CN103281166A - Hybrid automatic repeat request transmission method based on polarization code - Google Patents

Abstract

The invention discloses a hybrid automatic repeat request transmission method based on a polarization code. The hybrid automatic repeat request transmission method based on the polarization code comprises the following steps: after a coding bit sequence obtained after polarization coding is carried out to a sent information bit sequence is punched via a sending end, sending into a channel to be transmitted; decoding a received signal by a receiving end for CRC (cyclic redundancy check); if the received signal passes the check, feeding back an ACK (acknowledgement character) signal to the sending end, and otherwise, sending a NACK (negative acknowledgement) signal; if the sending end receives the NACK signal, sending one part of uncoded information bits to a receiving end again; according to the coding bit received for the first time and a newly-received information bit, decoding again by the receiving end; if a decoding result still does not pass the CRC, sending the other part of uncoded information bits to the receiving end again by the sending end; according to the coding bit received for the first time, the information bit received in the previous time and the newly-received information bit, decoding again by the receiving end; continuously executing the process; and finishing one whole transmission process until the sending end receives the ACK signal or the number of sending times reaches a preset maximum value.

Description

Hybrid automatic repeat request transmission method based on polarization code

Technical Field

The invention relates to a hybrid automatic repeat request transmission method based on a polarization code, which is used for solving the problem that transmission data is wrong due to the interference of a transmission channel on a communication process in a digital communication system; and more particularly, to a method for signal transmission through hybrid automatic repeat request in a digital communication system using a polar code as error correction coding. Belongs to the technical field of channel coding of digital communication.

Background

Polarization Codes (Polar Codes) are a well documented one proposed by e.arikan in 2009A constructive channel coding method for achieving channel capacity. Before polarization coding, N =2 is firstly carried outⁿIndependent binary input channels (or N successive uses of the same channel, i.e., N available time slots of a channel) are repeatedly polarized using the basic unit of channel polarization shown in fig. 1, where N is a natural number. The most basic channel polarization is for two identical unpolarized channels W: x → Y performs a single step polarization operation, where X is the set of channel input symbols (X takes values of {0,1} for a binary input channel) and Y is the set of channel output symbols. As shown in fig. 1, the input bits for the polarization channel are marked as u₁And u₂The two input bits are passed through a modulo two adder to obtain x₁On the other hand u₂Direct assignment to x₂I.e. x₁=u₁⊕u₂，x₂=u₂And behavior behavioris modulo two addition operation. Then x is processed₁And x₂After being respectively sent into unpolarized channels W, the obtained output is y₁And y₂. From the input of the channel polarization base unit (u)₁And u₂) And outputs of two channels (y)₁And y₂) Two unpolarized channels W that are originally independent are merged into a two-input two-output vector channel W₂:X²→Y²Wherein X is²And = X, operator is cartesian product. The vector channel comprises two sub-channels

(input is u)₁Output is y₁y₂) And

(input is u)₂The output is y₁y₂u₁) The two subchannels are two polarized channels. Through the single-step polarization process, the polarization state of the polarization state,

where I (-) represents a function of channel capacity. That is to say: after single-step polarization, under the condition that the sum capacity is kept unchanged, compared with the original unpolarized channel, the polarized channel capacity is deviated: one increasing and one decreasing. The deviation is more obvious if two groups of channels which are polarized once are subjected to single-step polarization operation between the two groups of mutually independent polarization channels with the same transition probability, the group of single-step polarization operation is called as second-layer polarization operation, and the previous group of single-step polarization operation is called as first-layer polarization operation. Every time one more polarization operation is performed, the number of channels required is doubled. Thus, for N =2ⁿComplete polarization of each channel is performed, N layers of polarization operation are required, and each layer of polarization operation comprises N single-step polarization operations. Unless otherwise specified, "polarize N channels" means complete polarization.

It has been theoretically proven that, after polarization operation is performed on a plurality of channels approaching infinity, a phenomenon occurs in which the capacity of a part of the channels is 1 (i.e. bits transmitted through the channels are always correctly received), the capacity of the rest of the channels is 0 (i.e. bits cannot be reliably transmitted at all), and the proportion of the channels with the capacity of 1 to the total channels is exactly the capacity of the original binary input discrete channel.

Fig. 2 is a schematic diagram showing a recursive structure of a channel polarization apparatus with a length N, wherein a minimum unit of the recursion (i.e., when N = 1) is the basic unit shown in fig. 1.

Referring to fig. 3, a recursive structure of a practical channel polarization apparatus is described, and a length N (for polarizing N channels) channel polarization apparatus may be used with a length of N

The channel polarization apparatus of (a) is represented by recursive operation, and the minimum unit in the recursive process (i.e. when N = 2) is the basic unit shown in fig. 1. In the channel polarization apparatus of fig. 2There is a bit reversal interleaver of length N, whose function is: firstly, the decimal serial number i of the input end is expressed as (b) according to binary system_nb_n-1…b₁) Wherein n = log₂N, and then the binary sequence is reversed to obtain (b)₁b₂…b_n) Finally, the decimal number is represented again as theta (i) as the output serial number corresponding to the input serial number i. The bit reversal interleaver is used to map the bits with input sequence number i to sequence number θ (i). Polarize N channels according to the coding rate (R), and choose K channels with the maximum capacity (or equivalently, choose K channels with the highest reliability, the reliability measure is obtained by using the density evolution (DensityEvolution) tool or calculating the Bhattacharyya parameter) to carry the bits for transmitting the message, and call the part of the bits as the information bits and the part of the channels as the information channels (wherein

For rounding-down operation), the remaining unselected channels transmit a predetermined bit sequence, which is called a fixed bit sequence, and the part of channels are called fixed channels (if the channels are symmetrical, all-zero sequences can be simply transmitted), so as to form a mapping relationship from K bits carrying information to N bits finally sent into the channels, and such a mapping relationship is a polar code whose code length (the number of bits included in the binary signal obtained after encoding) is equal to the length N of the channel polarization apparatus.

Binary signal sequence (u) comprising information bits and fixed bits and fed to channel polarization means₁,…,u_N) For code blocks (the order of which corresponds to the order of the polarisation channel into which it is fed, i.e. u_iIs sent into

And the serial number i is a positive integer from 1 to N,

indicating a polarized channel with index i obtained by polarizing N channels W). X obtained after coded code block passes through channel polarization device₁…x_NThrough the N independent channels W again, the received signal sequence is (y)₁,…,y_N)。

The above process can be equivalently described as: the sequence u = (u)₁,…,u_N) Multiplying by matrix G_NI.e. x = u · G_NWherein, the matrix

NxN matrix B_NIn order to permute the matrix in the reverse order of the bits, ${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HDA00003191318700012.png,HDA00003191318700052.png"\; state="\{\{state\}\}">F</figure-callout>}}_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$ upper label of

Expressing n F₂Kronecker product of (c). Matrix B_NThe method is obtained by rearranging each row of an NxN unit matrix according to the bit reverse order: for each index i ∈ {1,2, …, N }, (i-1) the binary representation is (b)_n,b_n-1,…,b₁) Finding a j e {1,2, …, N } such that the binary representation of (j-1) is (b)₁,b₂,…,b_n) Let B_NIs equal to I in row I_NRow j of (2).

If the code length of the polarization code is not a power of 2. For example: assuming code length

Whereinis a ceiling operation. It is necessary to construct an N-dimensional channel polarization transformation according to the above method. The transform requires N independent channels, where M channels are obtained by M independent uses of channel W, and the remaining N-M are virtual channels having the same input and output signal set as W but with zero channel capacity. The arrangement position of the virtual channels is determined according to the following method: an N-dimensional vector q is given, wherein the first N-M elements are 1, and the last M elements are 0, i.e.

Then, the vector is subjected to bit reversal rearrangement to obtain a puncture position indication sequence p = B_NQ. For sequence number i ∈ {1,2, …, N }, if p_i=1, it means that the i-th independent channel is a virtual channel; otherwise, it means that the ith independent channel is an independent use of the channel W. After the above operation, the polarization channel is obtained as the common polarization code

Selecting the most reliable K channels as information channels for carrying information bits; and setting the rest channels as fixed channels. The polarization code obtained by this method is called a punctured polarization code.

The puncturing polarization encoding process can also be equivalently described as: the sequence u = (u)₁,…,u_N) Multiplying by matrix G_NI.e. x = u · G_NWherein, the matrix

B_NIn order to permute the matrix in the reverse order of the bits, ${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HDA00003191318700012.png,HDA00003191318700052.png"\; state="\{\{state\}\}">F</figure-callout>}}_2\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$

denotes n F₂Kronecker product of (c). Then, the obtained vector x is punctured according to a puncturing position indication sequence p, wherein p_i=1 denotes chiseling bit x_i，p_i=0 denotes a reserved bit x_iTo obtain the final transmission code v = (v)₁,…,v_M)。

When constructing the polarization code, for general channels except the binary deleted channel, a density evolution tool is needed to calculate the reliability of the polarization channel. The method for calculating the reliability of the polarization code by using density evolution is briefly introduced as follows:

assuming that the transmitted information block is an all-zero sequence with a length of K, the coded codeword thereof is an all-zero sequence with a length of N. Transmitted via a channel, the receiving end can be based on the received sequence (y)₁…y_N) The value of the log-likelihood ratio (LLR) of each code bit is calculated. Reuse of

Representing the ith polarized channel

The probability density function of the LLR values of the received bits when the transmitted bits are zero. By means of the structure of the polarization code,

is obtained by recursive calculation according to the following method: $a_N^{\left(i\right)}=a_{N,1}^{\left(i\right)},$ $a_{2k,j}^{(2i-1)}=a_{k,2j-1}^{\left(i\right)}\&CirclePlus;a_{k,2j}^{\left(i\right)},$ $a_{2k,j}^{\left(2i\right)}=a_{k,2j-1}^{\left(i\right)}\&CircleTimes;a_{k,2j}^{\left(i\right)};$ wherein, operator behavior

Respectively representing a check node domain convolution and a variable node domain convolution.

For each value of k, there are i =1,2, …, k and

probability density function of LLR values for the jth code bit, where j =1,2, …, N.

Given a binary input channel W and its probability density function a that outputs LLR values when the input is a bit zero, the reliability of the channel can be evaluated by calculating its transmission error probability, which is calculated by the formula:

thereby can be based on

Obtaining individual polarization channels

The reliability of (2).

At the signal receiving end, the polar code decoder task is based on the received signal sequence (y)₁,…,y_N) Obtaining a transmission bit sequence (u)₁,…,u_N) A set of bit estimation sequences of

For punctured polarization codes, (y)₁…y_N) The code sequence number i of each bit in the code block can be determined by serial cancellation SC (successive cancellation) algorithm1 to N are decoded in sequence:

in the formula, the decision function of the information bits is:wherein, $P({\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,y_N|{\hat{u}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{u}}_{i-1},{\hat{u}}_i)=\frac{1}{2^{i-1}}\&CenterDot;W_N^{\left(i\right)}({\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,y_N,{\hat{u}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{u}}_{i-1}|{\hat{u}}_i);$ function(s) $W_N^{\left(i\right)}({\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\&CenterDot;\&CenterDot;\&CenterDot;y_N,u_1\&CenterDot;\&CenterDot;\&CenterDot;u_{i-1}|u_i)$ Polarized subchannel with serial number i

Is a transition probability function of (a) represents the transmission signal u_iThrough the channel

To obtain an output y₁…y_NAnd u₁…u_i-1The probability of (c).

The serial cancellation decoding method can also be described as a search process on a code tree (fig. 3 is a simple example). The serial offset decoding is gradually expanded on a code tree, one of two candidate paths with relative approximate probability values is selected at a time, and the expansion of the next path is continued on the basis of the path.

As an improvement of serial cancellation decoding, serial cancellation list decoding allows multiple candidate paths to be retained instead of just one, thereby enlarging the search range and reducing the probability of leaving the correct path during the search. The specific method comprises the following steps: all candidate paths and their corresponding reliability metric values are stored in a list. All candidate paths in the list are expanded synchronously, so the number of candidate paths in the list is doubled after each expansion. Then, those partial candidate paths with smaller reliability metric values are discarded to ensure that the number of candidate paths is always not more than half of the list size. And when the decoding is finished, finding out the path with the maximum reliability metric value from the table, wherein the corresponding bit estimation sequence is the decoding result.

Another improvement of serial cancellation decoding is serial cancellation stack decoding. It uses an ordered stack for storing the candidate paths, rather than a list. In the process of serial cancellation stack decoding, only one candidate path (located at the top of the stack) with the largest reliability metric is expanded each time. When the stack top path reaches a certain leaf node of the code tree, the decoding process is stopped, and the bit estimation sequence corresponding to the path is output as a decoding result.

If the information block contains cyclic redundancy information, namely the cyclic redundancy check result of the information block sequence is an all-zero sequence, the information block sequence can be decoded by using a serial offset list/stack decoding algorithm assisted by cyclic redundancy check. By adopting the decoding method, the anti-noise performance of the limited code length polarization code can be greatly improved.

In communication applications that are not sensitive to system delay, hybrid automatic repeat request (HARQ) is a common transmission method to improve system throughput.

The calculation formula of the throughput rate is as follows:

referring to fig. 4, a simple example of a hybrid automatic repeat request (HARQ) transmission is presented: when a certain information block is transmitted, a transmitting end encodes the information block (transmitting sequence 1) and then transmits the encoded information block into a channel, and if a receiving end decodes a received signal, the transmitting end finds that the transmission fails (if the cyclic redundancy check cannot be passed). At this time, the receiving end transmits a non-acknowledgement (NACK) message to the transmitting end through a feedback link, and the transmitting end re-encodes the information block for transmission (transmission sequence 2 … T). This process continues until the receiver decodes the message correctly, at which point the receiver sends an Acknowledgement (ACK) message to the sender, thereby completing the transmission of the pair of information blocks. HARQ technology has been widely used in existing communication systems (e.g., WCDMA, LTE, etc. systems).

In the present patent application, unless otherwise specified, the lower case english/greek alphabet is used uniformly to represent scalar quantities, such as x; the set is represented by capital English letters, such as X; vectors (or equivalent sequences) are represented by lower case bold english/greek letters, such as x; an element in a vector is represented by a lower case English/Greek letter (not bold) with the same name, and the index of the element in the vector is marked by a subscript, for example, the ith element of the vector x is marked by the symbol x_iRepresents; one sub-vector (x) of the vector x_i,x_i+1,…,x_j-1,x_j) By the symbol x_i:jRepresents; the squares being indicated by bold capital letters and their size being indicated by subscripts, e.g. X_NRepresenting an N x N square matrix.

The disadvantages of the prior art are as follows: because the code length of a practical coding system cannot be infinitely long, there are some channels with transmission performance that is not particularly good or poor after polarization operation for a limited number of channels. Therefore, under the existing decoding method, the noise immunity achieved by the polarization code with limited code length is not ideal. Therefore, the polar code is directly applied to the actual system, and the very ideal throughput rate cannot be obtained. On the other hand, most HARQ systems that have been applied to practical systems are based on turbo codes or LDPC codes, and are limited by the code construction method, and the adjustment range of the code length is limited, so that the system throughput and the channel capacity still have a large distance.

Disclosure of Invention

In view of the above, an object of the present invention is to provide a method for transmitting HARQ based on a polar code, so as to greatly improve the throughput of a communication system using the polar code as a channel code and improve the probability of correct bit decoding, so that the HARQ scheme based on the polar code of the present invention can be optimized to the maximum extent. Moreover, the method is simple and convenient to operate, is particularly suitable for being applied to an actual communication system, and has good practical prospect.

In order to achieve the above object, the present invention provides a hybrid automatic repeat request (HARQ) transmission method based on a polarization code, which is characterized in that: the signal sending end carries out primary polarization coding on an information bit sequence to be sent, and the obtained coded bits are sent to a channel for transmission after hole drilling; the signal receiving end decodes the received signal and performs Cyclic Redundancy Check (CRC) on the decoding result; if the verification is passed, the signal receiving end sends an Acknowledgement (ACK) signal to the sending end through a feedback link; otherwise, sending a non-acknowledgement (NACK) signal to the sending end; if the sending end receives the NACK signal, part of the information bits are sent to the receiving end through the channel without being coded, and the receiving end decodes again according to the coded bits received for the first time and the newly received information bits; if the decoding result still cannot pass the CRC, after receiving the NACK signal, the sending end sends the other part of information bits to the receiving end through the channel again without encoding, and the receiving end decodes again according to the encoding bits received for the first time, the information bits received for the previous time and the newly received information bits; the above process is continuously executed, and a complete transmission process is not finished until the sending end receives the ACK signal or the sending times reach the preset maximum value; the method comprises the following operation steps:

(1) determining the following transmission parameters according to the requirements and the channel parameters: the transmission aims at transmitting an information bit sequence which contains CRC check bits and has the length of K to a signal receiving end through a binary input memoryless channel W by using a polarization code with the code length of N0 within the maximum transmission times T by a signal transmitting end, and the maximum bit number which is allowed to be transmitted in total is Q within the T transmission times; wherein, the positive integer N₀Is a power of 2, and N₀The number set of the information channels required by the polarization coding is A when the number is more than or equal to K; the length of a bit sequence of a polarization code coding bit sequence after puncturing is M, the puncturing position indication sequence of the polarization code coding bit sequence is p, and channel serial numbers corresponding to information bits for preparing repeated transmission are sequentially stored in a retransmission serial number sequence r with the length of Q-M; after the 1 st, 2 nd, … … th and T th transmissions, the total number of bits received by the receiving end is: n is a radical of₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q；

(2) Encoding and initializing the transmission sequence: the information sequence with the length of K and the information sequence with the length of N which is known in advance at the receiving end and the transmitting end₀The fixed bit sequences of-K are combined according to the set A of sequence numbers of the information channels to form a fixed bit sequence of length N₀Bit sequence of

Then the bit sequence is processed

Sending the data into a traditional polarization code encoder for polarization coding, and obtaining M bits v after puncturing according to a puncturing position indication sequence p_1:M(ii) a Then, these are combinedBits and Q-M retransmission information bits z determined according to retransmission sequence number sequence r_1:Q-MCombined to form a sequence x of length Q to be transmitted_1:Q(ii) a Wherein,the natural number subscript k is the element number in the bit vector of the retransmission information, the maximum value is Q-M, and the length x of the sequence to be transmitted_1:QRespectively with v_1:MEqual, i.e. x_1:M=v_1:MThe last Q-M elements are respectively related to z_1:Q-MEqual, i.e. x_M+1:Q=z_1:M-Q(ii) a Then setting the initial value t =0 of the sending time counter;

(3) transmitting a bit sequence: after the value T of the sending time counter is added with 1, judging whether T is greater than T, if so, terminating the transmission process, declaring the transmission failure, and ending all operations of the method; otherwise, the signal transmitting end transmits a bit sequence according to the following method:

if t =1, sequentially transmitting the first N of the bit sequence to be transmitted₁A bit

Otherwise, the Nth bit sequence to be transmitted is transmitted in sequence_t-1+1 to Nth_tA bit, i.e.

(4) Receiving a bit sequence: the signal receiving end adopts a serial cancellation decoding algorithm to carry out serial cancellation decoding on the signal sequences y which are totally received from the channel after the previous t transmissions

Nt carries out polar code decoding, then carries out CRC check on the obtained decoded bit sequence, and judges whether the decoded bit sequence can pass the CRC check;

if the CRC fails, the receiving end sends a NACK signal to the sending end through a feedback link and returns to execute the step (3);

if the CRC passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.

Compared with the prior art, the method has the innovative advantages that: the invention improves the probability of correct decoding of the part of bits by retransmitting the bits carried by the part of information channels. The invention can make the HARQ scheme based on the polar code optimized to the utmost extent by puncturing the polar code and adjusting the sequence length of repeated transmission of partial information bits, the adjustment step is only 1 bit, and the throughput can be accurately estimated. Moreover, the method is realized by simple operation steps of punching, repeated transmission and the like on common polarization codes, the operation is simple and convenient, and the complexity of coding and decoding of the polarization codes is very low, so that the overall complexity of the operation of the method is obviously reduced compared with that of the conventional various transmission systems. Therefore, the invention is more suitable for application in an actual communication system and has good popularization and application prospects.

Drawings

Fig. 1 is a schematic diagram of a basic unit circuit structure of channel polarization.

Fig. 2 is a schematic diagram of a recursive structure of a channel polarization apparatus with a length N, wherein a minimum unit of the recursion (i.e., when N = 1) is the basic unit shown in fig. 1.

Fig. 3 is a code tree diagram of a polarization code with a code length N = 4. The solid black line in the figure indicates a path obtained by serial cancellation decoding, and the corresponding bit estimation sequence is (0110).

Fig. 4 is a timing diagram of an example of a hybrid automatic repeat request (HARQ) transmission.

Fig. 5 is a flowchart illustrating the operation steps of the polar code-based hybrid automatic repeat request transmission method according to the present invention.

Fig. 6 is a search flowchart of an optimal transmission parameter configuration given an information sequence length K, a maximum number of transmission times T, and a maximum number of transmission bits Q.

Fig. 7 is a flowchart showing the configuration of the transmission error probability sequence e, the sequence number set a of the information channel, the puncture position indication sequence p, and the channel sequence number sequence r corresponding to the retransmission information bit, under the condition that the given information sequence length K and the punctured bit sequence length m are taken as values.

Fig. 8 is a flowchart of searching the optimal allocation parameter set S and the throughput rate estimation value η in the optimal allocation when the information sequence length is K and the post-puncturing sequence length is m.

Fig. 9 is a graph comparing the estimated throughput value of the method of the present invention with the actual value obtained by the simulation example.

Fig. 10 is a diagram comparing the method of the present invention with the HARQ scheme based on LDPC codes and turbo codes.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the accompanying drawings.

The operation content of the hybrid automatic repeat request (HARQ) transmission method based on the punctured polarization code is as follows: the signal sending end carries out primary polarization coding on an information bit sequence to be sent, and the obtained coded bits are sent to a channel for transmission after hole drilling; the signal receiving end decodes the received signal and performs Cyclic Redundancy Check (CRC) on the decoding result; if the verification is passed, the signal receiving end sends an Acknowledgement (ACK) signal to the sending end through a feedback link; otherwise, sending a non-acknowledgement (NACK) signal to the sending end; if the sending end receives the NACK signal, part of the information bits are directly sent to the receiving end through a channel without being coded, and the receiving end decodes again according to the coded bits received for the first time and the newly received information bits; if the decoding result still cannot pass the CRC, after receiving the NACK signal, the sending end sends the other part of information bits to the receiving end through the channel again without encoding, and the receiving end decodes again according to the encoding bits received for the first time, the information bits received for the previous time and the newly received information bits; the above process is continuously executed, and a complete transmission process is not finished until the sending end receives the ACK signal or the sending times reach a preset maximum value. The method comprises the following operation steps:

referring to fig. 5, the specific operation steps of the method of the present invention are described:

step 1, determining the following transmission parameters according to the requirements and the channel parameters: the transmission aims at that the signal transmitting end is within the maximum transmitting times T and the used code length is N₀The polarization code of (1) transmits an information bit sequence containing CRC check bits and having a length of K to a signal receiving end through a binary input memoryless channel W, and the maximum bit number allowed to be transmitted in total is Q within T times of transmission; wherein, the positive integer N₀Is a power of 2, and N₀More than or equal to K; the sequence number set of an information channel required by polarization coding is A; the length of a bit sequence of a polarization code coding bit sequence after puncturing is M, the puncturing position indication sequence of the polarization code coding bit sequence is p, and channel serial numbers corresponding to information bits for preparing repeated transmission are sequentially stored in a retransmission serial number sequence r with the length of Q-M; after the 1 st, 2 nd, … … th and T th transmissions, the total number of bits received by the receiving end is: n is a radical of₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q。

In step 1, only three preset parameters are provided: the length K of the information sequence, the maximum number of transmissions T and the maximum number of transmitted bits Q, while the remaining parameters include the length N of the polar code₀A sequence number set A of information channels, a bit sequence length M after puncturing, a puncturing position indication sequence p, a retransmission sequence number r, and a total bit number N received by a receiving end after each transmission₁、N₂、……、N_TThe parameters of (a) are calculated by performing the following steps (see the search flow shown in fig. 6):

(11) initialization setting parameter set

Optimum throughput rate eta_opt=0, optimal post-puncturing bit sequence length m_opt=0, wherein,

representing an empty set; and initializing the set punctured bit sequence length m = K.

(12) Calculating to obtain a transmission error probability sequence e with the length of Q-m +1 according to the information sequence length K and the bit sequence length m after the punching, wherein the transmission error probability sequence e is used for storing the probability value of transmission error under a serial offset decoding algorithm when the total number n of sent bits is valued in { m, m +1, …, Q }; and simultaneously obtaining a sequence number set A of the corresponding information channel, a puncturing position indication sequence p and a channel sequence number sequence r corresponding to the retransmission information bit. This step includes the following operations (see fig. 7):

(121) according to the value of the length m of the bit sequence after the punching, a traditional punching polarization coding method is adopted to construct an information bit number of K and a code length before the punching of KAnd a punctured polarization code with a code length m after puncturing, wherein the sequence number set of the information channel is A, and the puncturing position indication sequence is p; then, the probability density function of the Log Likelihood Ratio (LLR) value of the received signal of each information channel when the all-zero sequence is sent is obtained by utilizing density evolution calculation

Wherein, the superscript i in the parentheses is the channel serial number and satisfies i ∈ A.

(122) And respectively initializing a transmission error probability sequence e and a channel sequence number sequence r corresponding to the retransmission information bit into a full-zero sequence with the length of Q-m +1 and a full-zero sequence with the length of Q-m, and commanding the channel sequence number k =1 corresponding to the retransmission information bit.

(123) For each channel in the sequence number set A belonging to the information channel, the probability of transmission error is calculated respectively $q_i=1-{\&Integral;}_{-\&infin;}^0{a}_{n_0}^{\left(i\right)}\left(x\right)\mathrm{dx},$ And updating the transmission error probability sequence $e_k=\underset{i\&Element;A}{\mathrm{\&Sigma;}}{q}_i.$

(124) Finding the information channel that is currently least reliable, i.e. selecting q from A_iThe information channel serial number i with the maximum value is set, and the channel serial number r corresponding to the retransmission information bit is set_k= i, and update probability density function of LLR corresponding to the channel

Where a is a probability density function of LLR values of a received signal when bit 0 is transmitted through channel W, and a is calculated

Representing a convolution.

(125) Judgment of k<Whether Q-m is established or not, if so, setting k = k +1, and then returning to execute the step (123); otherwise, according to the formula

Setting the last element in the transmission error probability sequence, recording the obtained transmission error probability sequence e, the sequence number set A of the information channel, the puncture position indication sequence p and the numerical value of the channel sequence number sequence r corresponding to the retransmission information bit, and ending the calculation process.

(13) Searching and obtaining an optimal configuration parameter set S and a throughput rate estimation value eta under optimal configuration when the length of an information sequence is K and the length of a bit sequence after puncturing is m; and judging eta>η_optIf yes, executing the subsequent step (14); otherwise, jumping to execute step (15). The search operation in this step includes the following (see fig. 8):

(131) initializing an optimal configuration parameter set when the information sequence length is K and the sequence length after puncturing is m

The estimated throughput value η =0 under the optimal configuration, and the transmission number of times l = 1;

(132) setting a temporary set T₁= S, and n = m is set;

(133) judging whether n belongs to S or not, if yes, skipping to execute the step (137); otherwise, performing a subsequent step (134);

(134) setting a temporary set T₂= S $, { n }, and then the set T will be aggregated₂After the elements in the tree are arranged from small to large, the values are assigned to n in sequence₁、n₂、……、n_l；

(135) According to the transmission error probability sequence e, calculating the maximum length of the information sequence when the length of the information sequence is K and the length of the punctured sequence is mThe total bit number of the sub-transmission and the receiving end after each transmission is n in turn₁、n₂、……、n_lTime throughput rate estimation $\mathrm{\&rho;}=\frac{K\&times;(1-e_{n_l-m+1})}{{\mathrm{\&Sigma;}}_{t=1}^l{n}_t\&times;(e_{n_{t-1}-m+1}-e_{n_t-m+1})+n_l\&times;e_{n_l-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">m</figure-callout>}+1}};$ In the formula, a natural number variable t is a temporary numerical value of a transmission number, and the maximum value is l;

(136) determining rho>If eta is true, set T₁= S $ { n }, and η = ρ is recorded; otherwise, directly executing step (137);

(137) judging whether n < Q is true, if yes, setting n = n +1, and returning to the step (133); otherwise, step (138) is performed.

(138) Recording the optimal configuration parameter set S = T when the number of elements in S is l₁And its corresponding throughput rate estimate η;

(139) judging whether l < T is true, if so, setting l = l +1, and returning to the step (132); otherwise, ending the searching process of the step (13).

(14) Recording and updating the configured transmission parameters: s_opt=S，η_opt=η，m_opt=m；

(15) Judging whether m < Q is true, if so, setting m = m +1, and then returning to execute the step (12); otherwise, performing a subsequent step (16);

(16) sorting and outputting parameters of the optimal configuration scheme: will S_optThe elements in the sequence are arranged from small to large and are sequentially assigned to N₁、N₂、……、N_T(ii) a Resetting M = M_optAnd

wherein,indicating a rounding up operation.

And 2, encoding and initializing a transmission sequence: the information sequence with the length of K and the information sequence with the length of N which is known in advance at the receiving end and the transmitting end₀The fixed bit sequences of-K are combined according to the set A of sequence numbers of the information channels to form a fixed bit sequence of length N₀Bit sequence of

Then the bit sequence is processedSending the data into a traditional polarization code encoder for polarization coding, and obtaining M bits v after puncturing according to a puncturing position indication sequence p_1:M(ii) a Then, these bits are compared with Q-M retransmission information bits z determined according to the sequence r of retransmission sequence numbers_1:Q-MCombined to form a sequence x of length Q to be transmitted_1:Q(ii) a Wherein,

the natural number subscript k is the element number in the bit vector of the retransmission information, the maximum value is Q-M, and the length x of the sequence to be transmitted_1:QRespectively with v_1:MEqual, i.e. x_1:M=v_1:MThe last Q-M elements are respectively related to z_1:Q-MEqual, i.e. x_M+1:Q=z_1:Q-M(ii) a The initial value t =0 of the transmission number counter is set again.

Step 3, sending a bit sequence: after the value T of the sending time counter is added with 1, judging whether T is greater than T, if so, terminating the transmission process, declaring the transmission failure, and ending all operations of the method; otherwise, the signal transmitting end transmits a bit sequence according to the following method:

if t =1, sequentially transmitting the first N of the bit sequence to be transmitted₁A bit

Otherwise, the Nth bit sequence to be transmitted is transmitted in sequence_t-1+1 to Nth_tA bit, i.e.

Step 4, receiving a bit sequence: the signal receiving end adopts a serial cancellation decoding algorithm to carry out serial cancellation decoding on the signal sequences which are totally received from the channel after the previous t transmissions

Carrying out polarization code decoding, carrying out CRC (cyclic redundancy check) on the obtained decoded bit sequence, and judging whether the decoded bit sequence can pass the CRC;

if the CRC fails, the receiving end sends a NACK signal to the sending end through a feedback link, and the step 3 is executed in a returning way;

if the CRC passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.

In step 4, the path metric calculation operation required for executing the decoding algorithm includes the following steps: ,

(41) by sequenceRepresents a certain decoding path and is the same as the decoding method of the conventional punctured polarization code, according to the received signal sequence y at the 1 st transmission_1:MAnd the channel transfer function of the polarized subchannel with the sequence number i $W_N^{\left(i\right)}(y_{1:M},u_{1:i-1}|u_i)$ Calculating conditional probabilities $P\left(y_{1:M}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}(y_{1:M},{\hat{u}}_{1:i-1}|{\hat{u}}_i)}{2^{i-1}};$ In the formula, transfer function

For passing through the channel

Transmitting bit u_iWhen the received signal is y_1:MAnd u_1:i-1The probability of (c).

(42) From received signal sequence obtained at 2 nd to t th transmission

The conditional probability is calculated with the transition probability function W (y | x) of the channel W

Here, the transition probability function W (y | x) is a probability that a received signal is y when a bit x is transmitted through the channel W. The method comprises the following steps:

(421) initial setup conditional probabilityAnd a sequence number offset value j =1 is set.

(422) Judgment of r_jWhether i is less than or equal to the value of i, if so, determining $P\left(y_{M+{1:N}_t}\right|{\hat{u}}_{1:i})=P\left(y_{M+{1:N}_t}\right|{\hat{u}}_{1:i})\&CenterDot;W\left(y_{M+j}\right|{\hat{u}}_{r_k});$ If not, then, $P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})\&times;(W\left(y_{M+j}\right|0)+W\left(y_{M+j}\right|1)).$

(423) j is judged<N_t-M is true, if yes, setting j = j +1, and returning to perform step (422); otherwise, the following step is performed (424).

(424) Recorded and obtainedAnd the calculation process is ended.

(43) According to the formula $P\left(y_{{1:N}_t}\right|{\hat{u}}_{1:i})=P\left(y_{1:M}\right|{\hat{u}}_{1:i})P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})$ Calculating when the transmitted signal isThe received signal isAnd represents a path of length i by the conditional probability value

Is measured.

The invention has been carried out a plurality of times of experiments and simulation use of the simulation embodiment, and the implementation process and performance analysis of the invention are described in detail with respect to the test results of the simulation embodiment as follows:

1. comparison of estimated values of throughput rates with actual values

Under a binary input additive white Gaussian noise (BAWGN) channel, taking symbol signal-to-noise ratios SNR = { -3.0,0.0,3.0} dB, information sequence lengths K =1024 and the lengths M of sequences after puncturing of polarization code coding output as experimental parameters of an embodiment that are respectively equal to {2656,1640,1184}, and comparing differences of estimated values and actual values of throughput rate by simulation, 30 bits are retransmitted each time, namely N is N_t+1-N_t=30，N₁If = M, the simulation quantity is at least 1000000 information blocks. The calculation and simulation results are shown in fig. 9.

It can be seen that the transmitted estimate is a very accurate lower bound of the actual value. Therefore, the estimation value is used for selecting the transmission scheme parameter configuration, and a very good optimization effect can be achieved.

2. Comparison with HARQ scheme based on LDPC code and turbo code

In a binary input additive white gaussian noise (BAWGN) channel, the length of an information sequence K =1024, the maximum number of transmission times T =6, and the maximum number of transmission bits Q = 16384. The transmission parameter configuration obtained by searching is shown in table 1 below, and the throughput rate curve is shown in fig. 10 by using the serial cancellation decoding algorithm.

Table 1 search derived optimal transmission parameter configuration

SNR(dB)	M	N1	N2	N3	N4	N5	N6
								-4.0	3262	3262	3348	3477	3666	3940	4874
-3.0	2729	2729	2800	2906	3059	3283	4033
								-2.0	2272	2272	2326	2410	2531	2713	3322
-1.0	1922	1922	1961	2026	2121	2263	2739
								-0.0	1665	1665	1699	1752	1829	1949	2351
1.0	1472	1472	1497	1536	1599	1693	2014
								2.0	1310	1310	1332	1363	1410	1482	1741
3.0	1200	1200	1217	1241	1276	1335	1540
								4.0	1120	1120	1133	1150	1172	1218	1375
5.0	1059	1059	1064	1075	1089	1121	1227
								6.0	1036	1036	1041	1048	1057	1076	1144
7.0	1027	1027	1029	1032	1038	1050	1099
								8.0	1024	1024	1025	1027	1030	1036	1063
9.0	1024	1024	1025	1027	1029	1032	1047
								10.0	1024	1024	1025	1026	1027	1029	1036

Referring to a graph comparing the scheme of the present invention with the HARQ scheme based on LDPC codes and turbo codes as shown in fig. 10, it can be seen from a comparison curve of throughput rates that: the method of the invention can obtain almost equivalent throughput rate compared with the best technical scheme adopting LDPC or Turbo code, and even can obtain better throughput rate under the conditions of medium and high signal-to-noise ratio. In addition, because the receiving end adopts a low-complexity serial offset decoding algorithm, and the selection rule of retransmission bits is simple, the construction and receiving complexity of the receiving end is far lower than that of the scheme based on the LDPC and Turbo codes.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A hybrid automatic repeat request (HARQ) transmission method based on a polar code, characterized in that: the signal sending end carries out primary polarization coding on an information bit sequence to be sent, and the obtained coded bits are sent to a channel for transmission after hole drilling; the signal receiving end decodes the received signal and performs Cyclic Redundancy Check (CRC) on the decoding result; if the verification is passed, the signal receiving end sends an Acknowledgement (ACK) signal to the sending end through a feedback link; otherwise, sending a non-acknowledgement (NACK) signal to the sending end; if the sending end receives the NACK signal, part of the information bits are sent to the receiving end through the channel without being coded, and the receiving end decodes again according to the coded bits received for the first time and the newly received information bits; if the decoding result still cannot pass the CRC, after receiving the NACK signal, the sending end sends the other part of information bits to the receiving end through the channel again without encoding, and the receiving end decodes again according to the encoding bits received for the first time, the information bits received for the previous time and the newly received information bits; the above process is continuously executed, and a complete transmission process is not finished until the sending end receives the ACK signal or the sending times reach the preset maximum value; the method comprises the following operation steps:

(1) determining the following transmission parameters according to the requirements and the channel parameters: the transmission aims at that the signal transmitting end is within the maximum transmitting times T and the used code length is N₀The polarization code of (1) transmits an information bit sequence containing CRC check bits and having a length of K to a signal receiving end through a binary input memoryless channel W, and the maximum bit number allowed to be transmitted in total is Q within T times of transmission; wherein, the positive integer N₀Is a power of 2, and N₀More than or equal to K; the sequence number set of an information channel required by polarization coding is A; the length of a bit sequence of a polarization code coding bit sequence after puncturing is M, the puncturing position indication sequence of the polarization code coding bit sequence is p, and channel serial numbers corresponding to information bits for preparing repeated transmission are sequentially stored in a retransmission serial number sequence r with the length of Q-M; after the 1 st, 2 nd, … … th and T th transmissions, the total number of bits received by the receiving end is: n is a radical of₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q；

(2) Encoding and initializing the transmission sequence: the information sequence with the length of K and the information sequence with the length of N which is known in advance at the receiving end and the transmitting end₀The fixed bit sequences of-K are combined according to the set A of sequence numbers of the information channels to form a fixed bit sequence of length N₀Bit sequence ofThen apply the sameBit sequence

Sending the data into a traditional polarization code encoder for polarization coding, and obtaining M bits v after puncturing according to a puncturing position indication sequence p_1:M(ii) a Then, these bits are compared with Q-M retransmission information bits z determined according to the sequence r of retransmission sequence numbers_1:Q-MCombined to form a sequence x of length Q to be transmitted_1:Q(ii) a Wherein,the natural number subscript k is the element number in the bit vector of the retransmission information, the maximum value is Q-M, and the length x of the sequence to be transmitted_1:QRespectively with v_1:MEqual, i.e. x_1:M=v_1:MThe last Q-M elements are respectively related to z_1:Q-MEqual, i.e. x_M+1:Q=z_1:Q-M(ii) a Then setting the initial value t =0 of the sending time counter;

(3) transmitting a bit sequence: after the value T of the sending time counter is added with 1, judging whether T is greater than T, if so, terminating the transmission process, declaring the transmission failure, and ending all operations of the method; otherwise, the signal transmitting end transmits a bit sequence according to the following method:

if t =1, sequentially transmitting the first N of the bit sequence to be transmitted₁A bit

(ii) a Otherwise, the Nth bit sequence to be transmitted is transmitted in sequence_t-1+1 to Nth_tA bit, i.e.

(4) Receiving a bit sequence: the signal receiving end adopts a serial cancellation decoding algorithm to carry out serial cancellation decoding on the signal sequences which are totally received from the channel after the previous t transmissions

Carrying out polarization code decoding, carrying out CRC (cyclic redundancy check) on the obtained decoded bit sequence, and judging whether the decoded bit sequence can pass the CRC;

if the CRC fails, the receiving end sends a NACK signal to the sending end through a feedback link and returns to execute the step (3);

if the CRC passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.

2. The method of claim 1, wherein: in the step (1), the preset parameters are only three: length K of information sequence, maximum number of transmission times T and maximum number of transmitted bits Q, and includes length N of polarization code₀A sequence number set A of information channels, a bit sequence length M after puncturing, a puncturing position indication sequence p, a retransmission sequence number r, and a total bit number N received by a receiving end after each transmission₁、N₂、……、N_TThe parameters are obtained by executing the following steps:

(11) initialization setting parameter setOptimum throughput rate eta_opt=0, optimal post-puncturing bit sequence length m_opt=0, wherein,

representing an empty set; initializing and setting the length m = K of the bit sequence after the punching;

(12) calculating to obtain a transmission error probability sequence e with the length of Q-m +1 according to the information sequence length K and the bit sequence length m after the punching, wherein the transmission error probability sequence e is used for storing the probability value of transmission error under a serial offset decoding algorithm when the total number n of sent bits is valued in { m, m +1, …, Q }; simultaneously obtaining a sequence number set A, a puncture position indication sequence p and a retransmission sequence number sequence r of the corresponding information channel;

(13) searching and obtaining the length of the bit sequence after the puncture when the length of the information sequence is KThe optimal configuration parameter set S is m and the throughput rate estimation value eta under the optimal configuration; and judging eta>η_optIf yes, executing the subsequent step (14); otherwise, jumping to execute the step (15);

(14) recording and updating the configured transmission parameters: s_opt=S，η_opt=η，m_opt=m；

(15) Judging whether m < Q is true, if so, setting m = m +1, and then returning to execute the step (12); otherwise, performing a subsequent step (16);

(16) sorting and outputting parameters of the optimal configuration scheme: will S_optThe elements in the sequence are arranged from small to large and are sequentially assigned to N₁、N₂、……、N_T(ii) a Resetting M = M_optAnd

wherein,

indicating a rounding up operation.

3. The method according to claim 2, characterized in that said step (12) comprises the following operations:

(121) according to the value of the length m of the bit sequence after the punching, a traditional punching polarization coding method is adopted to construct an information bit number of K and a code length before the punching of K

The code length after puncturing is m, wherein the serial number set of the information channel is A, and the puncturing position indication sequence is p; then, the probability density function of the log likelihood ratio LLR value of the received signal of each information channel when the all-zero sequence is sent is obtained by utilizing density evolution calculation

Wherein the superscript i in the parentheses is the channel number, andsatisfying i belongs to A;

(122) respectively initializing a transmission error probability sequence e and a channel sequence r corresponding to retransmission information bits into a full-zero sequence with the length of Q-m +1 and a full-zero sequence with the length of Q-m, and commanding a channel serial number k =1 corresponding to the retransmission information bits;

(123) for each channel in the sequence number set A belonging to the information channel, the probability of transmission error is calculated respectively $q_i=1-{\&Integral;}_{-\&infin;}^0{a}_{n_0}^{\left(i\right)}\left(x\right)\mathrm{dx},$ And updating the transmission error probability sequence $e_k=\underset{i\&Element;A}{\mathrm{\&Sigma;}}{q}_i;$

(124) Finding the information channel that is currently least reliable, i.e. selecting q from A_iThe information channel serial number i with the maximum value is set, and the channel serial number r corresponding to the retransmission information bit is set_k= i, and update probability density function of LLR corresponding to the channel

Where a is a probability density function of LLR values of a received signal when bit 0 is transmitted through channel W, and a is calculated

Represents a convolution;

(125) judgment of k<Whether Q-m is established or not, if so, setting k = k +1, and then returning to execute the step (123); otherwise, according to the formula

Setting the last element in the transmission error probability sequence, recording the obtained values of the transmission error probability sequence e, the sequence number set A of the information channel, the puncture position indication sequence p and the retransmission sequence number sequence r, and ending the calculation process.

4. The method according to claim 2, wherein the search operation in step (13) comprises the following:

(131) initializing an optimal configuration parameter set when the information sequence length is K and the sequence length after puncturing is m

The estimated throughput value η =0 under the optimal configuration, and the transmission number of times l = 1;

(132) setting a temporary set T₁= S, and n = m is set;

(133) judging whether n belongs to S or not, if yes, skipping to execute the step (137); otherwise, performing a subsequent step (134);

(134) setting a temporary set T₂= S $, { n }, and then the set T will be aggregated₂After the elements in the tree are arranged from small to large, the values are assigned to n in sequence₁、n₂、……、n_l；

(135) According to the transmission error probability sequence e, calculating that when the length of the information sequence is K, the length of the sequence after puncturing is m, the transmission is carried out for at most one time, and the total bit number received by the receiving end after each transmission is n in sequence₁、n₂、……、n_lTime throughput rate estimation $\mathrm{\&rho;}=\frac{K\&times;(1-e_{n_l-m+1})}{{\mathrm{\&Sigma;}}_{t=1}^l{n}_t\&times;(e_{n_{t-1}-m+1}-e_{n_t-m+1})+n_l\&times;e_{n_l-m+1}};$ In the formula, natural number variablet is a temporary numerical value of the transmission times sequence number, and the maximum value is l;

(136) determining rho>If eta is true, set T₁= S $ { n }, and η = ρ is recorded; otherwise, directly executing step (137);

(137) judging whether n < Q is true, if yes, setting n = n +1, and returning to the step (133); otherwise, step (138) is performed.

(138) Recording the optimal configuration parameter set S = T when the number of elements in S is l₁And its corresponding throughput rate estimate η;

(139) judging whether l < T is true, if so, setting l = l +1, and returning to the step (132); otherwise, ending the searching process of the step (13).

5. The method according to claim 1, wherein in step (4), the path metric calculation operation required for executing the decoding algorithm comprises the following steps:

(41) by sequence

Represents a certain decoding path and is the same as the decoding method of the conventional punctured polarization code, according to the received signal sequence y at the 1 st transmission_1:MAnd the channel transfer function of the polarized subchannel with the sequence number i $W_N^{\left(i\right)}(y_{1:M},u_{1:i-1}|u_i)$ Calculating conditional probabilities $P\left(y_{1:M}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}(y_{1:M},{\hat{u}}_{1:i}|{\hat{u}}_i)}{2^{i-1}};$ In the formula, transfer function

For passing through the channel

Transmitting bit u_iWhen the received signal is y_1:MAnd u_1:i-1The probability of (d);

(42) from received signal sequence obtained at 2 nd to t th transmission

The conditional probability is calculated with the transition probability function W (y | x) of the channel W

Wherein, the transition probability function W (y | x) is the probability that the received signal is y when the bit x is transmitted through the channel W;

(43) according to the formula $P\left(y_{1:N_t}\right|{\hat{u}}_{1:i})=P\left(y_{1:M}\right|{\hat{u}}_{1:i})\&CenterDot;P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})$ Calculating when the transmitted signal is

The received signal isAnd represents a path of length i by the conditional probability value

Is measured.

6. The method according to claim 5, characterized in that said step (42) comprises the following operations:

(421) initial setup conditional probability

And setting a serial number offset value j = 1;

(422) judgment of r_jWhether i is less than or equal to the value of i, if so, determining $P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})=P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})\&CenterDot;W\left(y_{M+j}\right|{\hat{u}}_{r_k});$ If not, then, $P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left(y_{{M+1:N}_t}\right|{\hat{u}}_{1:i})\&times;(W\left(y_{M+j}\right|0)+W\left(y_{M+j}\right|1));$

(423) j is judged<N_t-M is true, if yes, setting j = j +1, and returning to perform step (422); otherwise, performing a subsequent step (424);

(424) recorded and obtained

And the calculation process is ended.

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