CN109639393B - Sliding window network coding method based on quadratic permutation polynomial - Google Patents
Sliding window network coding method based on quadratic permutation polynomial Download PDFInfo
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Abstract
The invention belongs to the technical field of network coding, and discloses a sliding window network coding method based on a quadratic permutation polynomial, which comprises the following steps of (1) determining the size of a data packet to be transmitted in a wireless network; (2) determining a quadratic permutation polynomial; (3) determining the value of the quadratic permutation polynomial and the size of the sliding window; (4) the data packet enters a sliding window; (5) carrying out network coding on the data packet in the window and then transmitting the data packet; (6) the receiver receives the data packet and performs decoding operation until all the data packets are received and the original data packet is recovered; the sliding window network coding method provided by the invention only carries out coding operation on the data packet entering the sliding window, reduces the complexity and the calculation time of network coding/decoding operation, and realizes a rapid network coding mechanism, thereby maximally improving the data throughput of the wireless network and prolonging the network lifetime.
Description
Technical Field
The invention belongs to the technical field of network coding, and particularly relates to a sliding window network coding method based on a quadratic permutation polynomial.
Background
The method and device for determining sliding window data disclosed in the prior art are used for solving the problem that the sliding window data included in a certain moment is determined in the prior artThe statistics value, the number of the data needed to be acquired by the adopted mode is more, and the consumption of system resources is larger. The method and the device for controlling the sliding window to move disclosed by the prior art solve the problem that when no event is input into a server, the sliding window of the server cannot slide backwards, so that the event which falls into the sliding window before cannot be processed and output. A Quadratic Permutation Polynomial (QPP) interleaver disclosed in the prior art, for the sequence u input to the interleaverkBy the function f (i) ═ (f)1i+f2i) mod (k) interleaving to improve Turbo code performance. In the network coding method based on the sliding window disclosed in the prior art, the size of the sliding window is determined, and only data packets in the sliding window are coded, so that the reliability of network coding is further improved, the decoding complexity is obviously reduced, and the data throughput of a network is maximized and the network lifetime is greatly prolonged while the rapid network coding is realized.
However, in the prior art, the permutation polynomial is mainly used for the application of the interleaver and the Turbo code in some fields, and in the sliding window mechanism, strong theoretical support for the size of the sliding window, the size of the sliding cadence and the like is lacked. When a data packet is lost in the network, the following series of data packets cannot be transmitted immediately, so that a receiving node needs to cache a large number of data packets, and meanwhile, the size of a sliding window, the transmission control of data, and the scale of a decoding coefficient matrix are increased, and the decoding complexity is increased.
Disclosure of Invention
In view of the above defects or improvement requirements of the prior art, the present invention provides a sliding window network coding method based on quadratic permutation polynomial, which aims to improve the coding/decoding efficiency of network coding, thereby maximally improving the data throughput of the network and prolonging the network lifetime.
To achieve the above object, according to an aspect of the present invention, there is provided a sliding window network coding method based on quadratic permutation polynomial, including the steps of:
(1) determining the size of a data packet to be transmitted in a wireless network;
(2) constructing a quadratic permutation polynomial;
(3) determining the value of the quadratic permutation polynomial and the size of the sliding window;
(4) the data packet to be transmitted enters a sliding window, and the data packet in the sliding window is transmitted after network coding;
(5) the receiver decodes the received network code to recover the original data packet.
Preferably, in the sliding window network coding method based on quadratic permutation polynomial, the network coding is in the finite field GF (2)n) Wherein a linear combination of source vector coefficients is randomly selected, allowing input of combined data packets from intermediate nodes, each combined data packet comprising a linear combination of source data packets.
Preferably, in the sliding window network coding method based on quadratic permutation polynomial, quadratic permutation polynomial p (x) is defined as: p (x) ax2+ bx, where a, b, x are all non-negative integers, p (x) ax2The modulus of + bx is N.
Preferably, in the sliding window network coding method based on quadratic permutation polynomial, quadratic permutation polynomial p (x) -84 x is used2+41 × modulo 112, i.e., N ═ 112; the quadratic permutation polynomial p supports 4 window sizes, 56, 28, 14 and 7 respectively.
Preferably, in the sliding window network coding method based on the quadratic permutation polynomial, the size of the sliding window is adjusted according to the quadratic permutation polynomial in the sliding process to improve the performance of the sliding window.
Preferably, in the sliding window network coding method based on quadratic permutation polynomial, the method for recombining the data packet to be transmitted into the sliding window specifically includes:
for a linear combination subset R ═ G of the rows of the network node transmission matrix Gq0,…,Gq|R|-1F, starting from the sliding windowrComputing a related sliding window result edge er＝fr+w-1；
Encoding vector
Wherein, ciIs a random number and satisfies P { c }i＝1}＝1/2，
Refers to the ith sliding window, w refers to the length of the sliding window, and r refers to the starting value of the sliding window.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the sliding window network coding method based on the quadratic permutation polynomial only carries out coding operation on the data packets entering the sliding window, reduces the complexity and the calculation time of network coding/decoding operation, realizes rapid network coding, thereby maximally improving the data throughput of a wireless network and prolonging the network lifetime.
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FIG. 1 is a schematic flow chart of a sliding window network coding method based on quadratic permutation polynomial according to the present invention;
FIG. 2 is a diagram illustrating the length and external values of sub-windows in an embodiment of the present invention.
Fig. 3 is a schematic structural diagram of a sliding mechanism based on the sliding window length of the quadratic permutation polynomial according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The sliding window network coding method based on quadratic permutation polynomial provided by the embodiment, referring to fig. 1, includes the following steps:
(1) determining the size of a data packet to be transmitted in a wireless network;
(2) constructing a quadratic permutation polynomial;
(3) determining the value of the quadratic permutation polynomial and the size of the sliding window;
(4) the data packet to be transmitted enters a sliding window, and the data packet in the window is transmitted after network coding;
(5) and the receiver encodes and decodes the received network and recovers the original data packet until all the data packets are decoded.
The following is further described in conjunction with the specific embodiments. In an embodiment, a wireless network is represented as an undirected graph G ═ V, E, where V represents a set of nodes in the network and E represents a set of links. Each link E ═ j ∈ E represents a direct connection between node i and node j, and if (i, j) ∈ E and (j, i) ∈ E, assuming that the links are symmetric, whether the two links interfere with each other depends on the interference model used.
The network coding process in the embodiment is in the finite field GF (2)n) In which a linear combination of source vector coefficients is randomly selected. x is the number of0,x1,…,xn-1Representing the source data packet associated with the node. Linear network coding allows the input of combined data packets from intermediate nodes, each combined data packet containing a linear combination of source data packets.
In an embodiment, the quadratic permutation polynomial p (x) is defined as: p (x) ax2+ bx, where a, b, x are all non-negative integers, p (x) ax2The modulus of + bx is N.
Polynomial p (x) ax2+ bx (mod n) as an essential condition for the permutation polynomial includes:
1) for all N is more than or equal to 2, gcd (b, N) is 1, and each prime factor of N is a factor of a; the gcd (b, N) represents the greatest common divisor of the two positive integers b and N.
2) For all a and b (a ≧ 1, b ≧ 1), a + b is odd, gcd (b, N/2) ═ 1, and each prime factor of N not equal to 2 is a's factor.
Second order permutation polynomial p (x) ax2+ bx (mod N) in integer set ZNIs irreducible, if and only if N>gcd(N,2a)。
Let p (x) be 84x2Modulo +41x 112, i.e. N112, by looking at the factor of N112, we have that the quadratic permutation polynomial p supports 4 window sizes, 56, 28, 14 and 7 respectively, for accessing 2, 4, 8 and 16 external values simultaneously.
Fig. 2 illustrates that when N is 112, the parallelism of the parallel access method is 4, and when the length of the sub-window is 14, the external value is calculated by the maximum contention-free parallel access storage method; the number in each cell represents the external value eiIndex (i ═ 0,1,2, …, 111).
Fig. 3 illustrates a sliding mechanism structure proposed based on the sliding window length of the quadratic permutation polynomial in the embodiment. Assuming that the length of the data is N information bits, the length of the sliding window is w information bits or an integer multiple of w, and the sliding mechanism of the ith (i is more than or equal to 1 and less than or equal to N/w) sliding window is shown in FIG. 3; in order to effectively improve the performance of the sliding window, the size of the sliding window is adjusted according to the quadratic permutation polynomial in the sliding process; the sliding window length based on the quadratic permutation polynomial can adaptively adjust the length of each sliding window, and the sliding window length is prevented from being too large or too small.
The network node encodes the data packet using the encoding vector, recursively performs an encoding operation and obtains an encoded data packet.
Suppose a node has received and stored a set (a)1,X1),(a2,X2),…,(am,Xm) Wherein X isiRepresenting an information symbol, aiIs an additional code vector for the data packet. The node selects a set of coefficients ei＝(ei0,ei1,…,eim) Calculating linear combinations
A new encoded packet (a ', X') is generated based on the linear combination. The homologous encoding vector a' is not simply equal to e, since these coefficients are not identical to the original dataPacket X ═ X0,x1,…,xn-1) Related to, by comparison, obtaining
And repeatedly encoding on a plurality of nodes in the network to obtain an encoding vector, and generating a network encoding data packet.
The data packet to be transmitted enters a sliding window, and the data packet is recombined in the sliding window, which is as follows:
each time transmission of a data packet is started, the network node transmits a linear combination subset of the rows of the matrix G. First starting from the sliding window edge frAnd calculates the relative sliding window result edge er＝fr+ w-1. Let R ═ Gq0,…,Gq|R|-1Is the set of rows of the matrix G,
and
and
respectively representing sliding windows
The starting edge and the resulting edge. Coding vector grThe linear combination of the elements R starts to accumulate, i.e.:
ciis a random number and satisfies P { c }i＝1}＝1/2。
In a sliding window network coding method based on a quadratic permutation polynomial in a wireless network, O (N) time is needed for initializing a sliding window, O (e) time is needed for finding the sliding coding window, O (eTN) time is needed for constructing a sliding window for each te T, and the global situation is thatThe encoding of a code vector in a sliding window requires O (T)2N) time, total coding time is O (eT)2N)。
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A sliding window network coding method based on quadratic permutation polynomial is characterized by comprising the following steps:
(1) determining the size of a data packet to be transmitted in a wireless network;
(2) constructing a quadratic permutation polynomial;
(3) determining the value of the quadratic permutation polynomial and the size of the sliding window;
(4) the data packet to be transmitted enters a sliding window, and the data packet in the sliding window is transmitted after network coding;
(5) the receiver decodes the received network code to recover the original data packet;
the method for recombining the data packets to be transmitted into the sliding window specifically comprises the following steps:
for a linear combination subset R ═ G of the rows of the network node transmission matrix Gq0,…,Gq|R|-1F, starting from the sliding windowrComputing a related sliding window result edge er＝fr+w-1；
Encoding vector
Wherein, ciIs a random number and satisfies P { c }i＝1}＝1/2，
Refers to the ith sliding window, w refers to the length of the sliding window, r refers to the start of the sliding windowThe value is obtained.
2. The sliding-window network coding method of claim 1, wherein the network coding is in a finite field GF (2)n) Wherein a linear combination of source vector coefficients is randomly selected, allowing input of combined data packets from intermediate nodes, each combined data packet comprising a linear combination of source data packets.
3. A sliding window network coding method according to claim 1 or 2, characterized in that the quadratic permutation polynomial p (x) is defined as: p (x) ax2+ bx, where a, b, x are all non-negative integers, p (x) ax2The modulus of + bx is N.
4. A sliding window network coding method according to claim 1 or 2, wherein the quadratic permutation polynomial p (x) 84x is used2+41 × modulo 112, i.e., N ═ 112; the quadratic permutation polynomial p supports 4 window sizes, 56, 28, 14 and 7 respectively.
5. A sliding window network coding method according to claim 1 or 2, wherein the size of the sliding window is adjusted according to a quadratic permutation polynomial in the sliding process to improve the performance of the sliding window.
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