CN110460340B

CN110460340B - Self-adaptive construction and decoding method based on random convolutional network error correcting code

Info

Publication number: CN110460340B
Application number: CN201910626457.6A
Authority: CN
Inventors: 郭网媚; 刘明叶; 高晶亮; 田敏涵; 李永康; 张泽阳; 姚璐阳
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2019-07-11
Filing date: 2019-07-11
Publication date: 2022-04-05
Anticipated expiration: 2039-07-11
Also published as: CN110460340A

Abstract

The invention discloses a self-adaptive construction and decoding method based on random convolutional network error correcting codes, which solves the problem of high complexity of an error correcting coding and decoding algorithm in a network with unknown topology and transmission delay in the prior art, and comprises the following implementation steps: adaptively constructing random convolutional network codes; constructing a convolution error correcting code as an input code of random convolution network error correcting coding; decoding at a receiving end by using a q-element random convolutional network error correction decoding algorithm; and optimizing the algorithm. The invention provides a self-adaptive random convolutional network coding, and different nodes select local coding kernels with different lengths according to self conditions; searching error information by using all-zero test data, equating the collected combined errors to a signal source end and designing an error correcting code capable of correcting the errors; the error correction decoding algorithm based on the minimum network error weight of the combined errors is provided, and the coding and decoding algorithm with low complexity, low time delay and strong error correction capability is realized and is used for an actual network with unknown topology and transmission delay.

Description

Self-adaptive construction and decoding method based on random convolutional network error correcting code

Technical Field

The invention belongs to the technical field of network coding, mainly relates to a random convolutional network coding and decoding technology, and particularly relates to a self-adaptive construction and decoding method based on a random convolutional network error correcting code, which is used in an actual network with unknown network topology and time delay.

Background

Network coding was originally proposed by Ahlswede in 2000, the essence of which was to allow intermediate nodes to perform forwarding operations after processing received information. Many efforts have shown that network coding has potential advantages in terms of throughput, load balancing, security, etc., and has attracted widespread attention. Random Network Coding (RNC), which allows intermediate nodes to randomly select coding coefficients within a limited domain, is feasible for unknown topologies, and t.ho et al demonstrate that when the number of users is larger than the size of the coding domain, the probability of random successful coding approaches 1. Convolutional Network Coding (CNC) allows a combination of nodes to receive information from different input channels and different time slots, which is more feasible for actual communications. Errors always exist in a communication system, and even a single error can affect more symbols at a receiving node due to the mixing process of intermediate nodes, so that error correction is indispensable to RNC and CNC, and is an important guarantee for correct decoding.

Convolutional Network Error Correction Code (CNECC) was originally proposed by k.prasad et al and presented the construction and decoding algorithms of CNECC to correct a set of network errors for coherent networks. For error correction in random network coding, Koetter and Kschickang propose to represent code words by subspaces, Silva and Kschickang indicate that the boosted rank metric code is almost the optimal subspace code of random network coding, A.Wachter-Zeh and the like provide rank metric convolutional codes, namely, convolutional codes are used at a source end to correct errors, but the complexity of using the subspace codes and the rank distance codes is higher, and the realization is difficult. Yang et al propose a quasi-Viterbi decoding algorithm based on minimum error weight, and a generalized CNECC constructed by the method proposed by K.Prasad gives sufficient conditions for algorithm feasibility, but only considers a deterministic network and a binary finite field

And (4) decoding.

In summary, in the coding and decoding scheme based on the coherent network in the prior art, the coherent network is a network determined by topology and determined by encoding, and is not very suitable for a network with unknown topology and time delay.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the defects of the conventional network coding and decoding algorithm of the random coil machine, the self-adaptive construction and decoding method based on the random convolutional network error correcting code is provided, and has strong error correction capability and low complexity.

In order to realize the purpose of the invention, the invention adopts the following technical scheme:

step 1, self-adaptively constructing random convolutional network coding:

the source node sends all-zero data packets to the network to construct a random convolutional network code in a self-adaptive manner, starting from a small code domain, the length of a Local Encoding Kernel (LEK) is increased until all relevant receiving nodes can be translated into a stop, and at the moment, the coding is successful; the receiving node receives a combined error vector formed by the mixed superposition of the network errors through the intermediate nodes;

step 2, constructing a random convolution network error correcting code:

collecting network errors by using all-zero test data; the global coding core (GEK) is sent to the receiving nodes according to the time slot, so that the information of the transmission matrix is obtained in a distributed mode at the receiving nodes, and meanwhile, network errors are mixed according to the transmission coding coefficient, and combined errors are obtained in a distributed mode; when the network intermediate node uses a general polynomial as a coefficient, the adjoint matrix of the transmission matrix is used for replacing the inverse matrix of the transmission matrix, and the combination error is equivalent to the information source end; maximum weight T according to equivalent error of information source terminal_sSelecting the free distance more than or equal to 2T at the information source end_s+1 error correction code capable of correcting network errors as input code of the random convolutional network;

step 3, improving to obtain a q-element random convolutional network error correction decoding algorithm:

extending Viterbi-like decoding algorithms based on minimum network error weight to random convolutional networks and

field, forming q-aryA random convolutional network error correction decoding algorithm; the q-element random convolution network error correction decoding algorithm is based on the combined error vectors, the weight of each combined error vector is defined as the weight of the minimum network error vector, and a decoding path with the accumulated minimum error weight is searched; the algorithm is directly decoded at a receiving node and can correct any error in the error correction range of the random convolutional network error correction code;

step 4, optimizing the error correction decoding algorithm of the q-element random convolution network:

in the operation of optimizing the received sequence, updating the decoded sequence by subtracting the influence of the error-correcting decoded code word of the q-element random convolutional network and the estimated network error; the situation in the subsequent window is equivalently transformed into the first window by removing the influence caused by the input sequence before the window, and distributed decoding with low complexity and low decoding delay is realized.

The invention provides the whole technical scheme for realizing the self-adaptive construction and decoding method of the random convolutional network error correcting code through the four steps, has strong error correcting capability and low complexity, and is suitable for a network with unknown topology and time delay.

Advantageous effects

Compared with the prior art, the invention has the beneficial effects that:

the requirements of an actual network are met: the invention constructs random convolution network coding, combines the advantages of random network and convolution network, is suitable for network with unknown topology and time delay, and is more suitable for actual network.

The error correction capability is strong: and (3) encoding operation: the invention estimates the maximum weight of equivalent errors at the source for a set of network errors that may occur, and designs an error correction code that can correct the set of network errors before transmitting to the network. And (3) decoding operation: the q-element random convolution network error correction decoding algorithm provided by the invention can correct any error in the RCNECC error correction range based on the accumulative minimum weight decoding of combined errors.

The complexity is low: and (3) encoding operation: the invention constructs the random convolution network coding in a self-adaptive way, combines the advantages of RNC and CNC, selects local coding cores with different lengths according to the self conditions of different nodes, and has the advantages of shortest equivalent coding core length and low coding complexity. And (3) decoding operation: the q-element random convolution network error correction decoding algorithm can directly decode at a receiving node, and the receiving sequence updates the decoding sequence by subtracting the influence of the decoded word and the estimated network error, thereby reducing the complexity and the decoding time delay and realizing the distributed decoding.

Drawings

FIG. 1 is a diagram of a random convolutional network code with an input convolutional code employed in the present invention, and is a schematic flow chart of the present invention;

FIG. 2 is a random convolutional network code diagram of transmission rate 2 in the present invention;

FIG. 3 is a random convolution network code diagram at time t-0 in the present invention;

FIG. 4 is a random convolution network coding diagram at time t-1 in the present invention;

FIG. 5 is a diagram of the correct input and output of the decoding window [0,2] in the present invention;

FIG. 6 is a diagram of the error screening process in the decoding window [0,2] in the present invention.

Detailed Description

The invention is described in detail below with reference to the figures and examples.

Example 1:

the essence of network coding is to allow intermediate nodes to perform forwarding operations after processing received information, with potential advantages in terms of throughput, load balancing, security, etc., and to attract a wide range of attention. Random Network Coding (RNC) allows the intermediate nodes to randomly select coding coefficients within a limited domain, suitable for networks with unknown topology. Convolutional Network Coding (CNC) allows nodes to combine received information from different input channels and different time slots, feasible for a time-delayed network.

An algorithm for constructing a convolutional network error correcting code is provided in the prior art, and the algorithm has certain error correcting capability but is only suitable for a coherent network; subspace codes and rank distance codes are applied to error correction in a random network, but the complexity is high and the implementation is difficult; the mixing process of the intermediate nodes of the network makes the classical Viterbi algorithm based on hamming weight no longer suitable for error correction decoding in the network. In order to solve the problems, the invention develops research on the problems, and provides a self-adaptive construction and decoding method based on random convolutional network error correcting codes, wherein error correction is added in the encoding and decoding processes, the error correcting capability is strong, the complexity is low, and the method is suitable for actual networks.

The invention relates to a self-adaptive construction and decoding method based on a random convolution network error correcting code, which is shown in figure 1 and comprises the following steps:

step 1, self-adaptively constructing random convolutional network coding:

the source side sends omega packet all zero data to the network, so that the network starts adaptive construction. The convolutional network coding is physically realizable if and only if the local coding kernel constant term coefficient matrix K₀Is zero-power, the following operation ensures K₀Is a power of zero: the edges in the network are directional and numbered e_iI is more than or equal to 1 and less than or equal to | E |, and when the time is 0, the local coding core k with the inflection point E' > E_e',e,0If not, uniformly and randomly selecting from the small domain; after the initialization step, k_e',e,tCan be randomly and uniformly selected in a limited field. The Local Encoding Kernel (LEK) length is increased until the global encoding matrix at all relevant receiving nodes is full rank, at which time the encoding is successful and the lengths of the different LEKs may be different. The receiving node receives a combined error vector obtained by the mixed superposition of the network errors through the intermediate nodes.

Step 2, constructing a random convolution network error correcting code:

the self-adaptive random coding of the convolutional network, the information of the global coding core and the transmitted characters are transmitted to the receiving node together according to the time slot, therefore, the information M of the transmission matrix at each moment is acquired in a distributed mode at the receiving node_r,0,M_r,1z,M_r,τz^τ…, distributed computing combination errors

Using transmission matrices M_r(z)＝M_r,0+M_r,1z+…+M_r,τz^τThe adjoint matrix of + … replaces the inverse matrix thereof, avoiding the error of mapping the finite weight of the receiving end to the infinite weight of the source end; the combination error is multiplied by the adjoint matrix of the transmission matrix, so that the error generated by the network is equivalent to the source end; maximum weight T according to equivalent error of information source terminal_sSelecting the free distance more than or equal to 2T at the information source end_s+1 Random Convolutional Network Error Correction Code (RCNECC) capable of correcting network errors.

by y (z) ═ x (z) G_O,t(z)+e(z)F_t(z) obtaining: x (z) G_O,t(z)＝y(z)-e(z)F_t(z) the error sequences e (z) are superposed in a convolution-like manner in a staggered manner to form e (z) F_t(z) which characterizes the effect of any error vector in the network and is ultimately output at the receiving node. Due to the mixing process at the intermediate nodes, even a single error will affect more symbols at the receiving node where decoding is no longer possible based only on the minimum hamming distance between the output sequence and the input sequence, so decoding is based on combining error vectors, finding a new metric: defining the weight of each combined error vector as the weight of the minimum network error vector, and finding the decoding path with the accumulated minimum error weight. Extending a Viterbi-like decoding algorithm with minimal network error weight to a random convolutional network code sum

A domain, which forms a q-element random convolution network error correction decoding algorithm; the q-element random convolutional network error correction decoding algorithm can be directly decoded at a receiving node and can correct any error in an RCNECC error correction range.

in the operation of optimizing the received sequence, when only a unique combined error vector remains in the decoding window, the error needs to be removed from the decoded trellis diagram. Since a 1-bit message of the input sequence will affect the omega-bit message of the error-free output sequence, after removing the effect of the q-ary random convolutional network error correction decoding to decode the codeword, the first omega-bits of the received sequence are all zeros. The sequence is divided by the time delay factor z to be regarded as a newly received sequence, and the situation in the subsequent window can be equivalently transformed into the first window by removing the influence caused by the input sequence before the window, so that the distributed decoding with low complexity and decoding time delay is realized.

The idea of the invention is as follows: the source end sends zero data packets to the network to construct the random convolutional network coding adaptively, and is used for collecting combined error vectors for error correcting code design, because the combined error vectors can be used for estimating errors and equivalent errors of the source whether the combined error vectors are successful or not; equating the combined error vector to the information source end, and designing a random convolution network error correcting code capable of correcting the error at the information source end according to the maximum weight of the equivalent error; and performing error correction decoding at the receiving node by using a random convolutional network error correction decoding algorithm.

The invention constructs random convolution network coding, combines the advantages of random network and convolution network, and is suitable for topology unknown network and network with time delay; errors occurring in a network are equivalent to an information source end, a code word with error correction capability is designed before data is sent, error correction decoding is carried out on a receiving node, the error correction capability is strong, and meanwhile, the complexity of the whole coding and decoding process is low through an optimization algorithm.

Example 2

The self-adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that of the embodiment 1, and the self-adaptive construction random convolutional network coding in the step 1 specifically comprises the following steps:

sending omega packets of all-zero data to a network to enable the network to start adaptive construction; the convolutional network coding is physically realizable if and only if the local coding kernel constant term coefficient K₀The corresponding coding topology is ringless. The edges in the network are directional and numbered e_iI is more than or equal to 1 and less than or equal to | E |, and a pair of edges are marked as inflection points and are numbered as E '> E, namely the edge E' is more than the number of E. All the local coding cores and the global coding core have an initial value of 0, and when the time is 0, for e' being more than or equal to e, the order is givenIts local coding core k_e',e,0Otherwise, the local coding kernel K is uniformly and randomly selected from the small field, and this initialization step ensures that the local coding kernel K is locally encoded₀Is loopless. After initialization k_e',e,tCan be randomly selected.

K_v(z)＝(k_e′,e(z))_{e′∈In(v),e∈Out(v)}＝K_v,0+K_v,1z+K_v,2z²+.. locally encoding a kernel matrix for an intermediate node v at time t, wherein each element k is_e′,e(z)＝k_e′,e,0+k_e′,e,1z+k_e′,e,2z²+.. is a polynomial. Node v stores all incoming edges e' e in (v) received symbols y_e',tAnd randomly selecting t +1 item local coding kernel coefficient k for the output edge e of v_e',e,t. Then constructing a transmission data packet for each output edge e

And globally encode the kernel

Put in the packet head and send out.

At each time t, the receiving node r determines whether the global coding core it receives is full rank. If the rank is full, the success status of itself is set to 1 and an acknowledgement signal ACK is sent to its parent node. And the intermediate node v stops randomly selecting the local coding core and sends the ACK to the father node of the intermediate node v when receiving the ACK of all the child nodes. Subsequent encodings using the determined and stored

The length of the LEK is increased at each time instant until all receiving nodes have a transmission matrix of full rank.

The invention relates to a self-adaptive structured random convolutional network coding, which starts coding from a small coding domain, increases the length of a local coding core until all related receiving nodes can be decoded, allows different nodes to select the local coding cores with different lengths according to self conditions, ensures that the length of an equivalent coding core is as short as possible, reduces decoding time delay and storage requirements, can be applied to the condition of unknown topology and stops in limited time, and obtains output which is a combination error after the construction is successful.

Example 3

The adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that of the embodiment 1-2, the step 1 is the adaptive construction random convolutional network coding, and the mathematical model of the random convolutional network coding is as follows:

the convolutional network coding adopts a self-adaptive random coding mode, F_rThe information of (z) is transmitted to the receiving node in time slots together with the transmitted characters. The source generated data can be represented as:

x(z)＝x⁰+x¹·z+…+x^t-1·z^t-1+…，

the transmission matrix of the sink node r can be represented as:

M_r(z)＝M_r,0+M_r,1z+…+M_r,τz^τ+…，

the corresponding error-free output at each moment when passing through the random convolutional network should be:

the corresponding error output at each moment is as follows:

where z is a delay factor, x (z) is an input sequence, x_tIs the coefficient of x (z) at time t, M_r,tIs M_r(z) coefficients at time t, e (z) is the error sequence, e_tIs the coefficient at time t of e (z), F_r(z) removing the influence in the network caused by the mapping of the source side for the transmission matrix.

The invention constructs a random convolution network coding model, the transmitted data forms convolution in different time slots and is finally output to a receiving node according to time sequence, the process is expressed by a mathematical formula, and an output sequence after network errors are added is obtained by analysis, thereby being beneficial to the subsequent error correction coding and decoding operation.

Example 4:

the self-adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that of the embodiment 1-3, and the construction of the random convolutional network error correcting code in the step 2 specifically comprises the following steps:

2.1) random convolutional network coding collects the combined error vector at each moment by using all-zero test data in the self-adaptive construction process:

wherein l_tIs a matrix F_r(z) highest power series.

2.2) distributed acquisition of the Transmission matrix M_r(z) its determinant | M_r(z) | is a non-zero constant polynomial in inversion

Easily mapping the error of limited weight of the receiving end to the error of infinite weight of the source end, and removing M_r(z)^-1Does not affect the relationship of the corresponding error, so M is used_r(z) accompanying formula

Instead of the inverse matrix.

2.3) computing equivalent errors of the information source end

2.4) order W_H(y) denotes a given vector y ∈ F_qHamming weight of (i.e., a non-zero number of y coefficients); estimating a maximum weight T of an equivalent error at a source node_s＝max{W_H(E)}。

2.5) choosing the free distance at the source node to be 2T_s+1 error correction code capable of correcting equivalent errors.

According to the steps, aiming at a network error set which possibly occurs, when a network intermediate node uses a general polynomial as a coefficient, an adjoint matrix of a transmission matrix is used for replacing an inverse matrix of the network intermediate node, so that errors in the network are equivalent to a signal source end, an error correcting code is designed according to the maximum weight of the equivalent errors of the signal source end, the error correcting code capable of correcting the network error set is designed before being sent to the network, and therefore a decoding algorithm can correct code words in the error correcting range.

Example 5:

the adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that of the embodiments 1-4, and the q-element random convolutional network error correcting and decoding algorithm in the step 3 specifically comprises the following steps:

3.1) from y_r(z)＝x(z)G_O,r(z)+e(z)F_r(z) obtaining: x (z) G_O,r(z)＝y_r(z)-e(z)F_r(z) wherein G_O,r(z) is a generator matrix of the output convolutional code. Processing e (z) at the receiving node is equivalent to processing individual combined error vectors which are cross-superimposed in a convolution manner to form the final e (z) F_t(z) during decoding, all the combined error vectors are corrected, and all the network errors are corrected accordingly.

3.2) adding judgment before the decoding starts, judging whether the intersection of the output message subspace phi (t, l) and the error subspace delta (t, l) only has a null space, if so, the message sequence and the error sequence can be separated, and decoding in a sliding window at the moment to search a combined error vector; if there is no null space, the next time is determined until Φ (t, l) # Δ (t, l) {0 }.

The invention is based on the mixing process of the random convolutional network coding intermediate node, network errors can be diffused and more symbols are influenced at the receiving node, and the minimum Hamming distance decoding based on the input sequence and the output sequence at the receiving node is not feasible any more; inspired by the classic Viterbi algorithm, the decoding process can be implemented in a similar way, in the comparison operation, the hamming weight of the network error vector corresponding to each combined error is defined in advance, when the intersection of Φ (t, l) and Δ (t, l) has only zero space, the window sliding length is determined, decoding is started in the sliding window, the combined error vector is found, and thus the decoding path with the accumulated minimum network error weight is found on the output grid diagram.

Example 6:

the adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that in the embodiments 1-5 and the step 4, wherein the optimized q-element random convolutional network error correction decoding algorithm for realizing the distributed decoding with low complexity and decoding delay specifically comprises the following steps:

4.1) when an error occurs in the network and is uniquely determined in the decoding window, the effect of the combined error vector must be subtracted:

in the formula, y_r(z) as a receiving sequence with errors at the receiving node R epsilon R,

is an error-free received sequence.

4.2) assumption that x can be uniquely determined₀Since the nature of the convolutional network coding is known, the received sequence

Is to transmit a message x₀And x₁Minus the effect of the first bit of information in the output sequence:

deleting x₀After the influence of (c), the first ω bits of the received sequence are all zeros; will y_eff(z)/z is considered as the newly received sequence; the situation in the subsequent window is equivalently transformed into the first window by removing the effect of the input sequence preceding the window.

4.3) assuming a delay of L, i.e. x, for sequence decoding₀The character stream x may be received at the receiving node r from time 0 to L₀M₀,x₀M₁+x₁M₀,…,x₀M_L+…+x_LM₀And (4) uniquely determining. For having global coding core

The sink node r of (1), the necessary condition for decoding delay to be L is rank (F)₀,F₁,…,F_L) ω; combining the decoding condition phi (t, L) # delta (t, L) ═ 0}, obtaining the decoding time delay L of the q-element random convolution network error correction decoding algorithm_delay＝max{l,L}。

The invention optimizes the received sequence, updates the decoding sequence by subtracting the influence of decoded code words and estimated network errors, reduces the complexity of the algorithm, and obtains the decoding delay of the algorithm by combining the decoding delay of sequence decoding.

Example 7:

the adaptive construction and decoding method based on the random convolutional network error correcting code is the same as that of the embodiments 1 to 6, and the specific implementation method is as follows.

The edges in the network are directional and are numbered e_iAnd i is more than or equal to 1 and less than or equal to | E |. At the time 0, the initial values of all the local coding cores and the global coding core are 0, and an all-zero sequence is sent to enable the network to start self-adaptive random coding. For the inflection point with edge e' greater than e, let its local coding kernel k_e',e,0Otherwise, uniformly and randomly selecting from small domain, after the initialization step, k_e',e,tCan be randomly selected. At time t, the intermediate node v stores all the symbols y received by the incoming edges e' e in (v)_e',tAnd randomly selecting t +1 item local coding kernel coefficient k for the output edge e of v_e',e,t. Then, an output data packet is constructed for each output edge e, and a global coding core is put in a packet header to be sent out.

At each time t, the receiving node r determines whether the global coding core it receives is full rank. If the rank is full, an ACK is sent to its parent node. And the intermediate node v stops randomly selecting the local coding core and sends the ACK to the father node of the intermediate node v when receiving the ACK of all the child nodes. Later encoding is performed using the determined and stored k_e',eThe length of the LEK is increased at each time until all receiving nodes have a transmission matrix of full rank.

The mathematical model for constructing the successfully obtained random convolutional network code is as follows:

the convolutional network coding adopts a self-adaptive random coding mode, F_rThe information of (z) is transmitted to the receiving node in time slots together with the transmitted characters. The transmission matrix of the sink node r can be represented as:

M_r(z)＝M_r,0+M_r,1z+…+M_r,τz^τ+…，

the corresponding error output at each moment is as follows:

if the transmitted zero data is wrong in network transmission, the output sequence is a combined error; constructing a convolution error correcting code at the information source to correct the error according to the maximum weight of the equivalent error of the source node; inputting the code word into a network, a group of network errors of the random convolutional network can be corrected, and the method specifically comprises the following steps:

(1) random convolutional network coding gathers the combined error vector at each time using all-zero test data in the adaptive construction process:

wherein l_tIs a matrix F_rThe highest power of (z).

(2) Distributed acquisition transmission matrix M_r(z) its determinant | M_r(z) | is a non-zero constant polynomial in inversion

Instead of the inverse matrix.

(3) Computing source side equivalent error

(4) Let W_H(y) denotes a given vector y ∈ F_qHamming weight of (i.e., a non-zero number of y coefficients); calculating a maximum weight T of an equivalent error at a source node_s＝max{W_H(E)}。

(5) Selecting a free distance of 2T at the source node_s+1 error correction code capable of correcting equivalent errors.

The decoding algorithm used at the sink end is as follows: by y (z) ═ x (z) G_O,t(z)+e(z)F_t(z) obtaining: x (z) G_O,t(z)＝y(z)-e(z)F_t(z) processing the error sequence e (z) at the receiving node, which is equivalent to processing the combined error vector e (z) F_t(z) which characterizes the effect of any error vector e in the network. Although e (z) F_t(z) the convolution-wise mis-superposition creates a great difficulty for error correction, but still does not start with the simplest case first, i.e. all combination errors are not superposed, since F_t(z) tends to be very simple, so the combined error category is much smaller than the number of possible error vectors. In the comparison operation, the weight of each combined error vector is defined as the weight of the smallest error vector. Decoding is to find a decoding path with the smallest accumulated error weight on the output trellis diagram. If all the combined error vectors can be corrected, the network error is corrected, resulting in the correct input sequence. The algorithm is described as follows:

distributed decoding algorithm for convolutional network coding

For the received sequence y (z), the minimum weight decoding algorithm selects the error vector min { w } with the smallest weight at each instant_H(e_i) In view of eachThe combined error vectors do not overlap, and thus are equivalent to selecting the smallest weight net error vector w_H(e (z)). And w_HThe smaller the value of (e (z)) is, the smaller the value of p_eThe smaller, i.e. between the bit error rate p and y (z)_eThe smallest input sequence x (z). The whole decoding process is equivalent to searching the most similar code word x, so that the decoded code word

Probability of not being equal to transmitted codeword x

At the minimum, the temperature of the mixture is controlled,

and max. The decoding result is a MAP path.

For having global coding core

The sink node r, the necessary condition that the sequence decoding delay is L is rank (F)₀,F₁,…,F_L) ω. Combining the minimum weight decoding condition phi (t, L) # delta (t, L) ═ 0, the minimum decoding time delay of the minimum network weight decoding algorithm of the random convolutional network is L_delay＝max{l,L}。

Firstly, adaptively constructing random convolutional network codes, and designing a random convolutional network error correcting code capable of correcting a group of network error sets at a signal source end when the codes are successfully encoded; the data is sent to the network and decoded at the receiving node using a random convolutional network error correction decoding algorithm. The invention constructs random convolution network coding in a self-adaptive way, and the coding and decoding algorithms have error correction capability and reduce complexity and can be applied to actual networks.

The following mainly describes how the present invention uses theorem 1 to determine the decoding window length and the combined error vector.

Example 8:

the adaptive construction and decoding method based on random convolution network error correcting code is the same as the embodiments 1-7, phi (t, l) is output volumeThe product-code spanned message subspace, i.e., all elements in Φ (t, l), are [0, l]X in the window_lG_O,r(z)，x_l(z) all possible input sequences from time 0 to time l. Δ (t, l) denotes the subspace spanned by the error vectors, F_r(z) can be written as a power series

For any error vector e, a corresponding combined error vector at that time is obtained (eF)_r,0,eF_r,1,...,eF_r,l) Wherein eF_r,i(0. ltoreq. i.ltoreq.l) is a 1 x ω subvector, from which it is known that the combined error vector at each time instant is a 1 x (1+ l) ω line vector. The following theorem is given below:

theorem 1: for any different y, y 'e phi (t, l), y and y' are divisible on the receiving node and only if

For a linear code, y and y' are divisible at the receiving node and only if Φ (t, l) # Δ (t, l) {0 }.

And (3) proving that: for source s and receiver r, convolutional network coding can be viewed as a coding kernel of F_r(z) linear network coding.

The sufficiency: if it is satisfied with

I.e. y ' + g ≠ y + g ', meaning that y ' plus any one of w_H(e) After an error g caused by e ≦ t, it will not equal y plus any w_H(e ') value after error g ' caused by e ' of ≦ t. So y and y' are separable at the receiving node.

The necessity: if y and y ' are separable at the receiving node for any different y, y '. epsilon.phi (t, l), then for any g, g ' y ' + g ≠ y + g ', i.e. y ' ≠ y + (g ' -g), i.e. g

For linear coding, y and y ' are divisible at the receiving node only if Φ (t, l) # Δ (t, l) {0}, since any y, y ' ∈ Φ (t, l), there is y-y ' ∈ Φ (t, l). After the syndrome is confirmed.

From theorem 1, it can be known that the judgment is needed before decoding: t is l (l is more than or equal to l)_t) And judging whether the intersection of the corresponding phi (t, l) and delta (t, l) has a null space. The message sequence and the error sequence can be separated only in the null space, the length of a sliding window is obtained, a combined error vector is calculated in each window, and the combined error vector in the next window is obtained from the last combined error vector which can be extended. The method for determining the length of the decoding window and the error vector combination in the window is a key step in the decoding algorithm.

The following describes the whole encoding and decoding process of the present invention with reference to specific examples.

Example 9:

the adaptive construction and decoding method based on random convolutional network error correcting code are the same as embodiments 1-8, so as to

The random convolutional network coding above is taken as an example, and one possible network topology is shown in fig. 2.

The global codes of two outgoing edges of the source s are respectively

And

i.e. y_e1,t＝x_1,tAnd y_e2,t＝x_2,t. It is assumed that the probability of network errors occurring on each edge is the same and separated by at least a time interval of l + 1. The omega packet with all zero data is sent to the network and random convolutional network coding starts to construct the coding kernel adaptively.

At time 0, one possible allocation is shown in FIG. 3. At this time

The global coding core of the receiving node is not full rank, and the random coding construction is unsuccessful.

At time 1, core k is locally encoded_e',e,1Can be randomly and uniformly distributed from

Up-selected and the length of the local coding core plus 1, one possible allocation is shown in fig. 4. At this time

And receiving the global coding core full rank of the node, and successfully constructing the random coding.

eF_r,0＝{00,01,02,10,11,12,20,21,22}，eF_r,1And {00,01,02} is a combined error vector of possible outputs. Calculating the equivalent error of the source end to obtain T _s2, the free distance d is thus selected_free≥2T_sThe convolutional code with +1 ═ 5 is used as input convolutional code, and the generation matrix of the input convolutional code is selected as G_I(z)＝[1+z ² 1+z+z²]。

Assume that the input sequence is x (z) ═ 1+ z²+z⁵I.e., | x (z) | 6. By receiving node r₂The random convolutional network error correction decoding of RCNECC in q-element domain and the distributed decoding process thereof are illustrated as an example.

Distributively derived from the adaptive encoding process described above:

and

after this, the length of the sliding window is determined. By judging phi (r)₂,l)∩Δ(r₂And l) {0} indicates that l ═ 2 satisfies the condition.

Order to

Represents a sequence received at the ith time, wherein

When receiving

And then decoding is started.

As shown in fig. 5, the first, second and third branches on the tree represent

input information

0, 1 and 2, respectively. The combined error screening procedure in [0,2] window is as follows:

according to the algorithm described in example 7, if E ₀00 and E₁When 00, the cumulative error weight {00,00, E is set₂Is 0; if E is₀Not in the reference tables

Remove E from the tree view₀This branch, since there is theoretically no error vector that produces such a combination error. In the remaining path, do not belong to

Combined error of E₁And do not belong to

Combined error of E₂Is deleted. [0,2]Obtaining a unique combined error vector in a window

Its weight was 1. The whole process is shown in fig. 6.

Window [0,2]]An input sequence x can be determined₀1, sequence received

Subtracting the influence of the error vector, i.e. the only combined error vector in the sliding window, to obtain the correct output path:

the sequence received at time 3 is

The decoding window is slid forward by one instant to [1,3 ]]Window, received sequence minus decoded word x₀1 affects in the network:

can be seen as the output sequence in the first window, the decoding operation and 0,2]The operation in the window is the same. Similarly, when the output sequence is

Window [2,4 ]]Only a unique combined error vector remains, which means that the network error is distinguishable in both windows, so that the input sequence (0 → 1) can be uniquely determined. When the output sequence is

Then (0 → 0), (1), (0) are in the sliding window [4,6 ]]、[5,7]、[6,8]And (4) medium output. The input sequence (1 → 0 → 1 → 0 → 0 → 1) is obtained in a distributed manner. In fact, all combination errors are

This is the main reason for achieving distributed decoding, within the error correction capability of the generated convolutional code.

In short, the invention discloses a self-adaptive construction and decoding method of a random convolution network error correcting code, which solves the problems of actual networks with unknown topology and transmission delay in the prior artThe problem of high error correction complexity of a coding and decoding algorithm is solved by the following steps: adaptively constructing random convolutional network codes; constructing a random convolutional network error correcting code as an input convolutional code; decoding at a receiving end by using a q-element random convolutional network error correction decoding algorithm; and optimizing the error correction decoding algorithm of the q-element random convolutional network. The invention provides a coding algorithm for transmitting all-zero data self-adaptive construction random convolutional network based on the transmission process of a data packet in the random convolutional network, and different nodes are allowed to select local coding kernels with different lengths according to the self condition; equating errors in the network to a source end, and designing an error correcting code capable of correcting the errors before sending the message to the network; extending decoding algorithms for minimum network error weight to random code sums

A domain, which forms a q-element random convolution network error correction decoding algorithm based on the minimum network error vector corresponding to the combined error; the decoding sequence is updated by subtracting the influence of the decoded word and the estimated network error, so that the decoding algorithm with low complexity, low time delay and strong error correction capability is realized and is used for an actual network with unknown topology and transmission delay.

Claims

1. A self-adaptive construction and decoding method based on random convolutional network error correcting codes is characterized by comprising the following steps:

step 1, self-adaptively constructing random convolutional network coding:

the source node sends all-zero data packets to the network to construct a random convolutional network code in a self-adaptive manner, starting from a small code domain, the length of a local code core is increased until all relevant receiving nodes can decode, at the moment, the coding is successful, and the receiving nodes receive a combined error vector formed by mixing and overlapping network errors through intermediate nodes;

the random convolutional network coding is constructed in a self-adaptive mode, and the mathematical model of the random convolutional network is as follows:

the convolutional network coding adopts a self-adaptive random coding mode, and a transmission matrix M_r(z) information and transmitted charactersTogether transmitted in time slots to the receiving node, the transmission matrix of the sink node r can be distributively denoted as M_r(z)＝M_r,0+M_r,1z+…+M_r,tz^t+ …, the output with error at each moment is:

where z is a delay factor, x (z) is an input sequence, x_tIs the coefficient of x (z) at time t, M_r,tIs M_r(z) coefficients at time t, e (z) is the error sequence, e_tIs e (z) coefficient at time t, F_r(z) removing the influence caused in the network after the source-end mapping for the transmission matrix at the sink node r, F_r,tIs F_r(z) coefficients at time t;

step 2, constructing a random convolution network error correcting code:

collecting network errors by using all-zero test data; the global coding core is sent to the receiving node according to the time slot, so that the information of the transmission matrix is obtained in a distributed mode at the receiving node, and meanwhile, the network errors are mixed according to the transmission coding coefficient, and the combined errors are obtained in a distributed mode; when the network intermediate node uses a general polynomial as a coefficient, the adjoint matrix of the transmission matrix is used for replacing the inverse matrix of the transmission matrix, and the combination error is equivalent to the information source end; maximum weight T according to equivalent error of information source terminal_sSelecting the free distance more than or equal to 2T at the information source end_s+1 error correction code capable of correcting network errors as input code of the random convolutional network;

the method for constructing the random convolutional network error correcting code specifically comprises the following steps:

wherein l_tIs a matrix F_r(z) the highest power;

Replacing the inverse matrix;

2.3) computing equivalent errors of the information source end

2.4) order W_H(y) denotes a given vector

Hamming weight of (i.e., a non-zero number of y coefficients); calculating the maximum weight T of equivalent error at the source end_s＝max{W_H(E)}；

2.5) selecting the free distance more than or equal to 2T at the information source end_s+1 error correction code capable of correcting this network error;

a domain, which forms a q-element random convolution network error correction decoding algorithm; the q-element random convolution network error correction decoding algorithm is based on the combined error vectors, the weight of each combined error vector is defined as the weight of the minimum network error vector, and a decoding path with the accumulated minimum error weight is searched; the algorithm is directly decoded at a receiving node and can correct any error in the error correction range of the random convolutional network error correction code;

the improved q-element random convolution network error correction decoding algorithm specifically comprises the following steps:

3.1) from y_r(z)＝x(z)G_O,r(z)+e(z)F_r(z) obtaining: x (z) G_O,r(z)＝y_r(z)-e(z)F_r(z) wherein G_O,r(z) a generator matrix for outputting the convolutional code; e (z) is processed at the receiving node, the network errors are staggered and superposed in a convolution mode to form final e (z) F_r(z), thus equivalent to processing individual combined error vectors; defining the weight of each combined error vector as the weight of the minimum network error vector, and searching a decoding path with the accumulated minimum error weight; in the decoding process, all the combined error vectors are corrected, and all the network errors are corrected to obtain a correct input sequence;

3.2) adding judgment before decoding: judging whether the intersection of the output message subspace phi (r, l) and the error subspace delta (r, l) is only a null space; if only null space exists, the message sequence and the error sequence can be separated, the length of a sliding window is determined at the moment, decoding is carried out in the sliding window, and a combined error vector is searched and moved to the sliding window; if there is no null space, the next time is determined again until Φ (r, l) # Δ (r, l) ═ 0}, and then the decoding process in 3.1) is executed;

in the operation of optimizing the received sequence, updating the decoded sequence by subtracting the influence of the error-correcting decoded code word of the q-element random convolutional network and the estimated network error; the situation in the subsequent window can be equivalently transformed into the first window by removing the influence caused by the input sequence before the window, so that the distributed decoding with low complexity and low decoding time delay is realized;

the method comprises the following steps of optimizing a q-element random convolution network error correction decoding algorithm, wherein distributed decoding with low complexity and low decoding time delay is realized:

4.1) when an error occurs in the network and the combined error vector is uniquely determined in the decoding window, the effect of the combined error vector must be subtracted:

wherein, y_r(z) indicates that there is an erroneous output,

representing an updated error-free output;

4.2) assumption that the transmission message x can be uniquely determined₀The received sequence being known by the nature of the convolutional network coding

Is x₀And x₁Linear combination of (1), output sequence minus x₀The influence of (a):

deleting x₀After the influence of (3), the first omega bits of the received sequence are all zeros, and y is set_eff(z)/z is considered as the newly received sequence; the situation in the subsequent window is equivalently transformed into the first window by removing the influence caused by the input sequence before the window;

4.3) assume delay L of sequence decoding, i.e. at receiving node r, x₀Character stream x receivable from time 0 to L₀M_r,0,x₀M_r,1+x₁M_r,0,…,x₀M_r,L+…+x_LM_r,0Unique determination; for global coding core

The sink node r of (2), the necessary condition for the decoding delay to be L is rank (F)₀,F₁,…,F_L) ω; combining the decoding condition phi (r, L) # delta (r, L) ═ 0}, obtaining the decoding time delay L of the q-element random convolution network error correction decoding algorithm_delay＝max{L,l}。

2. The adaptive construction and decoding method of random convolutional network error correcting code according to claim 1, wherein the adaptive construction of random convolutional network coding in step 1 specifically comprises the following steps:

1.1) sending omega packets with all-zero data to the network, wherein omega is the transmission rate of the source message, so that the network starts adaptive construction;

1.2) convolutional network coding is physically realizable if and only if the local coding kernel constant term coefficient matrix K₀Is of power zero; for inflection point e' > e, let its local encoding kernel k_e',e,0If not, uniformly and randomly selecting from small domain, after initialization, k_e',e,tRandomly selecting in a small domain;

1.3) global coding core obtained by calculation

And the local coding cores are placed at the head of the data packet, the length of the local coding core is increased at each moment, and different nodes select the local coding cores with different lengths according to the self condition until all receiving nodes have the transmission matrix with full rank.