A DNA data storage method with controllable GC content and homopolymers

Abstract

This invention proposes a DNA data storage method with controllable GC content and homopolymers. The steps are as follows: performing LZW compression on the original text and converting the LZW-compressed text into a binary code stream; adding a Reed-Solomon error-correcting code to the binary code stream to generate a binary code stream with error correction; scrambling the binary code stream with error correction using a chaotic sequence generated by logical mapping to obtain a new binary sequence; and using a 64-ary encoding mapping table formed by selecting 64 mapping elements that meet the constraints from a base permutation set, transcoding the binary sequence into a DNA sequence using the 64-ary encoding mapping table, with each four bases being a mapping unit. This method fully considers data stability, decoding accuracy, and cost-effectiveness in the DNA storage process. Testing on Shakespeare's sonnets demonstrated its feasibility and effectiveness. Experimental results showed that the GC content of the encoded DNA sequence was maintained at 50%, and the homopolymer length did not exceed 2.

Description

Technical Field

[0001] The present invention relates to the technical field of DNA data storage, and in particular to a DNA data storage method with controllable GC content and homopolymer. Background Art

[0002] Currently, traditional physical storage media can no longer meet the exponentially growing demand for data storage. According to forecasts, by 2025, the amount of global data will grow to 1.75×10 14 GB. To address this challenge, information storage has begun using organic molecules such as DNA, oligopeptides, and metabolites. Compared to traditional storage media, these emerging storage media offer significant advantages in storage density, particularly due to the unique double-helix structure of DNA. Each gram of DNA can hold up to 455 exabytes (EB). Furthermore, under appropriate storage conditions, DNA has a half-life of approximately 521 years; if stored in silica, this half-life can exceed 2 million years. Due to its high storage density and long-term stability, DNA, an ancient information carrier, is considered a storage medium with great potential. During DNA data storage, the original information is first converted into a binary sequence and then converted into a DNA sequence according to specific encoding rules. These DNA sequences can be synthesized and stored in vivo or in vitro as oligonucleotides or double-stranded DNA, facilitating subsequent retrieval and access using relevant technologies. The latest third-generation DNA sequencing technology, with its rapid and accurate characteristics, makes reading and writing the information stored in DNA molecules even more convenient. At present, combined with the third-generation DNA molecular sequencing technology, a variety of random reading strategies have been proposed to achieve selective access to stored information, further improving the practicality and scalability of DNA data storage.

[0003] The ever-increasing global demand for information storage will make the storage density of traditional physical media unable to meet future needs. DNA information storage, as an emerging storage technology, has great potential and advantages. However, in DNA storage, designing a suitable encoding scheme is crucial. DNA bases, as a long-term storage medium with great potential, are of great significance for data that needs to be preserved for a long time. DNA molecules can maintain stability for at least thousands of years in a dry, cold and dark environment, unlike common large-scale physical media that require expensive data migration costs to adapt to environmental changes. Using DNA molecules for digital information storage, theoretically, it can reach 1EB / mm 3 The storage density is very high, and the information stored in the DNA molecules can be read at any time without the risk of the extraction method becoming outdated.

[0004] DNA sequences follow the constraints of biological synthesis and sequencing, which can effectively reduce errors in the subsequent reading process and improve decoding efficiency. Homopolymers and GC content are two important indicators for evaluating the performance of encoding schemes. For example, long strings of single-base repeats (homopolymers) with a length of more than 5 may introduce higher error rates during synthesis or sequencing. In addition, a GC content below 40% or above 60% (i.e., extreme GC content) is generally not conducive to the synthesis of DNA molecules. Church, Grass, Blawat, and Erlich adopted a binary transcoding strategy (0 represents A or G, 1 represents C or T) to control the GC content to avoid the appearance of long homopolymer sequences. Although the above methods can meet the requirements of biological sequences, the encoding efficiency of these algorithms is low. Subsequently, the paper [FENG L, FOH CH, CAI J, et al. LT codes decoding: design and analysis; proceedings of the 2009 IEEE International Symposium on Information Theory, F, 2009[C].] pointed out that Luby Transform codes ("LT codes") can effectively handle a large number of input symbol segments (also known as droplets, logical redundancy), providing an effective method for transmitting information over erasure channels. DNA fountain codes use Luby Transform codes ("LT codes") as an internal transcoding strategy, significantly reducing the introduced redundancy. To avoid extreme GC content and long homopolymers, fountain codes use a unique screening mechanism to select droplets that meet the constraints. Successful decoding of Luby Transform codes ("LT codes") requires a sufficient number of droplets. Too few droplets that meet the requirements will result in decoding failure. Increasing logical redundancy reduces information density and increases synthesis cost. At the same time, the transcoding method using Luby Transform code ("LT code") as the inner code is also very strict in the selection of input symbol segment length. If the input symbol segment length and the information eBCH code length are arbitrarily selected, it will lead to a decrease in the rate in a fading channel. To ensure the integrity of the information, Goldman adopted a four-fold physical redundancy method, that is, synthesizing an excess of DNA molecules to increase the number of DNA molecule copies for each sequence. However, this will increase the cost of subsequent DNA sequence synthesis. Therefore, when developing a transcoding algorithm, it is necessary to have the characteristics of high storage density and high robustness, be able to adapt to various types of data transcoding, and reasonably control costs to apply DNA information storage to practical scenarios.

[0005] Patent application number 201880048731.X discloses an exemplary method for storing input data on nucleic acids, comprising: converting the input data into a set of nucleotide sequences, and synthesizing a set of nucleic acids comprising the set of nucleotide sequences. The conversion comprises a data processing step, comprising converting the input data into a binary string; and a nucleotide encoding step, comprising converting the binary string using a 5-bit transcoding framework to obtain the set of nucleotide sequences. The invention allows for random data access, which is particularly advantageous when storing large amounts of data but only requiring access to a portion of the information at a given time. The stored data includes any type of data that can be represented digitally (i.e., as binary data), including, for example, text files, high-definition video, images, and / or audio. However, the encoding of the set of nucleotide sequences obtained by converting the binary string using the 5-bit transcoding framework may include sequences with a GC content exceeding 60%, such as "ACC" and "TGC." Furthermore, this encoding may also include homopolymer sequences with consecutive single nucleotides, such as "CCC." Summary of the Invention

[0006] To solve the technical problem of avoiding misreading of DNA sequences during sequencing, the present invention proposes a DNA data storage method with controllable GC content and homopolymers.

[0007] To achieve the above object, the technical solution of the present invention is implemented as follows: a DNA data storage method with controllable GC content and homopolymers, the steps of which are as follows:

[0008] Step 1: Perform LZW compression on the original text and convert the LZW compressed text into a binary code stream;

[0009] Step 2: Add RS error correction code to the binary code stream to generate a binary code stream with error correction code;

[0010] Step 3: Use the chaotic sequence generated by the logical mapping to scramble the binary code stream with the error correction code to obtain the final binary code stream to be converted into a DNA sequence;

[0011] Step 4: 64 base permutations and combinations that meet the constraints are selected from the base pairing to form a set of mapping elements to form a 64-element encoding mapping table, and the binary sequence is converted into a DNA sequence using the 64-element encoding mapping table.

[0012] Preferably, the DNA sequence is provided with an information load region and an RS error correction region, an index region is provided at the rear end of the RS error correction region, and primer regions are added at both ends of the DNA sequence; an RS error correction code is provided in the RS error correction region.

[0013] Preferably, the length of the information payload region is 129 bases, the length of the RS error correction region is 15 bases, there are 16 bases in the index region, and there are 20 bases in the primer region.

[0014] Preferably, the scrambling method is: using the chaotic sequence as the perturbation sequence to perform exclusive OR processing on the binary code stream after RS error correction coding.

[0015] Preferably, the method for generating the chaotic sequence by logical mapping is:

[0016] x n+1 = rx n (1 - x n )

[0017] where x n and x n+1 respectively represent the elements obtained in the nth and (n + 1)th iterations, and r is the control parameter; a chaotic sequence is generated when 3.569945627 < r ≤ 4;

[0018] Select the chaotic sequence generated with the control parameter r = 3.8 and the given parameter x0 = 4.0 to perform exclusive OR processing with the error-corrected binary code stream.

[0019] Preferably, the constraint conditions in step four include: the length of the homopolymer is less than 6; keeping the GC content in the DNA sequence between 40% and 60%; the method for forming the 64-ary coding mapping table is: taking every four-base permutation and combination in the 4 4 = 256 base pairing sets as a group of mapping elements, and screening the mapping elements considering the limitations of homopolymers and GC content.

[0020] Preferably, the 64-ary coding mapping table is:

[0021] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AGAC AGCA AGCT AGTC AGTG AGGA AGGT AGAG ACAG ACAC ACCA ACCT ACTC ACTG ACGA ACGT 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 CAAG CAAC CACA CACT CATC CATG CAGA CAGT CTAG CTAC CTCA CTCT CTTC CTTG CTGA CTGT 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 TCAG ACAC TCCA TCCT TCTC TCTG TCGA TCGT TGAG TGAC TGCA TGCT TGTC TGTG TGGA TGGT 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 GAAG GAAC GACA GACT GATC GATG GAGA GAGT GTAG GTAC GTCA GTCT GTTC GTTG GTGA GTGT .

[0022] Preferably, use the RS(255, 240) error correction code to correct each generated DNA sequence, correcting a certain number of insertion and deletion errors.

[0023] Preferably, the RS error correction code is the error correction code RS(255, 240, 15), where the error correction code block size is 240-bit payload, obtained by adding 15 bits of redundancy, and the error correction code RS(255, 240, 15) satisfies:

[0024] n - k ≥ E e + 2×E r

[0025] where n represents the number of bits with error correction code, k represents the number of information payload bits, and Ee Indicates erase error, E r Indicates a random error.

[0026] Preferably, the steps of the method for storing the text of Shakespeare's sonnets are as follows:

[0027] a) LZW compression is performed on Shakespeare's sonnets, which contain 97,343 bytes. The compressed text information is 24,963 bytes.

[0028] b) Convert the 24963 bytes into a binary stream according to the ASCII code, split each 240 bits into segments, and add 15 redundant bits to each segment;

[0029] c) The binary code stream with the RS error correction code is XORed with the chaotic sequence generated by the logical mapping. Every 24 bits of the scrambled binary code stream are encoded into 16 bases according to the 64-ary encoding mapping table. Finally, Shakespeare's sonnet is converted into 266,272 bases.

[0030] The present invention performs Lempel-Ziv-Welch (LZW) compression on the original text and converts it into a binary code stream. Next, Reed-Solomon (RS) error correction code is introduced into this binary code stream to generate a binary code stream with error correction code. Then, using the chaotic sequence generated by logical mapping, the binary code stream with error correction code is scrambled to generate a new binary sequence. In this process, each four bases are used as a mapping unit, and 64 mapping elements that meet the constraints are screened from a set of 256 base permutations to construct a 64-element encoding mapping table. Finally, this 64-element encoding mapping table is used to convert the binary sequence into the corresponding DNA sequence.

[0031] Compared with existing technologies, the present invention offers the following advantages: A DNA storage scheme based on a 64-tuple encoding mapping table combined with Reed-Solomon ("RS") encoding is proposed. This scheme encodes data into DNA sequences by subjecting the original text to Lempel-Ziv-Welch ("LZW") compression, adding RS encoding, and scrambling. The encoding process considers GC content constraints and avoids the restriction of long homopolymers to improve data stability and reliability. RS encoding is also introduced to correct the DNA sequence, enhancing decoding accuracy. This present invention fully considers data stability, decoding accuracy, and cost-effectiveness during the DNA storage process. Experimental testing on Shakespeare's sonnets demonstrated the feasibility and effectiveness of the present invention. Experimental results showed that the GC content of the encoded DNA sequence was maintained at 50%, and the homopolymer length did not exceed 2. With an error rate of 0.3%, the original information could be recovered error-free at a 10x sequencing depth. Simulations of primer design, PCR amplification, and sequence reading were also performed. This provides a reliable and efficient encoding scheme for DNA information storage. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0033] Figure 1 Flowchart of the present invention.

[0034] Figure 2 Figure 2 shows the sequence structure of the oligonucleotides designed for the present invention.

[0035] Figure 3 Schematic diagram of the self-correcting replacement, deletion, and insertion errors of the present invention.

[0036] Figure 4 The bifurcation diagram of the logic mapping of the present invention and the comparison diagram before and after scrambling, where: Figure 4 A is the logic mapping bifurcation diagram, Figure 4 B is a comparison chart of the {0, 1} content in the sequence before and after scrambling.

[0037] Figure 5 The figure is a comparison of the GC content ratio and homopolymer distribution of the present invention and the existing method, wherein: Figure 5 A is the GC content percentage of Text 1 (Shakespeare's sonnets) experiment. Figure 5B is the GC content percentage of Text 2 (DNA fountain code summary) experiment, Figure 5 C is the GC content percentage of Text 3 (the complete poem of Man Jiang Hong). Figure 5 D is the GC content ratio of Photo 1 (photographer 256), Figure 5 E is the experimental GC content percentage chart of character 1 (full characters on a 26-key keyboard), Figure 5 F is the homopolymer distribution diagram.

[0038] Figure 6 This is the error analysis and forward and reverse primer melting temperature diagram of the present invention, wherein, Figure 6 A is the base substitution rate of the 64-bit encoding table, Figure 6 B is the base substitution rate of the random coding table, Figure 6 C is the substitution rate between bases, Figure 6 D is the length distribution of deletions, Figure 6 E is the length distribution of insertions, Figure 6 F is the melting temperature diagram of forward and reverse primers.

[0039] Figure 7 Figure 2 is a graph showing the GC content distribution of the primers of the present invention.

[0040] Figure 8 This is a schematic diagram of the assembly of the information DNA of the present invention and the E. coli plasmid vector.

[0041] Figure 9 This is a comparison and decoding diagram of the five DNA sequences generated by PCR and the reference sequence. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0043] like Figure 1 A DNA data storage method with controllable GC content and homopolymers is presented. A DNA storage transcoding scheme based on a 64-ary encoding mapping table is proposed. First, the text to be read or written is compressed, and a Reed–Solomon ("RS") error correction code is added to correct the data. Then, a perturbation sequence is introduced to prevent consecutive occurrences of identical binary elements. Finally, the data is transcoded into a DNA base sequence according to the proposed 64-ary encoding mapping table. The steps of the present invention are as follows:

[0044] Step 1: Perform Lempel-Ziv-Welch ("LZW") compression on the original text and convert the LZW compressed text into a binary code stream.

[0045] An ideal transcoding scheme should satisfy the constraints of DNA encoding and be able to correct insertion and deletion errors. To this end, a transcoding scheme based on a 64-tuple encoding table is proposed.

[0046] Among them, the implementation steps of Lempel-Ziv-Welch ("LZW") compression are: I) initialize the dictionary to contain all possible single characters, and establish the current prefix S initialized to be empty; II) record that the current character C is the next character in the character stream; III) establish an intermediate register D, initialized to be empty, so as to facilitate loading the encoded character stream; IV) determine whether S+C is in the intermediate register D. If "yes", expand S with C, let S=P+C, and return to step II). If "no", output the codeword W=P+C corresponding to the current prefix, and add W to the intermediate register; V) let P=C, and return to step II). The LZW compression algorithm can be used to compress the file into an lz file (e.g., fastq.lz). In this embodiment, the file with storage is first preprocessed, compressed into a zip file using the Gzip algorithm, and further compressed using LZW to generate an lz file (e.g., fastq.gz.lz). Therefore, the storage method can store multiple files (such as 1-5, 5-10, 10-15, etc.) and different types of file formats (such as ".text", ".png", ".MP3", ".MP4", etc.). Take the output value of the LZW compression algorithm, convert it into a binary sequence, and then perform the next step of processing on these binary sequences. In the implementation process, the LZW compression algorithm is used, and repeated characters that appear more times can be represented by short codes, which can achieve a compression rate of 50% to a certain extent. At the same time, for storing multiple files, the LZW compression algorithm has a more outstanding compression rate when processing these large files. The LZW compression algorithm has a wide range of applicability for different file types, and can be used for lossless compression of different file types.

[0047] Constraints in DNA coding include GC content and no-run constraints. GC content refers to the ratio of the total number of G and C bases to the total number of bases in a DNA sequence. GC content is closely related to DNA sequence stability and melting point. To meet these constraints, the designed DNA sequence should be within the range of 40% ≤ GC(n) ≤ 60%. The GC content GC(n) is calculated as follows:

[0048]

[0049] Where GC(n) represents the GC content in a single DNA sequence, |G| and |C| represent the percentage of the net content of a single base "G" and a single base "C" in a single DNA sequence, respectively, and |m| represents the total number of oligonucleotides in the sequence.

[0050] To avoid long, repetitive base sequences (homopolymers), DNA sequences must meet run-length constraints. Long, consecutively repeated bases can cause misreading of the synthesized DNA sequence during subsequent sequencing, reducing decoding robustness. For example, in the sequence TCCCCAC, the base C is repeated. Therefore, during synthesis and sequencing, the long base C can easily be read as a short base C, increasing the error rate of DNA storage and reducing read and write accuracy. Limiting the length of homopolymers can prevent this from happening. For example, AAA is a relatively short homopolymer, with a length controlled between 3 and 5 bases, which can be accurately read by next-generation sequencers.

[0051] For codeword d(D1,D2,D3,...,D n ), where D i ∈(A,T,G,C), for any i, we have the following relationship:

[0052] D i ≠D i+3 ,i∈(1,2,3) (2)

[0053] Among them, D i is the current base, D i+3 are three consecutive bases in the current DNA sequence, and n is the total number of bases in the current DNA sequence.

[0054] Step 2: Split the binary code stream generated in Step 1 into 240-bit segments, and add redundant data to each subchain to generate a binary sequence with redundant bits. For example, a Reed–Solomon ("RS") error-correcting code is applied to multiple binary sequences, and the RS error-correcting code's character check blocks are used to generate binary sequences with check redundancy. Redundancy refers to the robustness against dropout provided by the excess synthetic oligonucleotides. The redundancy in string correction helps correct errors that occur during the oligonucleotide conversion process. The redundancy in block correction can correct for insertions, deletions, and complete loss of information.

[0055] A complete DNA sequence not only includes an information payload region and an error correction region, but also requires an index region to facilitate fast access to information. As previously mentioned, for processing Shakespeare's sonnets, the original text totaled 97,343 bytes. After LZW compression, error correction code addition, and scrambling, a 399,408-bit binary stream was generated. Based on a design scheme with a 129-base information payload region, a 15-base RS error correction region, a 16-base index region, and a 20-base primer region, 1,480 DNA sequences were synthesized. To enable random reads or direct access, each DNA sequence also includes a 16-base index region. For data less than 0.47GB, the index region allows for rapid location and access. Furthermore, primer regions were added to the DNA strands for data backup and sequencing library construction. According to the Illumina sequencing protocol, 20-base primers were added to each end of the single-stranded DNA sequence to facilitate library amplification.

[0056] During the encoding process, the present invention adds an error correction area to improve the stability of the data to prevent errors caused by base mutations. Mainstream error correction codes include Hamming error correction code ("Hamming Code") and Reed–Solomon ("RSCode") error correction code. In comparison, Hamming error correction code can only correct one error or detect multiple errors, while RS error correction code can correct any number of errors. When selecting a coding scheme, it is necessary to ensure the integrity of digital information and to reduce the content of DNA sequence as much as possible to reduce the synthesis cost. Taking into account the fidelity of the DNA sequence and the synthesis cost issues, the present invention selects RS error correction code as the error correction method in the encoding process. The design of each single-stranded DNA sequence fragment is as follows: Figure 2 shown.

[0057] Step 3: Use the chaotic sequence generated by the logical mapping to scramble the binary code stream with the error correction code to obtain a binary sequence.

[0058] Information scrambling is a common method in communications engineering, used to ensure signal transmission security, protect the copyright of transmitted information, and prevent illegal interception and theft. In satellite signal transmission, adding artificial noise is a common scrambling method. There are two approaches to signal scrambling: one is to scramble the coded signal sequence by superimposing a pseudorandom sequence, and the other is to use a cryptographic algorithm (such as DES) to encode and transmit the digitized coded signal in segments. In DNA storage, randomizing the input data with a pseudorandom sequence can effectively break up multi-bit repetitions (for example, 011111111110). Scrambling can reduce the occurrence of long homopolymers during the encoding process and prevent misreading during sequencing, thereby reducing the computational cost of decoding.

[0059] Taking into account the above two aspects, the present invention performs scrambling on the binary code stream after RS ​​error correction coding. In order to achieve a clear, effective and flexible effect, a logical mapping sequence is selected as the perturbation sequence, and the binary code stream after RS ​​error correction coding is subjected to XOR processing. Taking Shakespeare's sonnets as an example, the original text has a total of 97,343 bytes. After LZW compression processing and adding error correction codes, a binary code stream of 399,408 bits is obtained. Then, the present invention uses the chaotic sequence generated by the logical mapping to perform XOR processing on the binary code stream of RS error correction coding to avoid the appearance of long continuous identical elements (such as: 111111000000) in the binary code stream. Such scrambling processing can increase the security and stability of the coding.

[0060] Step 4: From 4 4 = 256 base pairs, 64 base permutations and combinations that meet the constraints are selected as a set of mapping elements to form a 64-element encoding mapping table, and the binary sequence is transcoded into a DNA sequence using the 64-element encoding mapping table.

[0061] The DNA information storage process mainly includes the following four steps: I) encoding digital information into a DNA sequence; II) synthesizing the DNA sequence; III) storing the DNA sequence synthesized in step II); IV) recovering the stored DNA information through sequencing. However, current high-throughput sequencing technologies (such as the Illumina sequencing method) may complicate the pairing between bases during the amplification of DNA sequences, which may cause base mutations and produce longer homopolymers, thereby interfering with the information carried by the original DNA sequence and causing misreading in the subsequent sequencing process. Therefore, in the process of DNA information storage, a good transcoding scheme should meet the following two constraints: 1) avoid long homopolymers; 2) avoid extreme GC content. In order to meet these constraints, the present invention starts from 4 4 = 64 combinations that meet the constraints are selected from 256 different base pairings, forming a 64-ary encoding mapping table.

[0062] In the process of converting binary code stream into DNA sequence, it is noted that when a binary code stream that is too long is mapped to a shorter DNA base sequence, irreversibility will occur, and when a binary code stream that is too short is mapped to a longer DNA base sequence, the information density will decrease and the synthesis cost will increase. 4=Every 4 base permutations and combinations in the 256 coding sets are taken as a group of mapping elements, and these mapping elements are screened by considering the restriction of homopolymers. For example, if the previous group of mapping elements is AAAA, the next group of mapping elements cannot have AAAA again, thereby avoiding the appearance of long homopolymer sequences. At the same time, while considering long homopolymer sequences, it is also noted that if the number of occurrences of bases G and C in each group of mapping elements is too high, extreme GC content will appear when transcoded into DNA sequences. For example, when a group of coding elements is GCGC, its GC content is as high as 100%, which will lead to problems such as difficulty in breaking hydrogen bonds and difficulty in denaturation during the synthesis of DNA sequences. Therefore, mapping elements with a GC content of less than 40% or greater than 60% are screened out from the coding set and excluded from the coding set. After screening, 64 coding mapping tables that meet the requirements are obtained, as shown in Table 1 below.

[0063] Table 1 64-bit encoding mapping table

[0064] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AGAC AGCA AGCT AGTC AGTG AGGA AGGT AGAG ACAG ACAC ACCA ACCT ACTC ACTG ACGA ACGT 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 CAAG CAAC CACA CACT CATC CATG CAGA CAGT CTAG CTAC CTCA CTCT CTTC CTTG CTGA CTGT 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 TCAG ACAC TCCA TCCT TCTC TCTG TCGA TCGT TGAG TGAC TGCA TGCT TGTC TGTG TGGA TGGT 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 GAAG GAAC GACA GACT GATC GATG GAGA GAGT GTAG GTAC GTCA GTCT GTTC GTTG GTGA GTGT

[0065] According to a 2018 study, the base substitution error rate is approximately 0.0015% to 0.0004%, with insertions and deletions being even less likely. Most errors are caused by base-to-base substitution errors, so a theoretical encoding scheme should be able to handle as many substitution errors as possible. Experimentally, factors such as extreme GC content and long homopolymer stretches (such as long homopolymer AAAAA) can lead to substitution errors during synthesis and sequencing. Homopolymer sequences longer than 6 are particularly prone to a significant increase in substitution error rates. Furthermore, DNA sequences with high GC content can exhibit high variability during PCR amplification. In 20 simulated populations sequenced using the IonTorrent PGM 16S rRNA gene, the coefficient of variation reached 11.8% across five separate sequencing runs. This increased coefficient of variation is attributed to increased variation during PCR due to differences in GC content within the base sequence. Once these differences occur, insertions, substitutions, and deletions within the base sequence increase. The 64-ary encoding mapping table proposed in this paper offers potential error correction advantages for variations caused by extreme GC content and substitution errors due to long homopolymers. Simple substitution, deletion and insertion errors can be corrected according to the encoding mapping table, as shown in the following example: Figure 3 The following is a brief description of these three error conditions:

[0066] Case 1: Replacement error

[0067] According to the above encoding method, a DNA sequence such as CTCTTCAGAGGATC is read. During the traversal process, each 4 bases are grouped together. If mapping elements such as TTCT and CCAG that are not in the 64-base encoding mapping table appear, it can be determined that a replacement error has occurred, and the correct mapping element is searched according to the 64-base encoding mapping table for correction.

[0068] Case 2: Deletion Error

[0069] Using the above encoding scheme, a DNA sequence such as "CTCTTCAGAGGATC..." is read. Each group of four bases is grouped together. While the first few groups of DNA sequences are error-free, the last group contains only the base C. Comparison reveals that this DNA sequence is shorter than the designed DNA sequence, indicating a deletion error. Since it's impossible to determine whether the mapped element is ****C or C****, no correction can be made using the 64-bit encoding mapping table. The only detection is a deletion error.

[0070] Case 3: Insert error

[0071] According to the above encoding method, when reading a DNA sequence such as: CTCTTCAGAGGATC..., the DNA sequence is divided into groups of 4 bases during the traversal process. In the reading result, if the second pair of bases in the previous group is CT, and when reading the first pair of bases in the next group, the original DNA sequence is CT, but AC appears in the read sequence, it means that an error has occurred. Then continue to traverse the subsequent bases until the end. By combining with the 64-element encoding mapping table, it can be found that an error has occurred before the AC mapping element, and continue to traverse to the end. When performing sequence alignment, if the number of bases in the read DNA sequence is greater than the number of bases in the designed DNA sequence, it can be determined that an insertion error has occurred. However, the 64-element encoding mapping table according to the present invention can only detect insertion errors and determine the error position, but cannot correct them based on the position. This situation is similar to a deletion error. It is impossible to accurately determine the true situation of the group of base sequences and it is impossible to determine the specific correction for the insertion error.

[0072] The above is a brief description of these three error situations. For some existing substitution errors, the present invention has the advantage of self-correcting performance. By comparing with the 64-ary coding mapping table of the present invention, substitution errors can also be corrected without adding RS error correction code, thereby greatly improving the coding efficiency and saving the cost of synthesizing DNA sequences. However, in actual operation, errors of the insertion and deletion types are often accompanied. In order to ensure the authenticity and integrity of the read information and avoid the situation where decoding fails due to insertion and deletion errors, it is impossible to completely correct the errors by relying solely on the 64-ary coding mapping table of the present invention. In combination with the advantages of the self-correction of the present invention, a relatively simple error correction code is introduced therein. Specifically, the RS (255, 240) error correction code is used to correct each DNA base sequence to ensure the integrity of the DNA sequence.

[0073] By introducing the RS (255, 240) error correction code, it is possible to correct a sufficient number of errors. By introducing 15 bits of error correction redundancy into the 240 information bits, according to the coding density of 2 bases for every 3 bits in the binary code stream of the present invention, the error correction redundancy bits are sufficient to correct various types of errors that occur when the information is transcoded into a DNA sequence. For a single DNA sequence, there are a total of 160 bases, and the RS redundancy bits can correct 10 base errors, with an error coverage rate of 6.25%, far exceeding the error rate of 0.0015% to 0.0004% indicated in the 2018 study, thereby ensuring the reliability of reading the DNA sequence. The RS error correction code is an error correction code scheme that can correct any number of errors. In the scheme of the present invention, the RS (255, 240) error correction code is applied to each DNA base sequence, which can correct a certain number of insertion and deletion errors, thereby enhancing the accuracy and stability of decoding.

[0074] By combining the application of static coding tables and RS error correction codes, the present invention can not only handle substitution type errors, but also correct a certain number of insertion and deletion errors, thereby improving the overall decoding capability and data fidelity.

[0075] Previous literature has proposed several calculation methods and concepts related to information density to evaluate the performance of coding schemes. Among them, the base coding density (bit / nt) describes the number of effective bits carried by a base in actual operation, without considering the effect of the number of molecular copies.

[0076]

[0077] In addition, some concepts have been proposed, such as coding potential and realized capacity, which involve complex theoretical derivations in information theory. However, in the field of DNA storage, these concepts have not been widely accepted due to the large differences in data used in actual applications.

[0078] In their research, the present invention used a DNA sequence length of 129 bases per segment as the information carrier, corresponding to 194 bits of information, and calculated the storage density. To further improve the encoding density, the present invention employed LZW compression before encoding, increasing the density of the stored file, thereby improving the net encoding efficiency of DNA information storage. Ultimately, the net information density achieved was 1.49 bits / nt, a higher encoding efficiency than the encoding method studied by Church, Goldman, et al., resulting in lower costs during synthesis and reading.

[0079]

[0080] As a preferred embodiment, the present invention uses Shakespeare's sonnets as an example to perform a reading test, and the specific steps are as follows:

[0081] I) First, LZW compression is performed on Shakespeare's sonnets (the original text has a total of 97,343 bytes), and the compressed text information is 24,963 bytes.

[0082] II) To ensure the recovery of the text and the fidelity of the original message, the 24,963 bytes were converted into a binary code stream and segmented into 240-bit segments, ensuring that each binary code segment converted into a DNA sequence conformed to 129 bases. Then, error correction redundancy was added to each 240-bit binary segment using the RS error correction coding procedure, adding 15 redundant bits to each segment to correct 10-bit errors.

[0083] III) Next, the chaotic sequence is scrambled on the binary code stream. After the chaotic sequence is added, every 3 bytes of the binary code stream (8 bits per byte, a total of 24 bits) are encoded into 16 bases according to the 64-ary encoding mapping table.

[0084] Ultimately, Shakespeare's sonnets are converted into 266,272 bases. Based on the above calculations, the present invention achieves a theoretical storage density of 399,408 bits / 266,272 bases = 1.5 bits / base. Combining the GC content and homopolymer constraints involved, a summary is listed in Table 2.

[0085] Table 2 Comparison with previous work

[0086]

[0087] In Table 2, Church comes from the literature [CHURCH GM, GAO Y, KOSURI S. Next-Generation Digital Information Storage in DNA [J]. Science, 2012, 337(6102): 1628.], Goldman comes from the literature [ORGANICK L, CHEN YJ, DUMAS ANG S, et al. Author Correction: Probing the physical limits of reliable DNA data retrieval [J]. Nature Communications, 2020, 11(1): 1080.], Grass comes from the literature [GRASS RN, HECKEL R, PUDDU M, et al. Robust Chemical Preservation of Digital Information on DNA in Silica with Error-Correcting Codes [J]. Angewandte Chemie, 2015, (54-8).], and Bornholt comes from the literature [BORNHOLT J, LOPEZR, CARMEAN DM, et al. A DNA-Based Archival Storage System [J]. IEEE Micro, 2016, PP(4):637-49.], Blawat comes from the literature [BLAWAT M, GAEDKE K, HUETTER I, et al. Forward Error Correction for DNA Data Storage[J]. Procedia Computer Science, 2016, 80:1011-22.], DNA fountain code comes from the literature [ERLICH Y, ZIELINSKID. DNA Fountain enables a robust and efficient storage architecture[J]. Cold Spring Harbor Laboratory, 2016, (6328).], and yin-yang coding comes from the literature [Towards practical and robust DNA-based dataarchiving using the yin-yang codec system[J]. Nature Computational Science.].As can be easily seen from Table 2, the present invention is superior to other coding schemes in terms of GC content control and avoiding long homopolymers. In terms of coding density, it is also slightly higher than the coding schemes of Church, Goldman, Grass, etc., so that the cost input can be reduced during synthesis and sequencing, and the authenticity and integrity of the stored information can be ensured during reading.

[0088] During the data transmission process, the purpose of scrambling is to randomize the original binary bit stream. To achieve this goal, in the binary bit stream after adding the error correction code, a specific chaotic sequence is used for scrambling and descrambling is performed before decoding. Specifically, a logical mapping chaotic sequence is introduced, and its expression is:

[0089] x n+1 =rx n (1 - x n ) (5)

[0090] where x n and x n+1 represent the elements obtained from the nth and (n + 1)th iterations respectively. For the case of 3.569945627 < r ≤ 4, using the characteristics of high sensitivity and unpredictability of the logical chaotic sequence, the above-mentioned sequence and the binary bit stream after adding the error correction code are XOR processed to avoid too many consecutive {0, 1} in the binary bit stream, thus preventing the occurrence of long consecutive identical bases in the subsequent DNA base sequence synthesis process. In addition, the process of adding the perturbation sequence can also play a role in encryption.

[0091] Figure 4 shows the proportion of {0, 1} elements before and after sequence scrambling and the chaotic degree of the sequence at different periods. According to Figure 4 (a) observation, the distribution density of the x(n) values generated by the logical mapping sequence between 3.7 < r ≤ 4 is much higher than that between 2.5 < r ≤ 3.7. Therefore, the chaotic sequence generated by r = 3.8 and the given parameter x0 = 4.0 is XOR processed with the binary bit stream. After the perturbation sequence is added, the number of 0s and 1s in the binary sequence is relatively evenly distributed around 50%.

[0092] A high GC content will cause hydrogen bonds to be difficult to break and make DNA denaturation difficult. To increase the melting point to break hydrogen bonds, an increase in temperature will increase the activity of DNA bases, thus increasing the probability of DNA base mutation and resulting in an increase in the error rate during DNA sequencing. Therefore, these factors need to be weighed when controlling the GC content.

[0093] The present invention and several other transcoding methods were tested on five different texts (i.e., Shakespeare sonnets, DNA fountain code abstracts, the entire poem "Aman Jiang Hong", the Photographer 256, and the full text of a 26-key keyboard) to compare their GC content. For each text, a sequencing depth of 10× was used, and the average GC content percentage of each transcoding scheme was calculated. The results are shown in Figure 2. Figure 5 (a) to (e) are shown. Figure 5 As can be seen, the DNA fountain code transcoding scheme controls the average GC content between 40% and 60%. Church's transcoding scheme maintains an average GC content between 25% and 80%. Grass's transcoding scheme slightly reduces the average GC content compared to Church's scheme, controlling it between 25% and 78%, but it does not fully meet the requirements of the sequencing method. Goldman's transcoding scheme controls the average GC content between 15% and 60%, which is still lower than DNA fountain codes and yin-yang coding.

[0094] Taking into account the requirements of the third-generation sequencing system for GC content and the constraints of upstream and downstream biological experiments, the present invention controls the average GC content between 49% and 51%, which better adapts to the requirements of the third-generation sequencing method in biological experiments. This can reduce the number of substitution, deletion and insertion errors of DNA bases during the sequencing process.

[0095] Currently, the most accurate third-generation sequencing technology cannot fully read DNA homopolymer sequences, especially when it comes to multiple consecutive base repeats. In the method of the present invention, by reducing the homopolymer length to a minimum, a 10× sequencing depth test was performed on the storage file Photo 1 (photographer 256). The performance of several different transcoding schemes in terms of homopolymer length distribution (denoted as length n) was compared. The specific results are as follows: Figure 5 As shown in Figure F, it can be seen that for the DNA fountain code and yin-yang coding transcoding schemes, the homopolymer length is mostly concentrated at n = 4. Compared with other transcoding schemes, the homopolymer lengths of these two schemes are longer. This is because they are dynamic codes and cannot control the generation of the next base, which is also a disadvantage of dynamic coding.

[0096] In contrast, the transcoding methods of Blawat and Bornholt mostly focus on homopolymer lengths between n = 1 and 2. In Grass's transcoding scheme, most homopolymer lengths are between n = 2 and 3, with the longest homopolymer length being n = 4. By comparison, the present invention successfully controls homopolymer lengths within the range of n = 1 to 2, meeting the homopolymer constraint requirements during sequencing.

[0097] In the Shakespeare sonnet simulation experiment, 64 mapping elements were randomly selected from the 256 encoding sets to construct the encoding mapping table. Then, the base substitution error rate between (G, C) and (T, G) in the 64-element encoding mapping table was compared with the difference between the random encoding table, such as Figure 6 A. Figure 6 The results show that when the 64-tuple encoding mapping table is used, the substitution error rate between (G, C) decreases by 1.08%, and the substitution error rate between (T, G) decreases by 18.01%. However, the base substitution error rate between (T, C) and (A, C) increases slightly, but does not exceed 10%. For details, see Figure 6 C. Obviously, the solution using the 64-ary encoding mapping table proposed by the present invention has a lower base substitution error probability than the random encoding table.

[0098] The present invention uses the Flye platform to assemble the DNA sequences generated by the complete Shakespeare sonnets from scratch. According to the 64-ary coding mapping table, these sequences generated a total of 266,272 bases (note that only the information area was analyzed for errors, and the index and other areas were not error-corrected). The present invention divides these DNA sequences into information payloads and RS error correction fragments (129nt+15nt), obtaining a total of 1850 DNA chains, which are then restored. Pseudo-random errors (the number of insertions and deletions is equal) are added to the generated DNA sequences. Simulations found that the frequency of the error of losing 200 bases is less than 1%, and the error frequency of inserting 20 bases is almost close to 0. Therefore, the encoding method based on the 64-ary coding mapping table can ensure high robustness recovery.

[0099] When recovering stored data, the key is to recover the information carried by the DNA sequence in the payload region. Reed-Solomon block codes, as a maximum distance separable code, effectively protect consecutive nucleotides. In the present invention, RS coding is used for error correction, with a block size of 240 bits of payload and 15 bits of redundancy added, i.e., RS(255,240,15).

[0100] According to information theory, errors can be divided into random errors and erasure errors. In order to solve these errors, this paper adopts the forward error correction method. In this method, random errors are unknown, while erasure errors are known. If E e Indicates erase error, with E r Indicates random errors, then RS(255,240,15) should meet the following conditions:

[0101] nk≥E e +2×E r (6)

[0102] Where n is the total number of bits in the current information segment, and k is the number of information payload bits in the current information segment.

[0103] When a base is inserted or deleted in a DNA sequence, this indicates an erasure error. Since erasure errors are known to exist, substitution errors (random errors) need to be considered when designing error-correcting codes. It is important to note that since no external error-correcting code is added to the primer and index regions for protection, only the information bits in the payload region are analyzed for single-fragment reads.

[0104] Table 3 Summary of the number of incorrectly substituted nucleotides

[0105] Text 1 Text 2 Photo 1 Total DNA bases 266272 2255 475653 Test the number of bases in a DNA chain 1290 1290 1290 Add replacement error 80 2 120 Can it be successfully restored? yes yes yes Total decoding rate 100％ 100％ 100％

[0106] Table 4 Summary of the number of inserted and deleted nucleotide errors

[0107] Text 1 Text 2 Photo 1 Total DNA bases 266272 2255 475653 Test the number of bases in a DNA chain 1290 1290 1290 Add insert, delete errors 20 5 20 Total decodable bases 1288 1290 1273 Partial decoding rate 99.84％ 100％ 98.68％

[0108] Based on the data in Table 3, experiments were conducted on three texts: Text 1 (Shakespeare's Sonnets), Text 2 (DNA Fountain Code Abstract), and Photo 1 (Photographer 256). For Text 1 (Shakespeare's Sonnets), a total of 266,272 nucleotides were synthesized, from which a subset of bases (129 nt × 10 strips, totaling 1,290 bases) was selected for testing. 80 base substitution errors were randomly introduced into each DNA sequence, and then an automatic recovery experiment was performed. By adding an RS (255,240) error correction code to the information payload, the original text was successfully recovered. The same processing as for Text 1 was performed on Text 2 (DNA Fountain Code Abstract) and Photo 1 (Photographer 256). The results are shown in Table 4.

[0109] Based on the results in Table 4, 1290 bases (129 nt × 10 strands) were randomly selected from all generated DNA sequences for simulation experiments involving insertion and deletion errors. For Text 1 (Shakespeare's Sonnets), DNA strands #1 to #5 were randomly subjected to insertion errors of 1 to 4 bases, respectively, while strands #6 to #10 were randomly subjected to deletion errors of 1 to 4 bases, respectively. During the simulation, the number of base errors among these 1290 test bases was counted. For the sequence labeled DNA strand #8 in Text 1, only two bases were deleted (actually, three bases should have been deleted), resulting in decoding failure and a decoding rate of 99.84%. For Text 2 (DNA Fountain Code Abstract), the number of errors introduced during the simulation was smaller and fully recovered. For photo 1 (Photographer 256), the same processing as for Text 1 (Shakespeare's Sonnets) was performed, with the results shown in Table 4.

[0110] According to the encoding rules mentioned above, Shakespeare's sonnets generated a total of 266,272 bases (1,850 DNA sequences). In order to obtain these DNA sequences, short homologs with a sequence length of 143 bases were first synthesized, and then primers were designed for the short homologs of 143 bases using the Oligo 7 program to facilitate subsequent PCR operations. Figure 2 Based on the DNA sequence design requirements and the melting temperature requirements in actual PCR operations, the primer sequence design for the short homolog was 20 bases ± 1 base, Tm = 53.9°C, and the final forward primers and reverse primers were shown in Table 5 (part).

[0111] The GC content test and melting temperature Tm statistics were performed on the above primer sequences. The results are as follows Figure 6 F and Figure 7 As shown, according to Figure 6 The melting temperatures of all designed primer sequences shown in F are within a reasonable range (45°C to 65°C). Figure 7 No primer sequences with excessive GC content were found, with the highest GC content being 56% and the lowest being 44%. Sequence recombinants were then performed using forward and reverse primers designed for the DNA sequence described above, combined with the transcoded DNA sequence of the present invention. GC content testing of the recombined sequences revealed that all sequences had GC contents between 40% and 60%, demonstrating that the primer design of the present invention is well-suited for DNA reading technology and prevents excessive reading errors.

[0112] Table 5 Forward and reverse DNA sequence primer design

[0113]

[0114] according to Figure 8As shown in the figure, the information DNA is recombined with the plasmid vector of E.coli. The recombinant E.coli plasmid vector contains resistance genes, integrase genes, starting replication sites along the direction of the information DNA sequence, etc. E.coli is then chemically transformed. In order to ensure the fidelity of the information DNA sequence during sequencing, a double-stranded design is adopted for the information DNA sequence. The forward sequencing is the information DNA sequence, and the reverse sequencing requires further transcription to obtain a sequence consistent with the information DNA sequence. The forward information DNA sequence is cut with EcoR I enzyme, and the reverse information DNA sequence is cut with Xba I enzyme. Then, the information DNA sequence is integrated into E.coli using T7 DNA ligase, thereby causing the information DNA to be replicated along with the E.coli plasmid vector to increase in value, as shown in FIG. Figure 8 In order to completely integrate the synthesized information DNA (96 kb) into the E. coli plasmid vector, the integration process was repeated twice.

[0115] The present invention uses excerpts from Shakespeare's sonnets to simulate PCR amplification of DNA sequences. First, after transcoding the original text into a DNA sequence, each 129 bases in the DNA sequence is divided into short homologs. Short homolog primers are designed using Oligo 7 primer design software, and finally recombined into a new DNA sequence. SnapGene software is used to simulate PCR on the recombinant DNA sequence, and a short homolog DNA sequence is intercepted and amplified 5 times by PCR. The melting temperature is set to Tm = 60 ° C. Finally, the information DNA sequence in the sequence after PCR amplification is intercepted and multiple sequence comparison is performed to restore the correct original sequence. The results are as follows: Figure 9 As shown. Figure 9 It can be seen that the encoding and error correction scheme designed by the present invention can completely restore the original information by decoding the DNA sequence generated after polymerase chain reaction (PCR) after multiple sequence alignment.

[0116] The present invention successfully simulates texts such as Shakespeare's sonnets, and analyzes GC content, homopolymers, and error correction performance. The proposed 64-element encoding mapping table can well meet the constraints in subsequent biological experiments. The present invention can avoid the increase in errors such as base substitutions, deletions, and insertions due to extreme GC content, and can also prevent misreading during sequencing due to long homopolymers. The present invention analyzes error correction performance and single-fragment reading performance, and performs recovery rate statistics on data reading of Shakespeare's sonnets, DNA fountain code abstract (text), full poem of "Man Jiang Hong" (text), Photographer 256 (picture), and full character (character) of a 26-key keyboard. In terms of coding efficiency, the coding storage density of the present invention is 1.49 bit / nt, which improves the coding density.

[0117] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A DNA data storage method with controllable GC content and homopolymer, characterized in that: The steps are as follows: Step 1: Perform LZW compression on the original text and convert the LZW compressed text into a binary code stream; Step 2: Add RS error correction code to the binary code stream to generate a binary code stream with error correction code; Step 3: Use the chaotic sequence generated by the logical mapping to scramble the binary code stream with the error correction code to obtain the final binary code stream to be converted into a DNA sequence; Step 4: 64 base pairing combinations that meet the constraints are selected as a set of mapping elements, each of which is a 64-element encoding mapping table. The binary sequence is converted into a DNA sequence using the 64-element encoding mapping table. The DNA sequence is provided with an information load region and a RS error correction region, an index region is provided at the rear end of the RS error correction region, and primer regions are added to both ends of the DNA sequence; an RS error correction code is provided in the RS error correction region; The scrambling method is as follows: using a chaotic sequence as a disturbance sequence and performing an exclusive OR process on a binary code stream that has undergone RS error correction coding; The method for generating chaotic sequence by logical mapping is: x n+1 =rx n (1-x n ) where x n and x n+1 represent the elements obtained in the n-th and (n + 1)-th iterations respectively, and r is a control parameter; a chaotic sequence is generated when 3.569945627 < r ≤ 4; The chaotic sequence generated by the control parameter r = 3.8 and the given parameter x0 = 4.0 is XORed with the error correction binary code stream; The constraints in step 4 include: the length of the homopolymer is less than 6; the GC content in the DNA sequence is kept between 40% and 60%; the method for forming the 64-ary encoding mapping table is: 4 =Every four base permutations in the 256 base pairing sets are taken as a set of mapping elements, and the mapping elements are screened considering the constraints of homopolymers and GC content.

2. The method for storing DNA data with controllable GC content and homopolymer according to claim 1, characterized in that: The length of the information payload region is 129 bases, the length of the RS error correction region is 15 bases, the index region is provided with 16 bases, and the primer region is provided with 20 bases.

3. The method for storing DNA data with controllable GC content and homopolymer according to claim 1 or 2, characterized in that: Each generated DNA sequence was corrected using RS (255,240) error correction code to correct a certain number of insertion and deletion errors.

4. The method for storing DNA data with controllable GC content and homopolymer according to claim 3, characterized in that: The RS error correction code is the error correction code RS(255,240,15), where the error correction code block size is 240 bits of payload, obtained by adding 15 bits of redundancy, and the error correction code RS(255,240,15) satisfies: n-k≥E e +2×E r Where n is the number of bits with error correction code, k is the number of bits of information payload, and E e Indicates erase error, E r Indicates a random error.

5. The method for storing DNA data with controllable GC content and homopolymer according to claim 4, characterized in that: The implementation method for text storage includes the following steps: a) performing LZW compression on the text to be stored containing multiple bytes to obtain compressed text information; b) converting the compressed text information into a binary code stream according to ASCII code, dividing each 240 bits into segments, and adding 15 redundant bits to each segment; c) XORing the binary code stream with the RS error correction code with the chaotic sequence generated by the logical mapping, encoding every 24 bits of the scrambled binary code stream into 16 bases according to the 64-ary encoding mapping table, and finally obtaining the converted base sequence.

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