft information sequence corresponding to the low-rate LDPC codeword is reconstructed, and the low-rate LDPC codeword is preferentially subjected to belief propagation decoding. The low-rate LDPC codeword that passes parity check is determined as successfully decoded, and the successfully decoded low-rate decoded bit sequence is determined as the second synchronization anchor point.

[0011] Optionally, in the first encoding mode, the total transmission bit rate is calculated as follows:

[0012] In the formula: The total transmission bit rate for the first encoding mode; This represents the bit rate of the LDPC code in the LDPC encoder.

[0013] Optionally, in the second encoding mode, the total transmission bit rate is calculated as follows:

[0014] In the formula: This represents the total transmission bit rate for the second encoding mode. The bit rate of the LDPC code in a high-bit-rate LDPC encoder; The bit rate of the LDPC code in a low-bit-rate LDPC encoder; The number of high-rate codewords consecutively arranged in the row direction of the combination matrix during the preset second sequence insertion period; The number of low-rate codewords inserted after each high-rate codeword sequence in the row direction of the combination matrix during the preset second sequence insertion period.

[0015] This invention also provides a direct transpose coding system for DNA data storage, the system comprising: The mode selection unit is used to acquire encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements; A first encoding mode transpose encoding unit is configured to: encode and transpose multiple input information bit sequences in a first encoding mode to obtain a first transpose matrix; insert a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and map it into a first DNA sequence matrix; pass the first DNA sequence matrix through a DNA channel to obtain a first received sequence matrix; perform synchronous decoding on the first received sequence matrix based on the marker sequence, and use the successfully decoded bit sequence as a first synchronization anchor; use the first synchronization anchor to assist other sequences in the first received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences; The second encoding mode transpose encoding unit is used to, in the second encoding mode, divide the multiple input information bit sequences into low information bit sequence groups and high information bit sequence groups, respectively encode the low information bit sequence groups at a low code rate and encode the high information bit sequence groups at a high code rate, and combine them to obtain a combination matrix; transpose the combination matrix to obtain a second transpose matrix and map it to a second DNA sequence matrix; pass the second DNA sequence matrix through a DNA channel to obtain a second received sequence matrix; perform low code rate decoding on the second received sequence matrix, and use the successfully decoded low code rate decoded bit sequences as second synchronization anchors; use the second synchronization anchors to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

[0016] This invention also provides a computer-readable storage medium storing a computer program or instructions thereon, which, when executed by a processor, implement the steps of the direct transpose encoding method for DNA data storage as described above.

[0017] This invention also provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the steps of the direct transpose encoding method for DNA data storage as described above.

[0018] As can be seen from the above technical solutions, the present invention has the following advantages: This invention provides a direct transpose encoding method and related apparatus for DNA data storage. The method includes: acquiring encoding requirements and multiple input information bit sequences; entering a corresponding encoding mode according to the encoding requirements; in the first encoding mode, encoding and transposing the multiple input information bit sequences to obtain a first transpose matrix; inserting a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and mapping it to a first DNA sequence matrix; passing the first DNA sequence matrix through a DNA channel to obtain a first received sequence matrix; synchronously decoding the first received sequence matrix based on the marker sequence, using the successfully decoded bit sequence as a first synchronization anchor; and using the first synchronization anchor to assist other sequences in the first received sequence matrix in iterative synchronization. First, decode the input information bit sequences to recover all decoded bit sequences. In the second encoding mode, divide the multiple input information bit sequences into low-information bit sequence groups and high-information bit sequence groups. Encode the low-information bit sequence groups at a low code rate and the high-information bit sequence groups at a high code rate, combining them to obtain a combination matrix. Transpose the combination matrix to obtain a second transpose matrix, which is then mapped to a second DNA sequence matrix. Pass the second DNA sequence matrix through a DNA channel to obtain a second received sequence matrix. Decode the second received sequence matrix at a low code rate, using the successfully decoded low-rate bit sequences as second synchronization anchors. Use the second synchronization anchors to assist in iterative synchronous decoding of other sequences in the second received sequence matrix, recovering all decoded bit sequences.

[0019] In this invention, under low code rate encoding requirements, the first encoding mode is entered, which effectively corrects synchronization and substitution errors based on the matrix transpose framework and with the help of the marker sequence as a synchronization reference point; under high code rate requirements, the second encoding mode is entered, which realizes the synchronization anchoring function based on the matrix transpose framework without the help of introducing explicit markers, thereby improving storage density and encoding efficiency, realizing the transformation and correction of synchronization errors into substitution errors, and thus improving DNA storage effect. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 A flowchart illustrating the steps of a direct transposition encoding method for DNA data storage provided in this embodiment of the invention; Figure 2 An encoding block diagram of the direct transpose marker code encoding scheme for the first encoding mode provided in the embodiments of the present invention; Figure 3 An encoding block diagram of a dual-rate LDPC encoding scheme for the second encoding mode provided in an embodiment of the present invention; Figure 4 A comparative analysis of the bit error rate (BER) performance of the traditional tag code scheme, embedded tag code scheme, direct transpose tag code encoding scheme, and dual-rate LDPC encoding scheme provided in the embodiments of the present invention under different synchronization error probabilities; Figure 5 This is a structural block diagram of a direct transpose coding system for DNA data storage provided in an embodiment of the present invention. Detailed Implementation

[0022] This invention provides a direct transpose encoding method and related apparatus for DNA data storage, which addresses the technical problem that existing error-correcting code encoding schemes for DNA storage have limited synchronous correction capabilities, resulting in poor DNA storage performance.

[0023] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0024] Please see Figure 1 This invention provides a direct transpose encoding method for DNA data storage, the method comprising: Step 101: Obtain the encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements.

[0025] It should be noted that in DNA data storage, the code rate represents storage efficiency; a higher code rate means less redundancy overhead, more effective data can be stored in the same length of DNA strand, and higher storage density and efficiency; a lower code rate means more redundant bits are added for error correction and synchronization, a smaller proportion of effective data, and lower storage efficiency.

[0026] The encoding requirements in this embodiment include high bitrate encoding requirements and low bitrate encoding requirements. For example, a preset bitrate threshold can be set according to the actual encoding requirements. If the bitrate encoding requirement is greater than or equal to the preset bitrate threshold, it is determined to be a high bitrate encoding requirement; otherwise, it is determined to be a low bitrate encoding requirement. The low bitrate encoding requirement corresponds to the first encoding mode, while the high bitrate encoding requirement corresponds to the second encoding mode.

[0027] Step 102: In the first encoding mode, multiple input information bit sequences are encoded and transposed to obtain a first transpose matrix; a tag sequence is inserted into the first transpose matrix to obtain a tag enhancement matrix and mapped to a first DNA sequence matrix; the first DNA sequence matrix is ​​passed through a DNA channel to obtain a first received sequence matrix; based on the tag sequence, the first received sequence matrix is ​​synchronously decoded, and the successfully decoded bit sequence is used as the first synchronization anchor; the first synchronization anchor is used to assist other sequences in the first received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

[0028] It should be noted that, in the first encoding mode, this embodiment adopts the Direct Transpose Marked Code (DMC) scheme to effectively correct synchronization and replacement errors. During the encoding process, the direct transpose architecture is used to change the arrangement of data in the DNA sequence, thereby changing the impact mode of errors. This allows traditional error correction codes (such as LDPC) to effectively correct synchronization errors that were originally difficult to handle, significantly improving the system's error resistance. At the same time, this embodiment introduces a marker sequence to provide an absolutely reliable synchronization reference point with a known position in the initial stage of decoding. This can directly correct the phase shift of the received sequence, ensuring that the decoding process can start quickly and stably, especially in high error rate environments, guaranteeing the success rate and speed of decoding.

[0029] Specifically, please refer to Figure 2 The direct transpose marker code encoding scheme implements the encoding process through an LDPC encoder, a direct transposer, and a marker code encoder, and implements the decoding process through a synchronous decoder and an LDPC decoder.

[0030] In one specific implementation, in the first encoding mode, encoding and transposing multiple input information bit sequences to obtain a first transpose matrix; inserting a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and mapping it to a first DNA sequence matrix includes: S11. Encode multiple input information bit sequences using an LDPC encoder to obtain multiple codeword sequences and form a codeword matrix; perform a transpose operation on the codeword matrix to obtain the first transpose matrix; S12. Insert the period according to the preset first sequence, and insert it into each of the first transpose matrices. Insert after the codeword sequence The label sequence is used to obtain the label enhancement matrix; the label enhancement matrix is ​​then mapped to DNA to obtain the first DNA sequence matrix.

[0031] like Figure 2 As shown, during the encoding process, the sequence of n input information bits is... Each codeword is encoded using an LDPC encoder to obtain n codeword sequences of length m. These codeword sequences constitute a codeword matrix ; For codeword matrix Perform the transpose operation to obtain First transpose matrix ; According to the preset first sequence insertion period, in the transpose matrix The marker sequence is inserted periodically, that is, every Insert after the codeword sequence The column label sequence yields a value of [size]. Marking enhancement matrix ; where the marker enhancement matrix The formula for calculating the number of columns in a matrix is:

[0032] In the formula: and All are even numbers to meet the requirements of the binary-to-base mapping rules; To indicate the number of columns in the augmentation matrix; The sequence number of the input information bit sequence; The number of consecutive codeword sequences within each preset first sequence insertion period in the first transpose matrix; The number of marker sequences inserted for each preset first sequence insertion period.

[0033] Enhance the marker matrix Convert to the first DNA sequence matrix X. Label each row of the enhancement matrix U. DNA strands are converted using the two-bit to nucleotide mapping rule (i.e., the base mapping rule). The mapping rule is:

[0034] The final size of the first DNA sequence matrix X is , ;in, This is the base symbol for a nucleotide.

[0035] So the total transmission bit rate in the first encoding mode Represented as:

[0036] This completes the encoding process under the first encoding mode.

[0037] The first DNA sequence matrix is ​​passed through a DNA channel to obtain the first received sequence matrix; specifically, let the i-th transmitted DNA sequence in the first DNA sequence matrix be... Then the corresponding received sequence is ,in This indicates the length of the received sequence. However, due to the presence of insertion, deletion, and substitution errors in the DNA channel, therefore... Usually not equal to .

[0038] In one specific embodiment, the process of synchronously decoding the first received sequence matrix based on the tag sequence and using the successfully decoded bit sequence as the first synchronization anchor point includes: S21. Based on the position and base symbol of the marker sequence, initialize the transmission symbol probability at the corresponding position in the first received sequence matrix, and calculate the corresponding transition probability; S22. Based on the DNA channel insertion, deletion and replacement error probability model, perform forward recursion and backward recursion calculations on each received sequence in the first received sequence matrix according to the transition probability, and obtain the forward coefficient and backward coefficient of each received sequence respectively. S23. Calculate the posterior probability of each transmitted symbol based on the forward and backward coefficients of the received sequence. S24. According to the mapping rule, convert the posterior probability of the transmitted symbol into the corresponding bit-level log-likelihood ratio; S25. Based on the bit-level log-likelihood ratio, perform confidence propagation decoding on the corresponding LDPC codeword; if the decoding result passes the parity check, the codeword is determined to be successfully decoded, and the successfully decoded codeword sequence is determined as the first synchronization anchor point.

[0039] For ease of understanding, this specific embodiment introduces an index offset during the decoding process. ,in Indicates the first in the transmission sequence The index offset between a symbol and its corresponding symbol in the received sequence.

[0040] (1) Initialize the symbol probability For the position and base symbol of the marker sequence, if If the base is the same as the labeled base, then Otherwise For unmarked locations, uniform initialization is used, i.e. ,in The corresponding transition probability is calculated based on the initial sign probability using the following formula.

[0041] Then the received symbols observed in the first received sequence matrix probability It is given by the following formula:

[0042] In the formula: Indicates the sending symbol The prior probability, This represents the transition probability of the sequencing channel (i.e., the DNA channel).

[0043] (2) Perform forward-backward calculations: Based on the DNA channel insertion, deletion, and replacement error probability model, forward and backward recursive calculations are performed on each received sequence in the first received sequence matrix according to the transition probability, obtaining the forward coefficients and backward coefficients of each received sequence. Among them, the forward coefficients... and backward coefficient Calculate using the following formulas respectively:

[0044] In the formula: When the index offset is v, in the i-th received sequence Below, the forward coefficients (forward probabilities) of the first k-1+v base symbols are received, where ; ,index Indicates the maximum number of consecutive bases inserted at any position; This represents the probability of a base insertion error. This represents the probability of a base deletion error. The probability that a base is transferred (i.e., there is neither insertion nor deletion at this position, a base symbol is transferred, which may be correct or may be a substitution).

[0045] In the formula: For the i-th received sequence at index offset v The backward coefficients (backward probabilities) for the last k-1+v base symbols to be received.

[0046] (3) Calculate the posterior probability: Calculate the given received sequence using the following formula. The symbol sent at time is posterior probability ,Right now:

[0047] In the formula: express The maximum value.

[0048] (4) Calculate the log-likelihood ratio (LLR): Convert the posterior probability of the symbol to the bit-level LLR using the following formula. The base sequence is reverse-mapped to a binary sequence, and each base symbol corresponds to two binary bits. The first bit is defined as the low bit and the second bit is defined as the high bit. For example, the LLR of the first bit depends on the probability ratio of whether the base is T / G or A / C; that is:

[0049] In the formula: The bit-level LLR is the bit-level LLR at the index of the j-th bit position in the i-th sequence; , , and They are respectively the i-th received sequence Next, the kth symbol is sent. base , , and The posterior probability.

[0050] (5) Perform LDPC decoding: Based on the bit-level log-likelihood ratio, perform belief propagation decoding on the corresponding LDPC codewords; if the decoding result passes the parity check, the codeword is considered successfully decoded. Specifically, the belief propagation (BP) algorithm is used to decode each LDPC codeword sequence to obtain the posterior LLR sequence. and decoding bit sequence And set a verification flag. :if Satisfies parity check. ;otherwise .

[0051] Finally, the first synchronization anchor is used to assist in iterative synchronization decoding of other sequences in the first received sequence matrix, recovering the decoded bit sequences of all bits. Understandably, the successfully decoded sequences are used as synchronization anchors to update the symbol probabilities.

[0052] First, calculate the external LLR:

[0053] In the formula: Let LLR be the external LLR indexed by the j-th bit position in the i-th sequence; For the posterior LLR at the index of the j-th bit position in the i-th sequence; The successfully decoded sequences are used as synchronization anchors, and then the symbol probabilities are updated using the following formula:

[0054] In the formula: , , and Let be the symbol probabilities of the k-th symbol in the i-th transmitted DNA sequence being the bases A, C, T, and G, respectively.

[0055] This embodiment employs the Synchronization Anchor Point Generation Iterative Decoding (SAGID) algorithm, which iteratively executes the above steps and fully utilizes the successfully decoded sequence as a synchronization anchor point, significantly improving synchronization recovery capability.

[0056] The direct transpose marker code encoding scheme of the first encoding mode provided in this invention, within the matrix transpose framework, utilizes marker sequences to provide stable and known synchronization reference points, enabling the transformation and correction of synchronization errors into substitution errors. This ensures that the decoding process can start and converge quickly and reliably in high error rate environments, thereby significantly improving robustness against synchronization errors and decoding speed. This mode is particularly suitable for DNA data storage scenarios with stringent data reliability requirements or poor initial synchronization conditions, providing superior decoding stability and timeliness while ensuring high error correction performance.

[0057] Step 103: In the second encoding mode, multiple input information bit sequences are divided into low-information bit sequence groups and high-information bit sequence groups. The low-information bit sequence groups are encoded at a low code rate, and the high-information bit sequence groups are encoded at a high code rate, respectively, and combined to obtain a combination matrix. The combination matrix is ​​transposed to obtain a second transpose matrix and mapped to a second DNA sequence matrix. The second DNA sequence matrix is ​​passed through a DNA channel to obtain a second received sequence matrix. The second received sequence matrix is ​​decoded at a low code rate, and the successfully decoded low-code-rate bit sequences are used as second synchronization anchors. The second synchronization anchors are used to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

[0058] It should be noted that, in the first encoding mode, this embodiment employs a dual-rate LDPC encoding (DDLC) scheme, which improves both overall error correction performance and code rate and storage efficiency. During encoding, a direct transpose architecture is used to change the arrangement of data in the DNA sequence, thereby altering the error impact pattern. This allows traditional error-correcting codes (such as LDPC) to effectively correct previously difficult-to-handle synchronization errors, significantly improving the system's error resistance. Simultaneously, this embodiment achieves synchronization anchoring without introducing explicit markers, eliminating the pure overhead of marking and thus significantly increasing storage density (code rate). By replacing pure markers with low-rate error-correcting codewords carrying valid information, these codewords, after being correctly decoded first during the decoding process, can also serve as synchronization anchors.

[0059] In one specific implementation, the process of dividing multiple input information bit sequences into low-information bit sequence groups and high-information bit sequence groups, performing low-rate encoding on the low-information bit sequence groups and high-rate encoding on the high-information bit sequence groups respectively, and combining them to obtain a combination matrix includes the following steps: S31. Divide multiple input information bit sequences into low information bit sequence groups and high information bit sequence groups; S32. The low-information bit sequence group is encoded at a low code rate using a low-code-rate LDPC encoder to obtain multiple low-code-rate codeword sequences; the high-information bit sequence group is encoded at a high code rate using a high-code-rate LDPC encoder to obtain multiple high-code-rate codeword sequences. S33. According to the preset second sequence insertion period, insert low code rate code word sequences after each high code rate code word sequence in the row direction to obtain a combination matrix.

[0060] Specifically, this was done to compare the total transmission bitrate of two coding modes under the same DNA storage physical conditions; such as Figure 3 As shown, the number of information bits in the input information bit sequence provided in this embodiment is First, input information bit sequence The data is divided into a low-information bit sequence group and a high-information bit sequence group, wherein the low-information bit sequence group includes... sequences, using a code rate of ... The low-rate LDPC encoder encodes low-information bit sequence groups; the high-information bit sequence groups include sequences, using a code rate of ... A high-rate LDPC encoder encodes high-information bit sequences; two LDPC encoders with different rates output codeword sequences with the same codeword length but different rates. This ensures that the codewords produced by the two encoders have the same length. Different information block lengths need to be selected for each encoder.

[0061] Then, according to the preset second sequence insertion period, a low-rate codeword sequence is inserted after each high-rate codeword sequence in the row direction, that is, each Insert after a high-bitrate codeword A low-coderate codeword is used to construct... The combination matrix D; where, .

[0062] Transpose the combined matrix D to obtain The second transpose matrix U is mapped to the second DNA sequence matrix X. During the mapping process, each row of the second transpose matrix U is mapped according to the base mapping rules for the DNA sequence. ,in .

[0063] Therefore, in the second encoding mode, the total transmission bit rate is calculated as follows:

[0064] In the formula: This represents the total transmission bit rate for the second encoding mode. The number of high-rate codewords consecutively arranged in the row direction of the combination matrix during the preset second sequence insertion period; This refers to the number of low-rate codewords inserted into the row direction of the combination matrix during the preset second sequence insertion period, following each high-rate codeword sequence.

[0065] This completes the encoding process under the second encoding mode.

[0066] Assumption , ,and Then we have:

[0067] This indicates that, under the same output scale (i.e., the DNA sequence length and number are the same in both the first and second DNA sequence matrices), the dual-rate LDPC encoding scheme in the second mode has a higher code rate than the direct transpose marker coding scheme in the first mode.

[0068] The second DNA sequence matrix is ​​passed through a DNA channel to obtain the second received sequence matrix; specifically, let the i-th transmitted DNA sequence in the second DNA sequence matrix be... Then the corresponding received sequence is ,in This indicates the length of the received sequence. However, due to the presence of insertion, deletion, and substitution errors in the DNA channel, therefore... Usually not equal to .

[0069] In one specific implementation, the process of performing low-rate decoding on the second received sequence matrix and using the successfully decoded low-rate decoded bit sequence as the second synchronization anchor point includes the following steps: S41. Uniformly initialize the transmission symbol probabilities at corresponding positions in the second received sequence matrix; S42. Based on the DNA channel insertion, deletion and replacement error probability model, perform forward recursion and backward recursion calculations on each received sequence in the second received sequence matrix according to the transmitted symbol probability, and obtain the forward coefficient and backward coefficient of each received sequence respectively. S43. Calculate the posterior probability of each transmitted symbol based on the forward and backward coefficients of the received sequence. S44. According to the mapping rule, convert the posterior probability of the transmitted symbol into the corresponding bit-level log-likelihood ratio; S45. From the bit-level log-likelihood ratio, reconstruct the soft information sequence corresponding to the low-rate LDPC codeword, and prioritize the belief propagation decoding of the low-rate LDPC codeword. S36. Determine the low-rate LDPC codeword that passes parity check as successfully decoded, and determine the successfully decoded low-rate decoded bit sequence as the second synchronization anchor point.

[0070] It should be noted that, compared to the direct transpose tag code encoding scheme that uses tag codes, this specific embodiment performs iterative decoding without predefined synchronization anchors. Therefore, the forward-backward algorithm can only recover the sequence length and cannot correct synchronization errors caused by insertion or deletion.

[0071] In this specific embodiment, the received sequenced DNA sequence matrix is ​​processed by a synchronous decoder. Perform decoding and utilize the successfully decoded sequence. Iterative synchronous decoding, using synchronization anchors as synchronization points, significantly improves synchronization recovery capabilities through a probabilistic reset mechanism. This initial stage is defined as the pre-synchronization decoding stage. In this stage, even without synchronization anchors, the direct transpose architecture can still convert some synchronization errors into substitution errors. These substitution errors can still be corrected by a low-rate LDPC decoder. Successfully decoded low-rate codeword sequences will be used as synchronization anchors in subsequent iterations to achieve joint correction of synchronization and substitution errors, ultimately recovering the original information sequence.

[0072] Aside from the addition of a pre-synchronization step, the decoding process of the dual-rate LDPC encoding scheme adopts the same implementation method as the synchronization anchor point generation iterative decoding algorithm in the first mode, and will not be elaborated here. The pre-synchronization mechanism achieves effective synchronization recovery without introducing additional marker redundancy by utilizing the inherent strong error correction capability of low-rate LDPC codewords.

[0073] The dual-rate LDPC encoding scheme of the second encoding mode provided in this invention achieves synchronization anchoring without introducing explicit markers, thereby improving both code rate and storage efficiency. It utilizes successfully decoded sequences as synchronization anchors to enhance overall error correction performance. This second encoding mode is suitable for DNA data storage systems with high storage efficiency requirements, and is particularly well-suited to the preference for short oligonucleotide chains in biochemical processes, maximizing information storage density while ensuring reliability.

[0074] The embodiments of this invention also provide corresponding simulation experiments to verify the system performance of the invention. Specifically, the bit error rate performance of the Direct Transposed Mark Code (DMC) scheme in the first mode and the Dual-Rate LDPC (DDLC) scheme in the second mode are simulated and analyzed. Simultaneously, by comparing with the Embedded Mark Code (EMC) scheme and the conventional Mark Code (MC) scheme, the superiority of the technical solution of this invention is verified.

[0075] To ensure fairness in the comparative experiment, all schemes were compared within the total bitrate. Performance was evaluated under the same conditions. The simulation environment used uniform parameter settings: (3,6)-regular LDPC codes were selected as the core error correction codes; the maximum number of iterations within the LDPC decoder was fixed at 30; and the iteration count of the overall iterative algorithm was denoted as... DNA sequence length set to The channel error probability configuration satisfies and The high-rate encoders in traditional marker code schemes, embedded marker code schemes, direct transposed marker code encoding schemes, and dual-rate LDPC encoding schemes all use LDPC codes with a code rate of 0.90, corresponding to an information bit length of 4104 and a codeword length of 4560.

[0076] The low-rate encoder in the dual-rate LDPC encoding scheme uses an LDPC code with a code rate of 0.50, an information bit length of 2280, and a codeword length of 4560. The dual-rate LDPC encoding scheme processes 200 information sequences. , The parameter configuration specifies that each data block contains 160 high-rate sequences and 40 low-rate sequences. The direct transpose marker code encoding scheme adopts... , The parameter combination satisfies the even number constraint and approximates the target code rate. Each data block contains 180 information sequences and 20 tag sequences.

[0077] Please see Figure 4 , Figure 4 The results show a comparison of the bit error rate performance of four schemes within a range of varying synchronization error probabilities. Simulation data indicates that when the number of iterations is set to... At that time, both schemes proposed in this invention significantly outperform the traditional embedded tag code scheme and the tag code scheme. Specifically, in the low error probability region, the direct transposed tag code encoding scheme exhibits better bit error rate performance than the dual-rate LDPC encoding scheme; when the error probability increases to At this point, the performance of the two schemes tends to be similar. When the number of iterations increases to... At this time, the dual-rate LDPC coding scheme demonstrates a performance advantage in the medium-to-high error probability region, with its bit error rate performance outperforming that of the direct transpose marker coding scheme. This indicates that the dual-rate LDPC coding scheme can achieve greater performance gains by increasing the number of iterations, demonstrating its robustness in complex channel environments.

[0078] The direct transpose coding system for DNA data storage provided in the embodiments of this application will be described below. The direct transpose coding system for DNA data storage described below can be referred to in correspondence with the direct transpose coding method for DNA data storage described above.

[0079] Please see Figure 5 This invention also provides a direct transpose coding system for DNA data storage, the system comprising: The mode selection unit 201 is used to acquire encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements; The first encoding mode transpose encoding unit 202 is used to encode and transpose multiple input information bit sequences in a first encoding mode to obtain a first transpose matrix; insert a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and map it into a first DNA sequence matrix; pass the first DNA sequence matrix through a DNA channel to obtain a first received sequence matrix; perform synchronous decoding on the first received sequence matrix based on the marker sequence, and use the successfully decoded bit sequence as a first synchronization anchor; use the first synchronization anchor to assist other sequences in the first received sequence matrix to perform iterative synchronous decoding to recover all decoded bit sequences; The second encoding mode transpose encoding unit 203 is used to divide multiple input information bit sequences into low information bit sequence groups and high information bit sequence groups in the second encoding mode, perform low code rate encoding on the low information bit sequence groups and high code rate encoding on the high information bit sequence groups respectively, and combine them to obtain a combination matrix; transpose the combination matrix to obtain a second transpose matrix and map it to a second DNA sequence matrix; pass the second DNA sequence matrix through a DNA channel to obtain a second received sequence matrix; perform low code rate decoding on the second received sequence matrix, and use the successfully decoded low code rate decoded bit sequences as second synchronization anchors; use the second synchronization anchors to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

[0080] This invention also provides a computer-readable storage medium storing a computer program or instructions thereon, which, when executed by a processor, implement the steps of any of the above-described direct transpose encoding methods for DNA data storage.

[0081] This invention also provides a computer program product, including a computer program or instructions, characterized in that, when the computer program or instructions are executed by a processor, they implement the steps of any of the above-mentioned direct transpose encoding methods for DNA data storage.

[0082] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0083] The terms "first," "second," etc., used in this specification and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented, for example, in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0084] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0085] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0086] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0087] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0088] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A direct transposition encoding method for DNA data storage, characterized in that, The method includes: Obtain the encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements; In the first encoding mode, multiple input information bit sequences are encoded and transposed to obtain a first transpose matrix; a marker sequence is inserted into the first transpose matrix to obtain a marker enhancement matrix, which is then mapped to a first DNA sequence matrix; the first DNA sequence matrix is ​​passed through a DNA channel to obtain a first received sequence matrix; based on the marker sequence, the first received sequence matrix is ​​synchronously decoded, and the successfully decoded bit sequence is used as a first synchronization anchor; the first synchronization anchor assists other sequences in the first received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences; In the second encoding mode, the multiple input information bit sequences are divided into low-information bit sequence groups and high-information bit sequence groups. The low-information bit sequence groups are encoded at a low code rate, and the high-information bit sequence groups are encoded at a high code rate, respectively, and combined to obtain a combination matrix. The combination matrix is ​​transposed to obtain a second transposed matrix, which is then mapped to a second DNA sequence matrix. The second DNA sequence matrix is ​​passed through a DNA channel to obtain a second received sequence matrix. The second received sequence matrix is ​​decoded at a low code rate, and the successfully decoded low-code-rate bit sequences are used as second synchronization anchors. The second synchronization anchors are used to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

2. The direct transpose encoding method according to claim 1, characterized in that, The first transpose matrix is ​​obtained by encoding and transposing multiple input information bit sequences. The step of inserting a marker sequence into the first transpose matrix to obtain a marker-enhanced matrix and mapping it to a first DNA sequence matrix includes: The multiple input information bit sequences are encoded by an LDPC encoder to obtain multiple codeword sequences and form a codeword matrix; the codeword matrix is ​​then transposed to obtain a first transpose matrix. According to the preset first sequence insertion period, insert each of the first transpose matrix... Insert after the codeword sequence The label sequence is used to obtain a label enhancement matrix; the label enhancement matrix is ​​then mapped to DNA to obtain a first DNA sequence matrix; The formula for calculating the number of columns in the marker enhancement matrix is ​​as follows: In the formula: To indicate the number of columns in the augmentation matrix; The sequence number of the input information bit sequence; The number of consecutive codeword sequences within each preset first sequence insertion period in the first transpose matrix; The number of marker sequences inserted for each preset first sequence insertion period.

3. The direct transpose encoding method according to claim 1, characterized in that, The step of dividing the multiple input information bit sequences into low-information bit sequence groups and high-information bit sequence groups, performing low-rate encoding on the low-information bit sequence groups and high-rate encoding on the high-information bit sequence groups respectively, and combining them to obtain a combination matrix includes: The multiple input information bit sequences are divided into a low information bit sequence group and a high information bit sequence group; The low-information bit sequence group is encoded at a low code rate using a low-code-rate LDPC encoder to obtain multiple low-code-rate codeword sequences; the high-information bit sequence group is encoded at a high code rate using a high-code-rate LDPC encoder to obtain multiple high-code-rate codeword sequences. According to the preset second sequence insertion period, the low code rate code word sequence is inserted after each high code rate code word sequence in the row direction arrangement to obtain a combination matrix.

4. The direct transpose encoding method according to claim 1, characterized in that, The step of synchronously decoding the first received sequence matrix based on the marked sequence, and using the successfully decoded bit sequence as the first synchronization anchor, includes: Based on the position and base symbol of the labeled sequence, the transmission symbol probability at the corresponding position in the first received sequence matrix is ​​initialized, and the corresponding transition probability is calculated. Based on the insertion, deletion and replacement error probability model of DNA channel, forward recursion and backward recursion calculations are performed on each received sequence in the first received sequence matrix according to the transition probability to obtain the forward coefficient and backward coefficient of each received sequence respectively. Based on the forward and backward coefficients of the received sequence, calculate the posterior probability of each transmitted symbol; According to the mapping rule, the posterior probability of the transmitted symbol is converted into the corresponding bit-level log-likelihood ratio; Based on the bit-level log-likelihood ratio, the corresponding LDPC codeword is decoded using confidence propagation. If the decoding result passes the parity check, the codeword is determined to be successfully decoded, and the successfully decoded codeword sequence is determined as the first synchronization anchor point.

5. The direct transpose encoding method according to claim 1, characterized in that, The step of performing low-rate decoding on the second received sequence matrix and using the successfully decoded low-rate decoded bit sequence as the second synchronization anchor includes: The transmission symbol probabilities at corresponding positions in the second received sequence matrix are uniformly initialized; Based on the insertion, deletion and replacement error probability model of DNA channel, forward recursion and backward recursion calculations are performed on each received sequence in the second received sequence matrix according to the probability of transmitted symbols, and the forward coefficient and backward coefficient of each received sequence are obtained respectively. Based on the forward and backward coefficients of the received sequence, calculate the posterior probability of each transmitted symbol; According to the mapping rule, the posterior probability of the transmitted symbol is converted into the corresponding bit-level log-likelihood ratio; From the bit-level log-likelihood ratio, the soft information sequence corresponding to the low-rate LDPC codeword is reconstructed, and the low-rate LDPC codeword is preferentially subjected to belief propagation decoding. The low-rate LDPC codeword that passes parity check is determined as successfully decoded, and the successfully decoded low-rate decoded bit sequence is determined as the second synchronization anchor point.

6. The direct transpose encoding method according to claim 2, characterized in that, In the first encoding mode, the total transmission bit rate is calculated as follows: In the formula: This represents the total transmission bit rate for the first encoding mode. This represents the bit rate of the LDPC code in the LDPC encoder.

7. The direct transpose encoding method according to claim 3, characterized in that, In the second encoding mode, the total transmission bit rate is calculated as follows: In the formula: This represents the total transmission bit rate for the second encoding mode. The bit rate of the LDPC code in a high-bit-rate LDPC encoder; The bit rate of the LDPC code in a low-bit-rate LDPC encoder; The number of high-rate codewords consecutively arranged in the row direction of the combination matrix during the preset second sequence insertion period; The number of low-rate codewords inserted after each high-rate codeword sequence in the row direction of the combination matrix during the preset second sequence insertion period.

8. A direct transpose coding system for DNA data storage, characterized in that, The system includes: The mode selection unit is used to acquire encoding requirements and multiple input information bit sequences, and enter the corresponding encoding mode according to the encoding requirements; A first encoding mode transpose encoding unit is configured to: encode and transpose multiple input information bit sequences in a first encoding mode to obtain a first transpose matrix; insert a marker sequence into the first transpose matrix to obtain a marker enhancement matrix and map it into a first DNA sequence matrix; pass the first DNA sequence matrix through a DNA channel to obtain a first received sequence matrix; perform synchronous decoding on the first received sequence matrix based on the marker sequence, and use the successfully decoded bit sequence as a first synchronization anchor; use the first synchronization anchor to assist other sequences in the first received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences; The second encoding mode transpose encoding unit is used to, in the second encoding mode, divide the multiple input information bit sequences into low information bit sequence groups and high information bit sequence groups, respectively encode the low information bit sequence groups at a low code rate and encode the high information bit sequence groups at a high code rate, and combine them to obtain a combination matrix; transpose the combination matrix to obtain a second transpose matrix and map it to a second DNA sequence matrix; pass the second DNA sequence matrix through a DNA channel to obtain a second received sequence matrix; perform low code rate decoding on the second received sequence matrix, and use the successfully decoded low code rate decoded bit sequences as second synchronization anchors; use the second synchronization anchors to assist other sequences in the second received sequence matrix in iterative synchronous decoding to recover all decoded bit sequences.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the direct transpose encoding method for DNA data storage as described in any one of claims 1-7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the direct transpose encoding method for DNA data storage as described in any one of claims 1-7.

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