CN113660064A - Multi-data-packet-based joint two-dimensional interleaving coding method suitable for power line communication system - Google Patents

Multi-data-packet-based joint two-dimensional interleaving coding method suitable for power line communication system Download PDF

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CN113660064A
CN113660064A CN202111078861.8A CN202111078861A CN113660064A CN 113660064 A CN113660064 A CN 113660064A CN 202111078861 A CN202111078861 A CN 202111078861A CN 113660064 A CN113660064 A CN 113660064A
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power line
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CN113660064B (en
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陈永红
刘峰
王星海
常诚
宋柯浔
李浩天
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Shenyang Aircraft Design Institute Yangzhou Collaborative Innovation Research Institute Co Ltd
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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
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0059—Convolutional codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B3/00—Line transmission systems
    • H04B3/54—Systems for transmission via power distribution lines
    • 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
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0071—Use of interleaving
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    • 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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Abstract

The invention provides a multi-data-packet-based joint two-dimensional interleaving coding method suitable for a power line communication system, and belongs to the field of power line communication. The power line communication system comprises a sending end, a channel and a receiving end. At a sending end, original communication data is divided into a plurality of data packets with equal length, and then Hamming code coding is carried out on data at the same positions of the data packets, namely a longitudinal interweaving Hamming code; next, respectively carrying out convolutional code coding on a plurality of data packets including the Hamming code parity check bit sequence, and the data packets are called transverse convolutional codes; finally, a plurality of data packets sequentially pass through the power line communication channel; at a receiving end, firstly, the received data is divided into a plurality of data packets in the same way, and the communication data in the power line communication system is recovered by respectively designing a decoding scheme according to the process corresponding to the transmitting end. When strong continuous burst interference exists in the power line communication system, the invention can obtain good bit error rate performance.

Description

Multi-data-packet-based joint two-dimensional interleaving coding method suitable for power line communication system
Technical Field
The invention provides a joint two-dimensional interleaving coding method based on multiple data packets, and aims to improve the reliability of a power line communication system. The coding scheme can effectively resist random errors and continuous burst interference in a power line communication channel, and has the characteristics of easy implementation and low complexity of a decoding algorithm.
Background
Power Line Communication (PLC) is a special Communication method that uses Power lines as transmission media to transmit data, and specifically, a high-frequency carrier signal carrying information is loaded on Power Line transmission current, and the carrier signal is separated and extracted by a user terminal receiver to achieve the purpose of Communication. The power line communication is suitable for an industrial scene with fixed layout of a power supply cable, rewiring is not needed, data communication can be completed through an existing power line layout structure, cost is saved to a certain extent, and energy utilization efficiency is improved. However, the power line communication system has inherent characteristics of large signal loss, susceptibility to noise interference, complex channel environment, and the like, and particularly, continuous burst interference may exist, which greatly affects the feasibility and reliability of the power line communication system. Therefore, the invention provides a multi-data-packet-based joint two-dimensional interleaving coding scheme suitable for a power line communication system so as to improve the bit error performance of the power line communication system.
The method is suitable for the power line communication scene with stronger continuous burst interference. At a sending end, original communication data is divided into a plurality of data packets with equal length, and then Hamming code coding is carried out on data at the same position of the data packets, wherein the step is called as a longitudinal interweaving Hamming code; next, convolutional code encoding is carried out on a plurality of data packets including the hamming code parity bit sequence, and the step is called transverse convolutional code; finally, a plurality of data packets sequentially pass through the power line communication channel; at a receiving end, firstly, the received data is divided into a plurality of data packets in the same way, and the communication data in the power line communication system is recovered by respectively designing a decoding scheme according to the process corresponding to the transmitting end. When strong continuous burst interference exists in the power line communication system, the scheme of the invention can obtain good bit error rate performance.
Disclosure of Invention
The invention provides a multi-data-packet-based combined two-dimensional interleaving coding (MPC) scheme suitable for a power line communication system in order to ensure the communication reliability under a strong interference environment based on a power line communication system transmission model.
The technical scheme of the invention is as follows:
a joint two-dimensional interleaving coding method based on multiple data packets and suitable for a power line communication system comprises the following specific steps:
firstly, a basic model of a power line communication system is established, wherein the basic model comprises a sending end, a channel and a receiving end. The sending end comprises two parts, namely an MPC coding part and a sending end processing part. In the MPC coding part, original data is firstly divided into a plurality of data packets with equal length, a Hamming code part is longitudinally interleaved to carry out Hamming code coding on data at the same position of the plurality of data packets, then a transverse convolutional code coding part carries out convolutional code coding on each data packet respectively, and finally the plurality of data packets are combined into a series of sequences; the processing part of the sending end comprises an inserting pilot frequency, OFDM modulation and a digital-to-analog conversion module.
The receiving end comprises two parts corresponding to the transmitting end, namely a receiving end processing part and an MPC decoding part. The MPC decoding part divides a receiving sequence processed by the receiving end processing part into a plurality of data packets in the same way as the sending end and performs Viterbi decoding on each data packet; and (4) carrying out longitudinal Hamming code syndrome decoding on the decoded sequence, and finally recovering the data packet subjected to decoding processing into a receiving sequence to finish the communication process of the power line system.
In the power line communication system of the present invention, a key problem is how to design a coding scheme to combat random errors and continuous burst interference that may occur in a power line communication channel, and then we present a specific implementation method. The encoding part is specifically as follows:
let the length of the original data be NbThe original data sequence is represented as
Figure BDA0003263122770000021
Wherein
Figure BDA0003263122770000022
1≤i≤Nb. Partitioning raw data into Npk＝2q-1 data packet, q ≧ 3,
Figure BDA0003263122770000023
each data packet is N in lengthlThe packet set divided by the packets is expressed as:
Figure BDA0003263122770000024
wherein u is u1To
Figure BDA0003263122770000025
Total NpkSet of several data packets, biI is more than or equal to 1 and less than or equal to N which are corresponding elements in the original data sequencepkNl. Note that N may be presentpkNl＞NbThe case of (1), namely, the data length is larger than the original data sequence after dividing the data packet. Therefore, the data packet is specially defined
Figure BDA0003263122770000026
Has a length of Na＝NlNpk-NbZero padding data, N is not less than 0a＜NlData packet
Figure BDA0003263122770000027
Satisfies the following conditions:
Figure BDA0003263122770000028
next, the information bit length is used as NpkCheck bit length of Np＝2qQ-1, code length NH＝Npk+NpOf Hamming code, i.e. (N)H,Npk) Hamming code, for NpkCoding the data information at the same position of each data packet, which is called longitudinal interleaving Hamming code, and setting (N)H,Npk) The generating matrix of the Hamming code is
Figure BDA0003263122770000029
Then hamming codeword v(i)Is shown as
Figure BDA00032631227700000210
Wherein
Figure BDA00032631227700000211
For longitudinally interleaving Hamming code words v(i)I is more than or equal to 1 and less than or equal to Nl,1≤j≤Np. After longitudinally interweaving Hamming codes, the data form is as follows:
Figure BDA0003263122770000031
wherein v isi，1≤i≤NpFor a data packet after the data is longitudinally interleaved with hamming codes,
Figure BDA0003263122770000032
the number of data packets is NpkIs changed into Np。
Next, (N) is usedcc,NpM) the convolutional code encodes each packet in equation (6), which is called horizontal convolutional code encoding. (N)cc,NpM) convolutional code means code lengthIs NccInformation bit length of NpThe convolutional code comprises m shift registers, and the form of data after being coded by the transverse convolutional code is as follows:
Figure BDA0003263122770000033
wherein
Figure BDA0003263122770000034
wi,jIs binary bit data generated by the data in (5) through a transverse convolution code, i is more than or equal to 1 and less than or equal to Np,1≤j≤NccThe relationship between the data w after encoding and the data v before encoding of the transverse convolutional code is directly related to the hardware structure of the convolutional code;
in the above process, packet division generates NaZero-compensating bit with efficiency of Rp＝Nb/NpkNlThe coding efficiency of the longitudinally interleaved Hamming code is RH＝Npk/(Npk+Np) The coding efficiency of the transverse convolutional code is Rcc＝Np/NccThen, the coding efficiency of the MPC coding scheme is:
Figure BDA0003263122770000035
finally, the data packet is merged and operated, and the sending sequence is in the form of
Figure BDA0003263122770000036
Fig. 2 is a schematic diagram of the above process. And then, a modulation signal s is formed by inserting a pilot frequency, OFDM modulation and a digital-to-analog conversion module, and finally, the modulation signal s reaches a receiving end through a power line communication channel.
The transmitted signal s from the transmitting end passes through the power line communication channel and is affected by multipath effect, continuous burst interference and white gaussian noise, and the signal reaches the receiving end in the form of r, as shown in the following formula
r＝h*s+n+np (7)
Wherein h is shownIndicating the time domain impulse response of the power line communication channel, indicating the convolution operation, n is Gaussian white noise, n ispIs the continuous burst interference of the equivalent BEC channel.
Considering the real propagation process of the communication system, the following two aspects are provided for evaluating the strength of the impulse interference signal: the duration of the interfering signal, the frequency of occurrence of the interfering signal.
Aiming at the duration of the interference signal, setting the physical meaning of the parameter beta as the number of communication symbols influenced by the interference signal, and giving a numerical value of the beta in simulation to correspondingly describe the duration of the interference signal: the larger beta, the longer the interfering signal duration; otherwise, the same principle is applied.
Aiming at the occurrence frequency of interference signals, according to the knowledge of a queuing theory, the occurrence probability of the interference signals in a communication system is designed to be subjected to uniform distribution, the frequency of the interference signals in the single communication process is subjected to Poisson distribution, a parameter lambda represents the mean value of the Poisson distribution, the physical meaning of the mean value is the mean value of the frequency of the interference signals in the single communication process, and the requirement of meeting the requirement of the average value of the frequency of the interference signals in the single communication process is met
Figure BDA0003263122770000041
Where T is the frequency of occurrence of the impulsive interference signal during a single communication. The influence of the pulse interference signal on the communication system can be simulated by the two parameters, and the modeling process of the pulse interference signal is completed.
Generally speaking, the burst interference in the power line communication channel is related by factors such as load access variation of the power line system, and has the characteristics of large intensity and short duration, and the intensity of the burst interference is far greater than the power of the communication signal, and is distinguishable at the receiving end.
At a receiving end, a received signal r firstly obtains a signal to be processed by an MPC decoding module through analog-to-digital conversion, channel estimation, frequency domain equalization and an OFDM demodulation module
Figure BDA0003263122770000042
And the transmitting endThe output signals obtained by the MPC coding module have the same form. The final receiving data of the receiving end can be obtained through data packet splitting corresponding to the transmitting end, Viterbi decoding of convolutional codes, syndrome decoding of Hamming codes and data packet merging in sequence
Figure BDA0003263122770000043
The invention has the beneficial effects that: the invention mainly relates to a joint two-dimensional interleaving coding scheme based on multiple data packets, which is applicable to a power line communication system with continuous burst interference.
Drawings
FIG. 1 is a basic model of the system;
FIG. 2 is a schematic diagram of MPC encoded data format;
FIG. 3 MPC code bit error rate performance curve under AWGN channel;
FIG. 4 is a MPC coding bit error rate performance curve under a power line multipath channel;
fig. 5 is a diagram of a power line communication system;
FIG. 6(2,1,2) is a diagram of a convolutional code structure;
fig. 7(2,1,2) convolutional code state transition diagram.
Detailed Description
The technical solution of the present application is further explained below with reference to the embodiments and the accompanying drawings.
To measure the reliability of the coding scheme designed by the present invention, we will examine the bit error performance of the scheme in the following two channel models.
Model 1: AWGN channel + successive burst interference
In this model, assuming a time-domain channel impulse response h ≡ 1, the received signal is in the form of
r＝s+n+np (9)
The received signal is mainly disturbed by white gaussian noise and successive bursts.
The simulation result of MPC coding designed by the present invention is shown in FIG. 3, and each coding mode adopts BPSK modulation and coherent demodulation method. Where the single-pulse interference persistence sign number is 6 and β follows a poisson distribution with an average value of λ 0.5. As can be seen from fig. 3, under the condition that the signal-to-noise ratio is lower than 5dB, the gaussian white noise interference is large, and at this time, random errors are large, and the decoder is easy to correct errors by using wrong information, so that errors are corrected more and more, and the MPC coding performance is worse than that of the MPC coding which is only applicable to convolutional code coding and no additional coding; therefore, the MPC with the lowest code rate has the worst performance, and the performance of the MPC with the lowest code rate is centered by using the performance of the convolutional code, but has the best performance when the MPC is not coded.
Under the condition that the signal-to-noise ratio is higher than 5dB, the convolutional code can utilize redundant information to carry out error correction, so the performance of the convolutional code is better than that of an uncoded system. However, the upper limit of the error correction capability of the convolutional code is low, and when a long continuous burst error occurs, the convolutional code cannot correct the error correctly, so that a high error bit level exists. Besides independent convolutional code coding in each data packet, MPC coding also carries out Hamming code coding between data packets, so that bits with longer distance can also be mutually corrected, thereby avoiding continuous error codes and having optimal performance. However, MPC coding also has an upper limit of error correction capability, so when the snr is sufficiently large, the effect of burst interference cannot be further eliminated, and at this time, the bit error level layer also occurs. Overall, the performance of using MPC coding under conditions where the signal-to-noise ratio is higher than 5dB is significantly better than the other cases.
Model 2: classical time domain multipath channel + continuous burst interference
According to the document [ A.M.Tonello, F.Versollatto, B.Bejar and S.Zazo, "A matching Algorithm for Random Modeling the PLC Channel," in IEEE Transactions on Power Delivery, vol.27, No.3, pp.1477-1484, July 2012, doi:10.1109/TPWRD.2012.2196714 ], a Fourier transform form of the time-domain Channel impulse response h is set, i.e., the frequency-domain Channel response characteristic is set to be
Figure BDA0003263122770000051
Where f is the frequency of the carrier signal, NpIs the number of paths of the multipath channel, A is the fading coefficient, giAnd ciTo take on values of [ -1,1 [)]Within a range ofUniformly distributed random variables, /)iFor the path length of the ith path in a multipath channel, parameter a0、a1、K1And K2Are all related to the structure of the power line itself, and v is the speed at which the communication signal is transmitted within the power line.
The simulation result of the MPC code designed by the present invention under the power line multipath channel model given in table 1 is shown in fig. 4, OFDM and channel estimation and equalization techniques are adopted, BPSK modulation and coherent demodulation methods are adopted as the modulation mode, the number of single pulse interference continuous symbols is β ═ 6, and β obeys poisson distribution with an average value of λ ═ 0.5. As can be seen from fig. 4, under the condition that the snr is lower than about 12dB, the effect of the gaussian white noise interference is large, which causes a large number of random errors in the received signal, and the decoder decodes the received signal with a large number of errors, which results in more decoding errors. Therefore, the system performance is best when not encoded, and the MPC system performance is worst when encoded twice.
TABLE 1 Power line multipath channel model simulation parameter Table
Figure BDA0003263122770000061
Under the condition that the signal-to-noise ratio is higher than 12dB, the convolutional code can carry out error correction by utilizing redundant information added by coding, so the performance of the convolutional code is better than that of an uncoded system. However, the error correction capability of the convolutional code is limited, only a part of errors can be corrected, and a large number of continuous errors can not be recovered by the convolutional code decoder. The multi-data packet joint coding technology adds constraint relation to bits among data packets, so that a receiver can recover received error signals crossing the data packets, and the influence of continuous burst interference is avoided. Therefore, the multi-packet joint coding technique has the best performance.
Fig. 4 shows that the joint two-dimensional interleaving coding scheme based on multiple data packets designed by the invention can be effectively applied to a power line communication system, and provides higher reliability gain.
Suppose that:
(1) the application scene is a power line communication system;
(2) the longitudinally interleaved Hamming code adopts (7,4) Hamming code and its corresponding syndrome hard decision decoding method;
(3) the transverse convolutional code adopts (2,1,2) convolutional code and a Viterbi soft decision decoding method corresponding to the convolutional code;
(4) the pilot frequency of the communication system selects a ZC sequence, and the channel equalization selects a zero forcing criterion.
Fig. 5 is a structure diagram of a complete power line communication system, which mainly comprises modules such as MPC coding, OFDM, channel estimation and the like designed by the present invention.
At the transmitting end, the Hamming code of the longitudinal interweaving (7,4) can select a generating matrix as shown in a formula (12).
Figure BDA0003263122770000071
The transverse convolutional code may adopt the structure shown in fig. 6.
Wherein D1And D2For two shift registers, the state transition diagram for the (2,1,2) convolutional code is shown in fig. 7. Wherein S0-S3 are 4 different states represented by two shift registers, and the numbers above the arrows indicate the corresponding relationship between 1-bit input bits and 2-bit output bits.
The power line communication system pilot frequency sequence adopts ZF sequence, i.e.
Figure BDA0003263122770000072
Wherein q is any positive integer, NZCIs the length of the pilot sequence, u is equal to NZCA prime integer of each other.

Claims (1)

1. A joint two-dimensional interleaving coding method based on multiple data packets and suitable for a power line communication system is characterized by comprising the following specific steps:
establishing a basic model of a power line communication system, which comprises a sending end, a channel and a receiving end; the sending end comprises two parts, namely an MPC coding part and a sending end processing part; in the MPC coding part, original data is firstly divided into a plurality of data packets with equal length, a Hamming code part is longitudinally interleaved to carry out Hamming code coding on data at the same position of the plurality of data packets, then a transverse convolutional code coding part carries out convolutional code coding on each data packet respectively, and finally the plurality of data packets are combined into a series of sequences; the processing part of the sending end comprises an inserting pilot frequency, an OFDM modulation and a digital-to-analog conversion module;
the receiving end comprises two parts corresponding to the transmitting end, namely a receiving end processing part and an MPC decoding part respectively; the MPC decoding part divides a receiving sequence processed by the receiving end processing part into a plurality of data packets in the same way as the sending end and performs Viterbi decoding on each data packet; the decoded sequence is subjected to longitudinal Hamming code syndrome decoding, and finally, the data packet subjected to decoding processing is recovered to a receiving sequence to complete the communication process of the power line system;
the encoding part is specifically as follows:
let the length of the original data be NbThe original data sequence is represented as
Figure FDA0003263122760000011
Wherein
Figure FDA0003263122760000012
1≤i≤Nb(ii) a Partitioning raw data into Npk＝2q-1 data packet, q ≧ 3,
Figure FDA0003263122760000013
each data packet is N in lengthlThe packet set divided by the packets is expressed as:
Figure FDA0003263122760000014
wherein u is u1To
Figure FDA0003263122760000015
Total NpkSet of several data packets, biI is more than or equal to 1 and less than or equal to N which are corresponding elements in the original data sequencepkNl(ii) a Note that N may be presentpkNl＞NbThe condition of (1), namely the data length is larger than the original data sequence after dividing the data packet; therefore, the data packet is specially defined
Figure FDA0003263122760000016
Has a length of Na＝NlNpk-NbZero padding data, N is not less than 0a＜NlData packet
Figure FDA0003263122760000017
Satisfies the following conditions:
Figure FDA0003263122760000018
next, the information bit length is used as NpkCheck bit length of Np＝2qQ-1, code length NH＝Npk+NpOf Hamming code, i.e. (N)H,Npk) Hamming code, for NpkCoding the data information at the same position of each data packet, which is called longitudinal interleaving Hamming code, and setting (N)H,Npk) The generating matrix of the Hamming code is
Figure FDA0003263122760000019
Then hamming codeword v(i)Is shown as
Figure FDA0003263122760000021
Wherein
Figure FDA0003263122760000022
For longitudinally interleaving Hamming code words v(i)I is more than or equal to 1 and less than or equal to Nl,1≤j≤Np(ii) a After longitudinally interweaving Hamming codes, the data form is as follows:
Figure FDA0003263122760000023
wherein v isi，1≤i≤NpFor a data packet after the data is longitudinally interleaved with hamming codes,
Figure FDA0003263122760000024
the number of data packets is NpkIs changed into Np；
Next, (N) is usedcc,NpM) the convolutional code encodes each packet in equation (6), which is called transverse convolutional code encoding; (N)cc,NpM) convolutional code means a code length of NccInformation bit length of NpThe convolutional code comprises m shift registers, and the form of data after being coded by the transverse convolutional code is as follows:
Figure FDA0003263122760000025
wherein
Figure FDA0003263122760000026
wi,jIs binary bit data generated by the data in (5) through a transverse convolution code, i is more than or equal to 1 and less than or equal to Np,1≤j≤NccThe relationship between the data w after encoding and the data v before encoding of the transverse convolutional code is directly related to the hardware structure of the convolutional code;
in the above process, packet division generates NaZero-compensating bit with efficiency of Rp＝Nb/NpkNlThe coding efficiency of the longitudinally interleaved Hamming code is RH＝Npk/(Npk+Np) Transverse directionCoding efficiency to convolutional code is Rcc＝Np/NccThen, the coding efficiency of the MPC coding scheme is:
Figure FDA0003263122760000027
finally, the data packet is merged and operated, and the sending sequence is in the form of
Figure FDA0003263122760000028
FIG. 2 is a schematic diagram of the above process; then, a modulation signal s is formed by inserting a pilot frequency, OFDM modulation and a digital-to-analog conversion module, and finally reaches a receiving end through a power line communication channel;
the transmitted signal s from the transmitting end passes through the power line communication channel and is affected by multipath effect, continuous burst interference and white gaussian noise, and the signal reaches the receiving end in the form of r, as shown in the following formula
r＝h*s+n+np (7)
H represents the time domain impulse response of the power line communication channel, x represents the convolution operation, n is Gaussian white noise, and n ispContinuous burst interference for equivalent BEC channels;
considering the real propagation process of the communication system, the following two aspects are provided for evaluating the strength of the impulse interference signal: the duration of the interfering signal, the frequency of occurrence of the interfering signal;
aiming at the duration of the interference signal, setting the physical meaning of the parameter beta as the number of communication symbols influenced by the interference signal, and giving a numerical value of the beta in simulation to correspondingly describe the duration of the interference signal: the larger beta, the longer the interfering signal duration; otherwise, the same principle is adopted;
aiming at the occurrence frequency of interference signals, according to the knowledge of a queuing theory, the occurrence probability of the interference signals in a communication system is designed to be subjected to uniform distribution, the frequency of the interference signals in the single communication process is subjected to Poisson distribution, a parameter lambda represents the mean value of the Poisson distribution, the physical meaning of the mean value is the mean value of the frequency of the interference signals in the single communication process, and the requirement of meeting the requirement of the average value of the frequency of the interference signals in the single communication process is met
Figure FDA0003263122760000031
Wherein T is the frequency of occurrence of the pulse interference signal in the single communication process; the influence of the pulse interference signal on the communication system can be simulated by the two parameters, and the modeling process of the pulse interference signal is completed;
the burst interference in the power line communication channel is related to load access variation factors of a power line system, and has the characteristics of high intensity and short duration, wherein the intensity of the burst interference is far greater than the power of a communication signal and is distinguishable at a receiving end;
at a receiving end, a received signal r firstly obtains a signal to be processed by an MPC decoding module through analog-to-digital conversion, channel estimation, frequency domain equalization and an OFDM demodulation module
Figure FDA0003263122760000032
The output signal form is the same as that of the output signal obtained by the MPC coding module of the sending end; the final receiving data of the receiving end can be obtained through data packet splitting corresponding to the transmitting end, Viterbi decoding of convolutional codes, syndrome decoding of Hamming codes and data packet merging in sequence
Figure FDA0003263122760000033
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