CN112350799B - Error correction method, system, device and medium for channel coding - Google Patents

Error correction method, system, device and medium for channel coding Download PDF

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CN112350799B
CN112350799B CN202011006117.2A CN202011006117A CN112350799B CN 112350799 B CN112350799 B CN 112350799B CN 202011006117 A CN202011006117 A CN 202011006117A CN 112350799 B CN112350799 B CN 112350799B
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redundant
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integer
remainder
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CN112350799A (en
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穆丽伟
陈梦兰
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South China Normal University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/22—Arrangements for detecting or preventing errors in the information received using redundant apparatus to increase reliability
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0076—Distributed coding, e.g. network coding, involving channel coding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/24—Testing correct operation
    • H04L1/245—Testing correct operation by using the properties of transmission codes
    • H04L1/246—Testing correct operation by using the properties of transmission codes two-level transmission codes, e.g. binary
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention provides an error correction method, a system, a device and a medium for channel coding, wherein the method executed by a transmitting end comprises the steps of acquiring a binary information sequence of a source; obtaining a non-redundant remainder sequence according to the source binary information sequence and a preset non-redundant module; encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module; obtaining a residual sequence according to the redundant remainder, performing molecular shift keying modulation on the sequence, and transmitting the modulated molecular information to a receiving end; the algebraic property of the coding and decoding processes in the method reduces the complexity of algorithm implementation, different redundancy numbers are represented by different types of molecules, and the molecules of different types cannot interfere with each other, so that the condition of intersymbol interference in the process is relieved, and the method can be widely applied to the technical field of communication.

Description

Error correction method, system, device and medium for channel coding
Technical Field
The invention belongs to the technical field of communication, and particularly relates to an error correction method, system, device and medium for channel coding.
Background
High reliability and low latency are two important indicators of future communication systems. Taking molecular communication as an example, a molecular communication system consists of nano-elements of 0.1 μm-10 μm, which transfer information by diffusion or through media such as calcium signals, microtubules, pheromones, bacteria, etc. The system in which molecules are transported through free diffusion channels is called the molecular diffusion system (molecular diffusion system, MDS). At the receiving end of the MDS, the symbol received at the current time is determined by all received molecules including the remaining molecules from the previous symbol, which may lead to inter-symbol interference (inter-symbol interference, ISI). ISI severely affects the demodulation process because the arrival profile of messenger molecules exhibits severe tailing characteristics. Thus, the error information received by the MDS receiver is mainly due to ISI.
The prior art proposes several approaches to solve the ISI problem in MDS, such as: the received signal is processed using an ISI cancellation module to remove ISI symbols. Next, several channel coding techniques have been proposed to mitigate intersymbol interference by adding redundant binary bits to the input information. Obviously, the additional ISI modules and highly redundant channel coding techniques of MDS systems consume more energy and increase transmission delay. Also for example: an ISI reducing technique in which an enzyme is added to a channel, in which excess messenger molecules in the channel react with the enzyme molecules and disappear in the transmission environment, is advantageous at the cost of a complex molecular synthesis mechanism at the transmitter side.
Disclosure of Invention
In view of the above, in order to partially solve one of the above technical problems, an embodiment of the present invention is to provide a highly reliable and low-delay error correction method for channel coding; meanwhile, the embodiment of the invention also provides a transmitting end system, a receiving end system, a device and a medium which can realize the corresponding method.
In a first aspect, an embodiment of the present invention provides an error correction method for channel coding, including the steps of:
acquiring a binary information sequence of a source;
obtaining a non-redundant remainder sequence according to the source binary information sequence and a preset non-redundant module;
encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module;
and obtaining a residual sequence according to the redundant remainder, performing molecular shift keying modulation on the residual sequence, and transmitting the modulated molecular information to a receiving end.
In some embodiments of the present invention, the step of obtaining a non-redundant remainder sequence according to a source binary information sequence and a preset non-redundant mode specifically includes:
dividing the binary information sequence to obtain a plurality of information blocks; and determining the length of the information block according to the non-redundant mode;
and converting the binary information sequence in the information block into a decimal information sequence to obtain a non-redundant remainder sequence.
In some embodiments of the present invention, the step of generating a redundancy remainder according to the first integer value and a preset redundancy modulus specifically includes:
determining a redundant remainder and a residual sequence through a first integer value and a preset redundant module; wherein the residual sequence includes a non-redundant remainder sequence and a redundant remainder.
In some embodiments of the present invention, the step of performing molecular shift keying modulation on the residual sequence specifically includes:
the binary sequence is converted to a pulse signal, the pulse signal comprising at least one molecular type, wherein the molecular type comprises an organic matter and a hydrofluorocarbon.
In a second aspect, an embodiment of the present invention provides an error correction method for channel coding, including the steps of:
acquiring molecular information of a transmitting end; the molecular information is obtained by molecular shift keying modulation;
decoding according to the molecular type and the molecular concentration of the molecular information;
correcting errors in the residual sequence obtained after decoding; the residual sequence comprises a redundant remainder sequence and a non-redundant remainder sequence;
the correction process comprises the following steps: generating a non-redundant modulo projection and a redundant modulo projection of a first integer value; replacing the first integer value according to the non-redundant modulo projection or the redundant modulo projection; the first integer value is encoded by a non-redundant remainder sequence.
In some embodiments of the present invention, the step of correcting an error in a residual sequence obtained after decoding specifically includes:
acquiring a first residual number of molecular information of a transmitting end, acquiring a second residual number of decoded information, and determining a single bit error according to the first residual number and the second residual number;
and determining that the single-bit errors belong to a correctable error set, and correcting the single-bit errors.
In a third aspect, the present invention further provides a transmitting end system for error correction of channel coding, including a preprocessing unit, a code conversion unit, and a transmission unit, where:
the preprocessing unit is used for acquiring a binary information sequence of the information source, dividing the binary information sequence into a plurality of information blocks and determining the length of the information blocks according to a non-redundant mode;
the code conversion unit is used for obtaining a non-redundant remainder sequence according to the information source binary information sequence and a preset non-redundant module; encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module; obtaining a residual sequence according to the redundant remainder;
and the transmission unit is used for carrying out molecular shift keying modulation on the residual sequence and transmitting the modulated molecular information to the receiving end system.
In a fourth aspect, the present invention further provides a receiving end system for error correction of channel coding, including a receiving unit and a correcting unit;
the receiving unit is used for acquiring the molecular information of the transmitting end; the molecular information is obtained by molecular shift keying modulation;
a correction unit that decodes according to the molecular type and the molecular concentration of the molecular information; correcting errors in the residual sequence obtained after decoding; wherein the residual sequence comprises a redundant remainder sequence and a non-redundant remainder sequence; wherein the correcting process comprises the following steps: generating a non-redundant modulo projection and a redundant modulo projection of a first integer value; replacing the first integer value according to the non-redundant modulo projection or the redundant modulo projection; the first integer value is encoded by a non-redundant remainder sequence.
In a fifth aspect, the present invention further provides an apparatus for error correction of channel coding, including:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement a method of error correction for channel coding in the first or second aspect.
In a sixth aspect, the present invention provides a storage medium having stored therein a processor executable program which when executed by a processor is for implementing the method as in the first or second aspect.
Advantages and benefits of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention:
according to the technical scheme, the transmission end encodes through a preset mode and a binary information sequence, and transmits through a molecular diffusion channel after being modulated through molecular shift keying. Demodulating at a receiving end through a molecular type, and correcting single errors in the decoded residual sequence; the algebraic property of the coding and decoding processes in the method reduces the complexity of algorithm implementation, different redundancy numbers are represented by different types of molecules, and the molecules of different types cannot interfere with each other, so that the condition of intersymbol interference in the process is relieved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart illustrating steps of an error correction method performed by a transmitting end in accordance with an embodiment of the present invention;
FIG. 2 is a flowchart illustrating the detailed steps of a method for error correction by channel coding at a receiving end according to an embodiment of the present invention;
FIG. 3 is a graph of Bit Error Rate (BER) performance of a transmission information sequence obtained by simulation in an embodiment of the present invention;
fig. 4 is a schematic diagram of an access device based on multiple security protocols according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
The core idea of the technical scheme provided by the embodiment of the invention is that the (k+1, k) redundant remainder system (redundant residue number system, RRNS) code is adopted, so that the high reliability and low delay of the communication process are improved. The description will take a molecular diffusion system (molecular diffusion system, MDS) as an embodiment, and the scheme combines the error correction performance of the (k+1, k) RRNS channel coding algorithm with the molecular shift keying (molecule shift keying, moSK) modulation technique. The RRNS code consists of k information bits and one extra redundant bit, and corrects a single error in an error space by an algebraic decoding method at a receiving end. In addition, the algebraic nature of the RRNS encoding and decoding algorithms reduces the complexity of algorithm implementation. And converting the binary sequence to be transmitted into a redundancy number sequence by adopting a (k+1, k) RRNS coding method, and then mapping each redundancy number to a corresponding molecular type. The different types of molecules represent different redundancy numbers, and the different types of molecules do not interfere with each other, which alleviates the inter-symbol interference in MDS.
In a first aspect, in the system of the present embodiment, a transmission terminal system and a reception terminal system are included.
The transmitting terminal system comprises a preprocessing unit, a code conversion unit and a transmission unit, wherein: the preprocessing unit is used for acquiring a binary information sequence of the information source, dividing the binary information sequence into a plurality of information blocks, and determining the length of the information blocks according to the non-redundant mode. The code conversion unit is used for obtaining a non-redundant remainder sequence according to the information source binary information sequence and a preset non-redundant module; encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module; and converting according to the redundant remainder to obtain a residual sequence. And the transmission unit is used for carrying out molecular shift keying modulation on the binary sequence and transmitting the modulated molecular information to the receiving end system.
The receiving terminal system includes a receiving unit and a correcting unit, wherein: the receiving unit is used for acquiring the molecular information of the transmitting end system; the molecular information is obtained by molecular shift keying modulation. A correction unit that decodes according to the molecular type and the molecular concentration of the molecular information; correcting errors in the residual sequence obtained after decoding; wherein the residual sequence includes a redundant remainder sequence and a non-redundant remainder sequence.
In a second aspect, as shown in fig. 1, an embodiment of the present invention further provides an error correction method for channel coding performed by a transmitting end, which mainly includes steps S01-S04:
s01, acquiring a binary information sequence of the information source. Specifically, a binary information sequence of data or signals to be transmitted by a source is obtained.
S02, obtaining a non-redundant remainder sequence according to the source binary information sequence and a preset non-redundant mode. Specifically, the obtained source binary information sequence is subjected to necessary preprocessing, wherein the preprocessing process comprises, but is not limited to, partitioning processing of the binary information sequence, and the block length of each partitioned unit block is determined according to a preset non-redundant module in the partitioning processing process. More specifically, in the present embodiment, step S02 can be further subdivided into steps S021 and S022:
s021, dividing the binary information sequence to obtain a plurality of information blocks; and determining the length of the information block based on the non-redundant mode. Specifically, the predetermined non-redundant mode is m i If i is equal to or greater than 1 and equal to or greater than k, the sequence of the obtained redundant mode is (m) 1 ，m 2 ...，m k ). Dividing the binary information sequence into blocks, wherein the block length of each unit block is B bits:
Figure BDA0002695943360000051
in the case of the formula (1),
Figure BDA0002695943360000059
is the largest integer less than x.
S022, converting the binary information sequence in the information block into a decimal information sequence to obtain a non-redundant remainder sequence. Each is put into
Figure BDA00026959433600000510
Conversion of a binary information sequence of bit lengths into decimal numbers x i (i=1, 2,..k), i.e., a non-redundant remainder, and the sequence consisting of non-redundant remainder is a non-redundant remainder sequence.
S03, encoding according to the non-redundant remainder sequence to obtain a first integer value; and generating a redundancy remainder according to the first integer value and a preset redundancy module. From x i (i=1, 2,.,. K) obtaining a first integer value X, and passing through the non-redundant module in step S02 and the preset redundant module m k+1 Generating a redundant remainder
Figure BDA0002695943360000052
Specifically, k+r bit mode (m 1 ，...，m k+r ) When r=1, then the range [0, m k )，/>
Figure BDA0002695943360000053
Called legal range, interval [ M k ，M)，
Figure BDA0002695943360000054
Figure BDA0002695943360000055
Is an illegal range, and [0, M) is a total range. For a first integer value X, X ε [0, M k ) Then (k+1) weight vector (x 1 ，x 2 ...，x k+1 ) Can be defined explicitly, wherein:
Figure BDA00026959433600000511
in an embodiment, the definition of the integer value X is:
Figure BDA0002695943360000056
/>
in the formula (3) of the present invention,
Figure BDA0002695943360000057
a i is a mixed base number, and a is more than or equal to 0 i ＜m i The calculation formula of the mixed base is as follows:
Figure BDA0002695943360000058
in some embodiments, in step S03, the process of generating a redundancy remainder according to the first integer value and the preset redundancy modulus further includes step S031, determining the redundancy remainder and the residual sequence by the first integer value and the preset redundancy modulus; wherein the residual sequence includes a non-redundant remainder sequence and a redundant remainder.
Specifically, for equation (2), at [0, M k ) The integer X corresponding to the range can be uniquely from any k long residual sequence
Figure BDA0002695943360000069
And (3) recovering. (k+1) weight vector (x 1 ，x 2 ...，x k+1 ) I.e. a residual sequence, in which (x 1 ，x 2 ...，x k ) For non-redundant remainder sequences and x k+1 I.e. redundancy residues.
S04, obtaining a residual sequence according to the redundant remainder, performing molecular shift keying modulation on the sequence, and transmitting the modulated molecular information to a receiving end. Specifically, the decimal sequence is first converted into a binary sequence, and then different types of molecules are used to represent different symbols through MoSK modulation. By using MoSK modulation, one symbol can transmit n bits of information. Since an n-bit long information sequence may represent 2n different symbols, this requires the sender to send 2n different types of molecules. The receiver receiving in one time slotThe type and concentration of the molecules reached decodes the symbols. The molecular type may be an organic chemical compound, such as a DNA fragment, a protein, a peptide, or a specifically formed molecule, such as a hydrofluorocarbon-based molecule. For example, in an embodiment, the transmitter at the transmitting end has at most
Figure BDA0002695943360000061
The type of molecule is used to transmit information to the receiving end. More specifically, N is transmitted TX Personal->
Figure BDA0002695943360000062
The type of molecule being pulsed to transmit a residual number x i ，x i ∈[0，m i ) Each x is i The number of emitted molecules is N TX . The molecular pulse is always transmitted at the beginning of a time slot with duration T s Also referred to as symbol duration.
As shown in fig. 2, the error correction method of channel coding performed by the receiving end corresponding to the transmitting end mainly includes steps S05-S06:
s05, acquiring molecular information of a transmitting end; decoding is performed according to the molecular type and the molecular concentration of the molecular information. The molecular information is data information which is modulated by molecular shift keying and then transmitted to the receiving end by the sending end. At the receiving end, at each symbol duration T s The most numerous molecular types received internally are demodulated.
S06, correcting errors in the residual sequence obtained after decoding; wherein the sequences include redundant remainder sequences and non-redundant remainder sequences. Wherein the correcting process comprises the following steps: generating a non-redundant modulo projection and a redundant modulo projection of a first integer value; replacing the first integer value according to the non-redundant modulo projection or the redundant modulo projection; the first integer value is encoded by a non-redundant remainder sequence.
Specifically, according to the division of the synthesis section in step S03, the method is represented by (x 1 ，x 2 ，...，x i ...，x k+r ) A legal number X, i.e. the first integer value in S03, represented by any k-bit remainder of (a); for example, if a firstThe ith remainder is wrong and becomes a different integer
Figure BDA0002695943360000063
According to this feature, at the receiving end, single symbol errors generated in the demodulated residue sequence can be corrected by steps S07-S08:
s07, if the integer is calculated by the formula (3)
Figure BDA0002695943360000064
Is illegal, then->
Figure BDA0002695943360000065
Figure BDA0002695943360000066
M defined as X i And (5) projection.
S08, if m k+1 Projection of (a)
Figure BDA0002695943360000067
Legal, then the redundancy number is wrong, corrected to be +.>
Figure BDA0002695943360000068
If two legal projections occur, for example: />
Figure BDA0002695943360000071
and />
Figure BDA0002695943360000072
Then assume a non-redundant number x i Error, but->
Figure BDA0002695943360000073
Is the correct number after correction. If three or more legal projections are found, no error correction is performed and decoding is stopped.
It should be appreciated that in some embodiments, the process of correcting symbol errors in the residual sequence resulting from decoding may be accomplished by the Barsi-Maestrini algorithmThe (k+1, k) RRNS code can be obtained by finding the appropriate redundancy modulo m k+1 To correct a single symbol error. The process comprises the steps of S061 and S062:
s061, acquiring a first residual number of molecular information of a transmitting end, acquiring a second residual number of decoded information, and determining a single bit error according to the first residual number and the second residual number; more specifically, step S061 may be further subdivided into steps S0611-S0614:
s0611, RRNS in the embodiment is defined as k+r pairwise prime positive integers (m 1 ，...，m k+r ) And m is 1 ＜m 2 ＜…＜m k+r For example: (m) i ，m j )＝1，i≠j。(m i ，...，m k+r ) Referred to as a modulus, in which the (m 1 ，m 2 ，...，m k ) Called non-redundant mode, an additional r modes (m k+1 ，m k+2 ...，m k+r ) Referred to as redundancy model. Obtaining a predetermined non-redundant modular sequence (m 1 ，m 2 ...，m k ) For each modulo m in the sequence i 1.ltoreq.i.ltoreq.k, and for each integer
Figure BDA0002695943360000074
Determining the smallest integer +.>
Figure BDA0002695943360000075
Let inequality (1) be for each m j ≠m i (1. Ltoreq.j. Ltoreq.k) is true:
Figure BDA0002695943360000076
for each die m i Defined integer
Figure BDA0002695943360000077
Healthy integer ++>
Figure BDA0002695943360000078
A partial order is determined in the set of (1), i.e. in the set of +.>
Figure BDA0002695943360000079
In (a) if->
Figure BDA00026959433600000710
Figure BDA00026959433600000711
Then not +.>
Figure BDA00026959433600000712
Is a consequence of the above.
S0612, for each m i Define an integer set
Figure BDA00026959433600000713
Is a subset P of i ，P i Any element->
Figure BDA00026959433600000714
Part is not element->
Figure BDA00026959433600000715
Is->
Figure BDA00026959433600000716
Any element->
Figure BDA00026959433600000717
Nor->
Figure BDA00026959433600000718
Is a consequence of the above. P (P) i The potential of the catalyst is represented as card (P i )：
Figure BDA00026959433600000722
wherein ,
Figure BDA00026959433600000723
is the smallest integer greater than x.
S0613, the present embodiment defines m R ＝m k +1 is a pair of prime numbers given by m i (1. Ltoreq.i.ltoreq.k) to make
Figure BDA00026959433600000719
Thereafter, a subset P of positive integers is determined R Make the following steps
Figure BDA00026959433600000720
For P R Each element of (2)
Figure BDA00026959433600000721
When t is not equal to j, t is not less than 1 and not more than k+1, and j is not less than 1 and not more than k.
S0614, slave subset P 1 ，P 2 ，...，P K ，P R Using the relation:
Figure BDA0002695943360000081
/>
in formula (8), p i ∈P i ，e i ∈E i ，e i ，p i ∈(0，m i )，
Figure BDA0002695943360000082
Determining subclass { E 1 ，E 2 ，...，E k ，E R}, wherein Ei Is a set of correctable errors, +.>
Figure BDA00026959433600000816
So that m is the modulus 1 ，m 2 ...，m k ，m R In RRNS code of (c), single symbol error correction is possible.
S062, when the single-bit errors belong to the correctable error set, correcting the single-bit errors. For example, in an embodiment the ith remainder corresponds to two words in binary form
Figure BDA0002695943360000083
and />
Figure BDA0002695943360000084
The hamming distance is 1./>
Figure BDA0002695943360000085
and />
Figure BDA0002695943360000086
Are respectively by->
Figure BDA0002695943360000087
and />
Figure BDA0002695943360000088
The number of residuals obtained. Then if the sender sends->
Figure BDA0002695943360000089
The receiving end receives as->
Figure BDA00026959433600000810
A single bit error +.>
Figure BDA00026959433600000811
When (when)
Figure BDA00026959433600000815
Figure BDA00026959433600000813
When it is, it can be corrected. If the decoding of the redundant modulus is unsuccessful, a larger m is selected R And proceeds from step S0612. If the decoding is for some non-redundant m i Unsuccessful, try to correct the card (E i ) A better estimation is made and the process is iterated starting from step S0611.
In steps S061 and S062, the single error is corrected by using the (k+1, k) RRNS code, and the algebraic feature of the code makes the coding and decoding algorithm simple, so that resources can be effectively saved, and the hardware implementation is convenient. The ability to detect two symbol errors and correct one bit digital errors also makes it possible to apply them to DNA storage systems.
The simulation results of the present embodiment will be described in detail below:
the simulation parameters are shown in Table 1, where d is the initial position of the molecule, i.e., the distance between the center of the released transmitter node and the receiving center, T S Is the symbol duration, T SS Is the sampling interval, r r Is the radius of the receiver, D is the diffusion coefficient, p react Is the absorption probability of the receiver.
TABLE 1
D 79.4μm 2 /s p react 1
d 1μm rr 4μm
T s 0.030s T SS 0.015s
A uniformly distributed binary information sequence with probabilities 0 and 1 of 0.5 is encoded as an RRNS codeword sequence. Each residual in the RRNS codeword sequence is MoSK modulated and transmitted at the beginning of each symbol duration. The number of released molecules follows a poisson distribution with mean p=800. Bit Error Rate (BER) performance using RRNS coding and MoSK modulation techniques in MDS, where signal-to-noise ratio (SNR) values are defined as:
Figure BDA00026959433600000814
in formula (9), μ rx And sigma are the average amplitude of the received signal and the sum of the amplitudes following a gaussian distribution N (0, sigma 2 ) Is used for the channel noise of the mobile station. As shown in fig. 3, RRNS-MoSK represents encoding a binary information sequence using (4, 3) RRNS encoding modulo (11, 16, 17, 69), where m 4 =69, obtained using Barsi-Maestrini algorithm method. RNS (residue number sequence) -MoSK is obtained by performing a binary-residual transform method under the condition of modulus (11, 16, 17) to obtain an RNS code, then performing MoSK modulation on the RNS code, and demodulating the received signal at the receiving end without performing error correction at the receiving end. In fig. 3, 64MoSK represents that every 4 bits in the information sequence are converted into integers for MoSK modulation and demodulation. As can be seen from fig. 3, the error correction capability of rrns-MoSK is much better in single symbol errors than RNS-MoSK and 64 MoSK. While the performance of RNS-MoSK and 64MoSK are very similar, the (k+1, k) RRNS coding fully embodies its advantages.
In a third aspect, as shown in fig. 4, an embodiment of the present invention further provides an apparatus for error correction of channel coding, including at least one processor; at least one memory for storing at least one program; the at least one program, when executed by the at least one processor, causes the at least one processor to implement an error correction method of channel coding as in the first aspect.
The embodiment of the present invention also provides a storage medium having a program stored therein, the program being executed by a processor as in the second aspect.
From the above specific implementation process, it can be summarized that, compared with the prior art, the technical solution provided by the present invention has the following advantages or advantages:
1. the algebraic property of the coding and decoding algorithm in the embodiment provided by the invention reduces the complexity of algorithm implementation.
2. In the embodiment provided by the invention, the binary sequence to be transmitted is converted into the redundant number sequence by adopting the (k+1, k) RRNS coding method, and then each redundant number is mapped to the corresponding molecular type. The different types of molecules represent different redundancy numbers, and the different types of molecules do not interfere with each other, which alleviates the problem of intersymbol interference in MDS.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the invention is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the functions and/or features may be integrated in a single physical device and/or software module or may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the invention, which is to be defined in the appended claims and their full scope of equivalents.
Wherein the functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method of the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain or store the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium may even be paper or other suitable medium upon which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the above embodiments, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the present invention, and these equivalent modifications and substitutions are intended to be included in the scope of the present invention as defined in the appended claims.

Claims (8)

1. An error correction method for channel coding, comprising the steps of:
acquiring a binary information sequence of a source;
obtaining a non-redundant remainder sequence according to the information source binary information sequence and a preset non-redundant module;
encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module;
obtaining a residual sequence according to the redundant remainder, performing molecular shift keying modulation on the residual sequence, and transmitting the modulated molecular information to a receiving end;
wherein the step of performing molecular shift keying modulation on the residual sequence comprises the following steps:
converting the residual sequence to obtain a pulse signal, wherein the pulse signal comprises at least one molecular type, and the molecular type comprises organic matters and hydrofluorocarbons;
wherein, for the residual sequence, the method further comprises the step of correcting symbol errors in the residual sequence, and specifically comprises the following steps:
determining a correctable error set according to a preset non-redundant mode;
when the symbol errors in the residual error sequence belong to the correctable error set, correcting the symbol errors;
wherein, the step of determining the correctable error set according to a preset non-redundant mode further comprises the steps of:
obtaining a predetermined non-redundant modular sequence (m 1 ,m 2 …,m k ) For each modulo m in the sequence i 1.ltoreq.i.ltoreq.k, and for each integer
Figure FDA0004149003490000011
Determining the smallest integer +.>
Figure FDA0004149003490000012
Let the following inequality for each m j ≠m i I is less than or equal to j is less than or equal to k and is true:
Figure FDA0004149003490000013
for each die m i Defined integer
Figure FDA0004149003490000014
At integer +.>
Figure FDA0004149003490000015
A partial order is determined in the set of (1), i.e. in the set of +.>
Figure FDA0004149003490000016
In the case of
Figure FDA0004149003490000017
Figure FDA0004149003490000018
Then not +.>
Figure FDA0004149003490000019
Subsequent to (a);
for each m i Define an integer set
Figure FDA00041490034900000110
Is a subset P of i ，P i Any element->
Figure FDA00041490034900000111
Are not elements->
Figure FDA00041490034900000112
Subsequent to (i.e.)>
Figure FDA00041490034900000113
Any element->
Figure FDA00041490034900000114
Nor->
Figure FDA00041490034900000115
Subsequent to (a); p (P) i The potential of the catalyst is represented as card (P i )：
card(P i )＝2[log 2 m i ]
wherein ,
Figure FDA00041490034900000116
is the smallest integer greater than x;
definition m R ＝m k +1 is a pair of prime numbers given by m i 1.ltoreq.i.ltoreq.k to make
Figure FDA00041490034900000117
Thereafter, a subset P of positive integers is determined R Make the following steps
Figure FDA0004149003490000021
For P R Each element of (2)
Figure FDA0004149003490000022
When t is not equal to j, t is not less than 1 and not more than k+1, and j is not less than 1 and not more than k;
from subset P 1 ,P 2 ,…,P K ,P R Using the relation:
Figure FDA0004149003490000023
determining subclass { E 1 ,E 2 ,…,E k ,E R}, wherein ,pi ∈P i ,e i ∈E i ,e i ,p i ∈(0,m i ),
Figure FDA0004149003490000024
E i Is a set of correctable errors, +.>
Figure FDA0004149003490000025
/>
2. The method for error correction of channel coding according to claim 1, wherein said step of obtaining a non-redundant remainder sequence from said source binary information sequence and a predetermined non-redundant modulus comprises:
dividing the binary information sequence to obtain a plurality of information blocks; and determining the length of the information block according to the non-redundant mode;
and converting the binary information sequence in the information block into a decimal information sequence to obtain the non-redundant remainder sequence.
3. The method for error correction of channel coding according to claim 1, wherein said step of generating a redundancy remainder from said first integer value and a predetermined redundancy modulus comprises:
determining the redundancy remainder and a residual sequence through the first integer value and a preset redundancy module;
wherein the residual sequence comprises the non-redundant remainder sequence and a redundant remainder.
4. An error correction method for channel coding, comprising the steps of:
acquiring molecular information of a transmitting end; the molecular information is obtained by molecular shift keying modulation;
decoding according to the molecular type and the molecular concentration of the molecular information;
determining symbol errors in a residual sequence obtained after decoding, and correcting the symbol errors; the residual sequence comprises a redundant remainder sequence and a non-redundant remainder sequence;
the correcting process comprises the following steps: generating a non-redundant modulo projection and a redundant modulo projection of a first integer value; replacing the first integer value according to the non-redundant modulo projection or redundant modulo projection; the first integer value is obtained by encoding the non-redundant remainder sequence;
wherein the molecular shift keying modulation process comprises:
converting the residual sequence to obtain a pulse signal, wherein the pulse signal comprises at least one molecular type, and the molecular type comprises organic matters and hydrofluorocarbons;
the step of correcting the symbol errors in the decoded residual sequence further comprises:
determining a correctable error set according to a preset non-redundant mode;
when the symbol errors in the residual error sequence belong to the correctable error set, correcting the symbol errors;
wherein, the step of determining the correctable error set according to a preset non-redundant mode further comprises the steps of:
obtaining a predetermined non-redundant modular sequence (m 1 ,m 2 …,m k ) For each modulo m in the sequence i 1.ltoreq.i.ltoreq.k, and for each integer
Figure FDA0004149003490000031
Determining the smallest integer +.>
Figure FDA0004149003490000032
Let the following inequality for each m j ≠m i I is less than or equal to j is less than or equal to k and is true:
Figure FDA0004149003490000033
for each die m i Defined integer
Figure FDA0004149003490000034
At integer +.>
Figure FDA0004149003490000035
A partial order is determined in the set of (1), i.e. in the set of +.>
Figure FDA0004149003490000036
In the case of
Figure FDA0004149003490000037
Figure FDA0004149003490000038
Then not +.>
Figure FDA0004149003490000039
Subsequent to (a);
for each m i Define an integer set
Figure FDA00041490034900000310
Is a subset P of i ，P i Any element->
Figure FDA00041490034900000311
Are not elements->
Figure FDA00041490034900000312
Subsequent to (i.e.)>
Figure FDA00041490034900000313
Any element->
Figure FDA00041490034900000314
Nor->
Figure FDA00041490034900000315
Subsequent to (a); p (P) i The potential of the catalyst is represented as card (P i )：
card(P i )＝2[log 2 m i ]
wherein ,
Figure FDA00041490034900000316
is the smallest integer greater than x;
definition m R ＝m k +1 is a pair of prime numbers given by m i 1.ltoreq.i.ltoreq.k to make
Figure FDA00041490034900000317
Thereafter, a subset P of positive integers is determined R Make the following steps
Figure FDA00041490034900000318
For P R Each element of (2)
Figure FDA00041490034900000319
When t is not equal to j, t is not less than 1 and not more than k+1, and j is not less than 1 and not more than k;
from subset P 1 ,P 2 ,…,P K ,P R Using the relation:
Figure FDA00041490034900000320
determining subclass { E 1 ,E 2 ,…,E k ,E R}, wherein ,pi ∈P i ,e i ∈E i ,e i ,p i ∈(0,m i ),
Figure FDA00041490034900000321
E i Is a collection of errors that can be corrected,/>
Figure FDA00041490034900000322
5. a transmitting end system of error correction of channel coding, comprising a preprocessing unit, a code conversion unit and a transmission unit, wherein:
the preprocessing unit is used for acquiring a binary information sequence of an information source, dividing the binary information sequence into a plurality of information blocks, and determining the length of the information blocks according to a preset non-redundant mode;
the code conversion unit is used for obtaining a non-redundant remainder sequence according to the information source binary information sequence and a preset non-redundant module; encoding according to the non-redundant remainder sequence to obtain a first integer value; generating a redundancy remainder according to the first integer value and a preset redundancy module; obtaining a residual sequence according to the redundant remainder;
the transmission unit is used for carrying out molecular shift keying modulation on the residual sequence and transmitting the modulated molecular information to the receiving end system;
wherein the performing molecular shift keying modulation on the residual sequence includes:
converting the residual sequence to obtain a pulse signal, wherein the pulse signal comprises at least one molecular type, and the molecular type comprises organic matters and hydrofluorocarbons;
wherein, for the residual sequence, the method further comprises the step of correcting symbol errors in the residual sequence, and specifically comprises the following steps:
determining a correctable error set according to a preset non-redundant mode;
when the symbol errors in the residual error sequence belong to the correctable error set, correcting the symbol errors;
wherein, the step of determining the correctable error set according to a preset non-redundant mode further comprises the steps of:
obtaining a predetermined non-redundant modular sequence (m 1 ,m 2 …,m k ) For the followingEach modulo m in the sequence i 1.ltoreq.i.ltoreq.k, and for each integer
Figure FDA0004149003490000041
Determining the smallest integer +.>
Figure FDA0004149003490000042
Let the following inequality for each m j ≠m i I is less than or equal to j is less than or equal to k and is true:
Figure FDA0004149003490000043
for each die m i Defined integer
Figure FDA0004149003490000044
At integer +.>
Figure FDA0004149003490000045
A partial order is determined in the set of (1), i.e. in the set of +.>
Figure FDA0004149003490000046
In the case of
Figure FDA0004149003490000047
Figure FDA0004149003490000048
Then not +.>
Figure FDA0004149003490000049
Subsequent to (a);
for each m i Define an integer set
Figure FDA00041490034900000410
Is a subset P of i ，P i Any element->
Figure FDA00041490034900000411
Are not elements->
Figure FDA00041490034900000412
Subsequent to (i.e.)>
Figure FDA00041490034900000413
Any element->
Figure FDA00041490034900000414
Nor->
Figure FDA00041490034900000415
Subsequent to (a); p (P) i The potential of the catalyst is represented as card (P i )：
card(P i )＝2[log 2 m i ]
wherein ,
Figure FDA00041490034900000416
is the smallest integer greater than x; />
Definition m R ＝m k +1 is a pair of prime numbers given by m i 1.ltoreq.i.ltoreq.k to make
Figure FDA00041490034900000417
Thereafter, a subset P of positive integers is determined R Make the following steps
Figure FDA0004149003490000051
For P R Each element of (2)
Figure FDA0004149003490000052
When t is not equal to j, t is not less than 1 and not more than k+1, and j is not less than 1 and not more than k;
from subset P 1 ,P 2 ,…,P K ,P R Using the relation:
Figure FDA0004149003490000053
determining subclass { E 1 ,E 2 ,…,E k ,E R}, wherein ,pi ∈P i ,e i ∈E i ,e i ,p i ∈(0,m i ),
Figure FDA0004149003490000054
E i Is a set of correctable errors, +.>
Figure FDA0004149003490000055
6. A receiver system for error correction of channel coding, comprising a receiving unit and a correcting unit, wherein: the receiving unit is used for acquiring the molecular information of the transmitting end system; the molecular information is obtained by molecular shift keying modulation;
the correction unit decodes according to the molecular type and the molecular concentration of the molecular information; correcting errors in the residual sequence obtained after decoding; the residual sequence comprises a redundant remainder sequence and a non-redundant remainder sequence;
wherein the molecular shift keying modulation comprises:
converting the residual sequence to obtain a pulse signal, wherein the pulse signal comprises at least one molecular type, and the molecular type comprises organic matters and hydrofluorocarbons;
the step of correcting errors in the decoded residual sequence further comprises:
determining a correctable error set according to a preset non-redundant mode;
when the symbol errors in the residual error sequence belong to the correctable error set, correcting the symbol errors;
wherein, the step of determining the correctable error set according to a preset non-redundant mode further comprises the steps of:
obtaining a predetermined non-redundant modular sequence (m 1 ,m 2 …,m k ) For each modulo m in the sequence i 1.ltoreq.i.ltoreq.k, and for each integer
Figure FDA0004149003490000056
Determining the smallest integer +.>
Figure FDA0004149003490000057
Let the following inequality for each m j ≠m i I is less than or equal to j is less than or equal to k and is true:
Figure FDA0004149003490000058
for each die m i Defined integer
Figure FDA0004149003490000059
At integer +.>
Figure FDA00041490034900000510
A partial order is determined in the set of (1), i.e. in the set of +.>
Figure FDA00041490034900000511
In the case of
Figure FDA00041490034900000512
Figure FDA00041490034900000513
Then not +.>
Figure FDA00041490034900000514
Subsequent to (a);
for each m i Define an integer set
Figure FDA00041490034900000515
Is a subset P of i ，P i Any element->
Figure FDA00041490034900000516
Are not elements->
Figure FDA00041490034900000517
Subsequent to (i.e.)>
Figure FDA0004149003490000061
Any element->
Figure FDA0004149003490000062
Nor->
Figure FDA0004149003490000063
Subsequent to (a); p (P) i The potential of the catalyst is represented as card (P i )：
card(P i )＝2[log 2 m i ]
wherein ,
Figure FDA0004149003490000064
is the smallest integer greater than x;
definition m R ＝m k +1 is a pair of prime numbers given by m i 1.ltoreq.i.ltoreq.k to make
Figure FDA0004149003490000065
Thereafter, a subset P of positive integers is determined R Make->
Figure FDA0004149003490000066
For P R Each element of (2)
Figure FDA0004149003490000067
When t is not equal to j, t is not less than 1 and not more than k+1, and j is not less than 1 and not more than k;
from subset P 1 ,P 2 ,…,P K ,P R Using the relation:
Figure FDA0004149003490000068
determining subclass { E 1 ,E 2 ,…,E k ,E R}, wherein ,pi ∈P i ,e i ∈E i ,e i ,p i ∈(0,m i ),
Figure FDA0004149003490000069
E i Is a set of correctable errors, +.>
Figure FDA00041490034900000610
7. An apparatus for error correction for channel coding, comprising:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement a channel coding error correction method as claimed in any one of claims 1-4.
8. A storage medium having stored therein a program executable by a processor, characterized in that: the processor executable program when executed by a processor is for implementing a channel coding error correction method as claimed in any one of claims 1-4.
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