KR20130101602A - Approximate decoding method for network coded linearly correlated sources - Google Patents

Abstract

PURPOSE: An approximate decoding method for network-coded and linearly-correlated source data is provided to restore data by using a network coding technique. CONSTITUTION: Source data is transmitted to a network coding node (S1). A network coding technique is applied to the transmitted source data, and then the source data is transmitted to a decoder (S2). If packets of the data transmitted to the decoder are not sufficient or a network coding coefficient matrix causes a singularity problem, the decoder performs approximate decoding based on linear correlation (S3). [Reference numerals] (S1) Step of transmitting source data to a network coding node; (S2) Step of applying a network coding technique to the transmitted source data of the S1 step to be transmitted to a decoder; (S3) Step of performing approximate decoding based on linear correlation when packets of the data transmitted to the decoder of the S2 step are not sufficient or a network coding coefficient matrix causes a singularity problem

Description

Approximate Decoding Method for Network Coded Linearly Correlated Sources}

The present invention relates to a method for reconstructing encoded linear relation data using a network coding technique. In particular, the present invention is an approximate decoding method for approximate restoration of data when there are not enough data packets, and the data used here is data having a linear relationship.

Recently, sensor networks have been used in various fields such as regional information such as temperature and military information use (Rout, RR, Ghosh, SK, and Chakrabarti, S., "A network coding based probabilistic routing scheme for wireless sensor network," in Wireless Communication). and Sensor Networks (WCSN), Dec. 2010.). One of the key research topics in the field of sensor networks is an efficient solution for delivering information over time.

Network coding is a technique that provides an effective distributed delivery algorithm in networks with different paths and data sources (Ahlswede, R., Cai, N., Li, S.-YR, and Yeung, RW, "Network information flow," 46, 1204-1216, July 2000.). Network coding is based on network nodes capable of performing basic operations on information streams.

A communication network using a network coding technique mixes different packets at intermediate intermediate nodes or routers, unlike a general communication network. Packets generated at the transmitting end of a general communication network are delivered to the receiving end without change at the intermediate transit node or router. However, a network using a network coding scheme allows for the mixing of different packets at intermediate intermediary nodes or routers, or for changing the contents of packets.

 On the other hand, in the case of a communication network using a network coding scheme, the original data is transmitted in encoded pieces of data instead of being transmitted directly. For example, such encoded data pieces may be referred to as data packets. The receiving end of the network coding receives the data packets and restores the original data.

In data transmission using network coding, due to external factors such as dynamic propensity of channel environment, original data can not be restored when each node does not receive enough data packets for data recovery. This can be a fatal weakness in applications where there is a time constraint to ignore delayed packets. In order to overcome this problem, an approximate decoding algorithm has been introduced that recovers the original data with good accuracy even when useful packets are not sufficiently provided for complete data recovery (Park, H., Thomos, N., and Frossard, P., "Transmission of correlated information sources with network coding," in Proc. EUSIPCO-2010, 1389-1393, Aug. 2010.). However, the approximate decoding algorithm assumes a correlation based on a simple optimal matching method, and does not consider the correlation between the actual data clearly. Therefore, the conventional approximate decoding technique has a limitation that its performance is not always guaranteed and is limited.

An approximate decoding method of original data having a network coded linear correlation according to the present invention aims to solve the following problems.

First, it is intended to be used in a network system that restores data using a network coding technique.

Second, even if there are not enough data packets for data recovery in a network system, the data is about to be restored.

Third, the data recovery rate is to be improved by using the linear correlation of the data.

The solution of the present invention is not limited to those mentioned above, and other solutions not mentioned can be clearly understood by those skilled in the art from the following description.

An approximate decoding method of original data having a network coded linear correlation according to the present invention is a method of decoding data transmitted in a network system in which data having a linear correlation is transmitted through a network coding technique.

In the approximate decoding method for linear correlation data according to the present invention, in step S1 in which the source data is transmitted to the network coding node, in step S2 transmitted by the network coding technique to the source data transmitted in step S1 and the decoder S2 in the decoder In the step S3, if the packet of data transmitted to the decoder is insufficient or the network coding coefficient matrix causes a singular problem, the method includes performing an approximate decoding based on linear correlation.

Data transmitted in a network system is characterized by having a linear correlation.

The result of performing the approximate decoding in step S3 is characterized by the following equation.

는 유한 필드(finite field) 내에서 행렬 간의 곱이며, 1_(N-K)는 (N-K)개의 1 값을 갖는 벡터이다.Where C is a network coding coefficient matrix, D is a constraint matrix,

Is a product between matrices in a finite field, and 1 _(NK) is a vector having (NK) 1 values.

The similarity factor defining a linear correlation between the data △ is preferably in the form of 2 ^K, k is 0 ≤ k ≤ M - more have a value in the second range is improved, the accuracy of the restoration.

The approximate decoding method of the original data having the network coded linear correlation according to the present invention uses the insufficient data when the source data for data decoding is not sufficiently transmitted in the event of a network system failure or other reasons. Decode That is, the present invention is used to decode data in a sufficient system environment if only a certain level of quality is guaranteed.

The effects of the present invention are not limited to those mentioned above, and other effects not mentioned can be clearly understood by those skilled in the art from the following description.

1 shows an example of a distributed data transmission system to which the present invention can be applied.
2 is a flowchart schematically showing a procedure of an approximate decoding method according to the present invention.
3 is a result of decoding an original image by an approximate decoding method according to the present invention and a result of decoding by a conventional approximation decoding method.
4 is a graph showing the results of an approximate decoding method of the present invention with respect to different values of Δ.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

The terms first, second, A, B, etc., may be used to describe various components, but the components are not limited by the terms, but may be used to distinguish one component from another . For example, without departing from the scope of the present invention, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

As used herein, the singular forms "a,""an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It is to be understood that the present invention means that there is a part or a combination thereof, and does not exclude the presence or addition possibility of one or more other features or numbers, step operation components, parts or combinations thereof.

The present invention is used in a system to which network coding is applied. 1 shows an example of a distributed data transmission system to which the present invention can be applied. Data transmitted in this system has a constant correlation with each other. The correlation data may be external correlation such as data measured through the sensor network, or high correlation data between adjacent data such as an image in a video sequence. Research on the transmission of such correlation data has been widely performed in distributed systems. The network coding technique has been studied as a technique of transmitting correlation data through a network. The present invention is a technique for approximately decoding data when packet loss occurs in a system using a network coding technique.

An object of the present invention is to provide an approximate decoding method in consideration of correlation between data. In particular, the present invention studies an approximate decoding technique for data having a linear correlation. The present invention greatly improves the accuracy of the approximate decoding for data having linear correlation. The effects of the present invention will be described later.

In the present invention, random linear network coding (RLNC) is used (Ho, T., M'edard, M., Shi, J., Effros, M., and Karger, DR, "On randomized network). coding, "in Proc. Allerton Annual Conf. Commun., Control, and Comput., Oct. 2003.). Distributed solutions based on RLNC generally perform almost similarly as global optimization solutions, such as linear network coding, while maintaining low coordination and low communication costs between nodes.

The present invention contemplates the transmission of an associated data source encoded based on the RLNC in a sensor using an ad-hoc network where data is lost. In general, associative source transmission has been studied based on a system that jointly correlates highly correlated data, encodes them in a compressed form using correlation coefficients, and then jointly decodes them (Slepian, D. and Wolf, JK, "Noiseless coding). of correlated information sources, "19, 471-480, Jul. 1973.). However, the present invention aims to focus on associated data where compression has not occurred. In the present invention, the association data is transmitted using network coding and jointly decoded in a timely manner.

RLNC  Based encoding

First, the RLNC-based encoding used in the present invention will be described. Assume an ad-hoc network consisting of a source, an intermediate node, and a client node. Source data is passed to the client node through an intermediate node capable of network coding.

Hereinafter, x ₁ , ..., x _N are referred to as N non-negative correlation source data. Since the RLNC operation is performed in GF (Galois Field), each x _n corresponds to an element belonging to the GF. The RLNC operation may be performed by an identity function that maps the value of one field to the corresponding value of another area.

로 정의하고, 이때

로 정의된다. 여기서 윗첨자

는 유한 필드(finite field)에 존재하는 요소를 의미한다. 유사하게, 역식별 함수는

으로 정의되고, 이때

로 정의된다. 따라서 RLNC에 있는 노드 k는 아래의 식과 같이 전송할 수 있다.In particular, in the present invention, an identification function

Is defined as

. Superscript here

Denotes an element present in a finite field. Similarly, the reverse identification function

Is defined as

. Therefore, node k in RLNC can be transmitted as shown below.

과 코딩 계수 c_n(k)의 선형 조합을 의미한다.

과

는 각각 GF에서 정의된 가산 연산과 곱셈 연산을 나타낸다. y와 c는 항상 GF에 존재하는 요소이다.This expression

And a linear combination of the coding coefficients c _n (k).

and

Denotes addition and multiplication operations, respectively, defined in GF. y and c are always present in GF.

라고 가정한다.Coding coefficients are chosen from GFs that are uniformly and randomly 2 ^{M in} size (denoted GF (2 ^M )). Packets generated at each node are delivered to neighboring nodes that are in the direction of a sink or client node. In the present invention, the size of the source data group is increased so that a coding operation that operates correctly at (GF (2 ^M )) is possible.

.

는 아래의 수학식 1과 같이 표현될 수 있다.If K linearly independent packets y (1), ..., y (K) are available at the decoder, then the linear system

May be expressed as Equation 1 below.

는 유한 필드 내에서 행렬 간의 곱을 의미하고, K × N 크기의 행렬

는 행 벡터

로 구성된 네트워크 코딩 계수 행렬에 해당한다.here

Denotes the product of matrices within a finite field, a matrix of size K × N

Row vector

Corresponds to the network coding coefficient matrix consisting of.

approximation Decryption  summary

As mentioned above, this invention improves the problem of the conventional approximation decoding method. Here, the outline of the approximate decoding method will be explained.

집합을 전송받은 경우, 디코더는 소스 데이터를 복원하게 된다. 만약 K = N이라면, 즉 네트워크 코딩 계수 행렬

가 풀 랭크(full-rank)를 이루게 된다면

는 상기 수학식 1로 표현되는 선형 시스템으로부터

식으로 결정된다.

은 코딩 계수 행렬

의 역행렬이며, 유한 필드에 가우시안(Gaussian) 소거법을 적용하여 도출될 수 있다.Decoder is network coded packet

When receiving the set, the decoder will restore the source data. If K = N, i.e. network coding coefficient matrix

If is full-rank

Is a linear system represented by Equation 1

Determined by the equation.

Is a coding coefficient matrix

It is the inverse of, and can be derived by applying Gaussian elimination to the finite field.

)의 개수가 무한히 많아질 수 있다. 이 경우에 코딩 계수 행렬을 풀 랭크로 만들기 위해서는 추가적인 제한조건이 부여되어 한다. 근사 복호화 기법에서 입력 데이터의 상관관계는 추가적인 제한 조건(행렬 D)을 설정하여 이용할 수 있다. 행렬 D에서 추가적인 제한 조건은 입력 데이터 간의 상관관계 모델에 기반하여 결정된다. However, if there is not enough packets received at the decoder (i.e., K <N), the solution to the linear system (

) Can be infinitely large. In this case, additional constraints must be given to make the coding coefficient matrix full rank. In the approximate decoding technique, correlation of input data may be used by setting an additional constraint condition (matrix D). Additional constraints in matrix D are determined based on the correlation model between the input data.

의 위치에 대응된다. 최종적으로 원본 데이터의 근사값

는 아래의 수학식 2와 같이 나타낼 수 있다.
Park et al. Used a simple approximation decoding algorithm (Park, H., Thomos, N., and Frossard, P., "Transmission of correlated information sources with network coding," in Proc. EUSIPCO-2010, 1389). -1393, Aug. 2010.). A matrix D of size (NK) x N consists of zero, except for two elements, each row having a value of "1". This is the best match of the data

Corresponds to the position of. Finally approximation of original data

May be expressed as Equation 2 below.

는 (N-K)크기의 0 (zero)를 갖는 벡터이다.here

Is a vector with zero (zero) of size (NK).

The approximate decoding algorithm described can recover the original data, but the approach to constructing the matrix D allows the algorithm to exhibit limited performance. This limitation is due to the dependence on optimal matching data based on the heuristic approach.

In order to overcome this limitation, the present invention studies the correlation of source data and improves the approximate decoding. Hereinafter, the essential contents of the present invention will be described.

Approximation to Linear Correlation Data Decryption

는 n개의 요소를 갖는 소스 데이터의 N번째 집합이라고 하자. 이 데이터는 아래의 수학식 3과 같은 관계를 갖는다.

Let N be the Nth set of source data with n elements. This data has a relationship as in Equation 3 below.

는 각각 모두 1로 구성된 벡터 및 유사성 인자(similarity factor)를 갖는 벡터이다. 유사성 인자는

범위이고, 이는 두 개의 데이터 집합이 얼마나 상관성이 있는지를 나타낸다. △ 값이 커지면 데이터 상관성은 낮아지는 것을 의미하며, △ 값이 작아지면 상관성이 높아지는 것을 의미한다.
Where 1 and

Are vectors with a vector of all 1s and a similarity factor. Similarity factor is

Range, which indicates how correlated the two data sets are. A larger value of Δ means lower data correlation, and a smaller value of Δ means higher correlation.

In the present invention, it is assumed that a condition as shown in Equation 4 below must be satisfied in order to reduce the complexity due to additional operations.

로 표현될 수도 있다. 따라서 유사성 인자는 아래의 수학식 5로 표현되는 범위 내에 있다 할 수 있다.
Or equivalent

. &Lt; / RTI &gt; Therefore, the similarity factor may be in the range represented by Equation 5 below.

범위 내에 있어야 한다.In addition x _N is

Must be in range

If Δ = 0, that is, two data sets are perfectly adjusted, the conventional approximation decoding method completely recovers the source data. Therefore, the present invention considers only the case where Δ> 0. The similarity factor Δ is determined within the integer region and is present in the GF in the approximate decoding algorithm.

In consideration of the similarity factor, the source data may be calculated as in Equation 6 below.

Where 1 _(NK) is a vector having (NK) 1 values. Equation 6 is similar to Equation 2 above, but the approach of considering the similarity factor in the source data is clearly different.

인 실수 영역에서의 연산과 달리, GF에서의 동등한 연산인

는 △ 뿐만 아니라 다른 값 또한 결과물로 산출될 수 있다.Full recovery of the original data is sufficiently known that △ information is known, namely

Unlike operations in real realm

Not only Δ but also other values can be calculated as a result.

의 값을 예시한다.Table 1 below shows the possible possibilities for different Δ in GF (2 ⁸ )

Illustrates the value of.

의 결과를 연구하는 것이 필수적이다. 이에 관해서는 후술하는 "선형 상관관계를 갖는 근사 복호법의 특성"에서 구체적으로 설명하겠다. Since the operation result in the GF directly affects the decoding performance,

It is essential to study the results. This will be described in detail later in "Characteristics of Approximation Decoding with Linear Correlation".

In summary, the similarity factor (△) is used instead of the unreceived data packet value, and each column of the constraint matrix D uses 1 for the two correlated columns, and all remaining columns are 0 (zero). As a result, the use of the constraint matrix D makes the matrix [C ^T D ^T ] ^T a full-rank matrix, and the source data can be decoded.

Approximation with Linear Correlation Decryption  characteristic

Hereinafter, (1) the relationship between the value of Δ and the expected distortion result value, and (2) the value of Δ representing the optimal decoding performance will be described.

를 고려한다. 먼저 △가 예상되는 왜곡 결과 값에 주는 영향을 설명한다.
In the analysis below, it is assumed that the size of the GF is 2 ^M (ie GF (2 ^M )). The similarity factor Δ is determined within the real domain but is finite field element during the decoding process.

Consider. First, the influence of Δ on the expected distortion result value will be described.

(Property 1) △ similarity factor, performance of an approximate decoding algorithm for the linear correlation data is a maximum when the △ 2 ^K in the form of (0 ≤ k <M).

The proof for characteristic 1 is intended to show that the expected approximate decoding method becomes minimal when Δ = 2 ^K. All elements can be represented by binary numbers present in GF (2 ^M ). In order to completely recover (distortion does not exist), it is necessary to satisfy the following condition.

이다. 상기 수학식 7의 연산은 GF에서 수행되기 때문에,

의 이진 표현에서 1 값을 갖는 비트(bit)의 위치 및 △의 이진 표현에서 1 비트의 위치가 같다면 상기 수학식 7은 만족하지 않는다. 이는 같은 위치에서 두 개의 1이 중첩되면

에서 캐리지 리턴(carriage return)이 일어나기 때문이다. 따라서 복호 에러를 최소화하기

및 △의 같은 위치에서 1이 중복되는 개수는 최소화되어야 한다. 소스 데이터에 존재하는 모든 가능한 x에 대하여 △의 이진 표현에서 1의 최소 개수는 하나(one)이다. 결과적으로 △는 2^k의 형태를 가져야 한다. △의 이진 표현의 (k+1)번째 위치에서 하나의 1 비트만이 존재하게 된다. 결국 상기 특성 1에 대한 증명이 완료된다.here,

to be. Since the operation of Equation 7 is performed in GF,

If the position of a bit having a value of 1 in the binary representation of and the position of 1 bit in the binary representation of? Are the same, Equation 7 is not satisfied. This means that if two 1s overlap in the same position

This is because a carriage return occurs at. Therefore, to minimize the decoding error

And the number of overlapping 1 at the same position of Δ should be minimized. For every possible x present in the source data, the minimum number of 1s in the binary representation of Δ is one. As a result, Δ should have the form of 2 ^k . Only one bit exists in the (k + 1) th position of the binary representation of Δ. As a result, the proof for characteristic 1 is completed.

Δ in the 2 ^k form maximizes the approximate decoding performance for linear correlation data. Now, when Δ has a 2 ^k form, it will be described which k values minimize the decoding error. The analysis discussed below assumes that the coding coefficient matrix is not singular.

(Characteristic 2): If the type of the similarity factor △ △ ^K = 2, the performance of the decoding method, the approximate linear relationship for the data was determined as the mean absolute error is increased the smaller the k value. Where 0 ≦ k ≦ M-2.

는 소스 데이터이고,

는 x가 근사 복호법에 의해 근사적으로 복호된 값이라고 하자(이하 데이터는 이탤릭체로 표기함).

및

는 각각

및

에 속하는 요소이다. Hereinafter will be demonstrated for the characteristic 2.

Is the source data,

Let x be a value that is approximately decoded by the approximate decoding method (hereinafter, the data is written in italics).

And

Respectively

And

Element to belong to.

는 아래의 수학식 8로 나타낼 수 있다.
From Equation 7

May be represented by Equation 8 below.

에 있는 비트 1이 △에서의 비트 1과 동일한 위치에 있다면 에러가 발생한다. 이는 XOR의 캐리지 리턴이

+ △에서 발생하기 때문이다. 만약 △ = 2^k라면, 최하위비트로부터 (k+1) 번째 비트 위치는 1로 설정된다. 따라서

의 이진 표현이 아래의 수학식 9와 같다면 복호 에러가 발생한다.
As described above with respect to characteristic 1,

If bit 1 in is at the same position as bit 1 in Δ, an error occurs. This means that a carriage return of XOR

This is because it occurs at + △. If Δ = ^2k , the (k + 1) th bit position from the least significant bit is set to one. therefore

If the binary representation of is equal to Equation 9 below, a decoding error occurs.

와

는

의 최하위비트로부터 k 번째 비트 위치에서 각각 1과 0으로 나타난다.here

Wow

The

1 and 0, respectively, at the k th bit position from the least significant bit of.

-

는 아래의 수학식 10과 같이 표현 가능하다.
Corresponding error

-

Can be expressed as in Equation 10 below.

부터

까지의 비트는 복호화 성능에 영향을 주지 못한다. 따라서 복호 에러는 상기 수학식 10에서 볼 수 있듯이 2△이다. 상응하는 확률은 다음과 같이 획득될 수 있다.

에 대하여 n 비트((k+1) 번째 비트부터 (k+n) 번째 비트까지)는 고정되고, 다른 M - n 비트는 0 또는 1로 설정될 수 있다. 따라서 가능한 복호 에러로는 2^M-n 개가 있다. 발생 가능한 모든 경우의 수가

이기 때문에 상응하는 복호 에러의 확률은

과 같이 표현된다.

from

Bits up to do not affect decoding performance. Therefore, the decoding error is 2Δ as shown in Equation 10 above. The corresponding probability can be obtained as follows.

For n bits (from (k + 1) th bit to (k + n) th bit), the other M-n bits can be set to 0 or 1. Therefore, there are 2 ^Mn possible decoding errors. The number of possible cases

Since the probability of the corresponding decoding error is

It is expressed as

Therefore, the mean absolute error is represented by Equation 11 below.

Equation 11 is a function of increasing with respect to k (k ≦ M-2). This condition is derived from Equation 9 above. Therefore, the smaller the value of k is, the better the decoding performance is. Eventually, this proved to be characteristic 2.

Characteristic 2 means that more correlated source data (i.e., data with small k values) is more accurately recovered by approximate decoding.

2 is a flowchart schematically showing a procedure of an approximate decoding method according to the present invention. Hereinafter, the order of the approximate decoding method according to the present invention will be summarized.

In the approximate decoding method for linear correlation data according to the present invention, in step S1 in which the source data is transmitted to the network coding node, in step S2 transmitted by the network coding technique to the source data transmitted in step S1 and the decoder S2 in the decoder In the step S3, if the packet of data transmitted to the decoder is insufficient or the network coding coefficient matrix causes a singular problem, the method includes performing an approximate decoding based on linear correlation.

과 같은 선형 상관관계를 갖는 것을 특징으로 한다.Here, the data transmitted from the network system may be

It is characterized by having a linear correlation as shown.

은 1로만 구성된 벡터,

는 유사성 인자(factor)를 갖는 벡터이다.Where X _N is the Nth set of source data with n elements,

Is a vector of ones only,

Is a vector with a similarity factor.

범위일 수 있다.Where the similarity factor △ is

Lt; / RTI &gt;

과 같이 표현되는 것을 특징으로 한다.The result of performing the approximate decoding in step S3 is shown in Equation 6 above.

It is characterized by being expressed as.

는 유한 필드 내에서 행렬 간의 곱이며, 1_(N-K)는 (N-K)개의 1 값을 갖는 벡터이다. 유사성 인자 △는 2^K의 형태인 것이 바람직하다.
Where C is a coding coefficient matrix, D is a constraint matrix,

Is a product between matrices in a finite field, and 1 _(NK) is a vector having (NK) 1 values. △ similarity factor is preferably in the form of ^K 2.

Effect experiment on the present invention

,

및

에 대해 적용해보고자 한다. 소스 데이터 사이의 변화 정도는 유사성 인자 △로 설명된다.

은 256 × 256 크기의 픽셀을 갖는 표준 그레이 스케일(gray scale) 이미지를 표현하고, 각 픽셀 값은 M = 8인 GF(2^M) 내에 존재한다고 가정한다. RLNC에 기반하여 인코딩된 패킷은

로 표현된다. 근사 복호법의 성능에 초점을 맞추기 위하여 요구되는 패킷은 2/3 이고(즉 패킷 손실률은 1/3임), △는 수신기에서 이용가능하다고 가정한다. 전술한 바와 같이 복호화 과정에서는 GF연산을 사용하기 때문에 △는 하나 이상의 숫자로 이루어진 집합

이되어 왜곡이 발생하게 된다. 2 개의 수신 패킷 Y(1) 및 Y(2)가 있다고 하면, 아래의 수학식 12로 표현되는 선형 시스템

을 갖게 된다.
Approximate decoding method for linear correlation data has been described. In the following experiment, three correlation source data images

,

And

I would like to apply for. The degree of change between the source data is described by the similarity factor Δ.

Represents a standard gray scale image with pixels of size 256 × 256, and assume that each pixel value is within GF ( ^2M ) with M = 8. Packets encoded based on RLNC are

Lt; / RTI &gt; To focus on the performance of the approximate decoding method, it is assumed that the required packet is 2/3 (i.e. the packet loss rate is 1/3), and Δ is available at the receiver. As described above, since the GF operation is used in the decoding process, Δ is a set of one or more numbers.

This causes distortion. If there are two received packets Y (1) and Y (2), a linear system represented by Equation 12 below

.

및

는 각각

및

에 속한

번째 요소이다. 이 경우 D = [1 1 0]이다. GF에서의 분배 법칙에 따라 아래의 수학식 13이 주어진다.

And

Respectively

And

Belong to

Second element. In this case D = [1 1 0]. The following equation (13) is given according to the law of distribution in GF.

Equation 13 may be represented by Equation 14 below.

는 아래의 수학식 15와 같이 표현된다.
So finally decoded

Is expressed by Equation 15 below.

3 is a result of decoding an original image by an approximate decoding method according to the present invention and a result of decoding by a conventional approximation decoding method. Fig. 3 (a) is an original image with Δ = 16, Fig. 3 (b) is an image decoded according to the present invention when Δ = 16, and Fig. 3 (c) is decoded according to the present invention when Δ = 32. 3 (d) is an image decoded according to the present invention when Δ = 15, and FIG. 3 (e) is an image decoded according to the conventional approximation decoding method when Δ = 16.

3 (a) is an original image correlated with Δ = 16. Comparing FIG. 3 (b), FIG. 3 (c) and FIG. 3 (d), it is possible to verify a decoding method for correlation data according to the present invention. When Δ = ^2k (16 and 32 in FIG. 3 (b) and 3 (c) respectively) is Δ ≠ 2 ^k (15 in FIG. 3 (d)), the decoded result is better. Able to know.

Furthermore, comparing FIG. 3 (b) and FIG. 3 (c), it can be seen that the smaller the value of k, the better the result. Compared with the conventional approximation decoding method, it can be seen that the decoding result of the correlation data according to the present invention is much better (compare Fig. 3 (b) and Fig. 3 (e)).

4 is a graph showing the results of an approximate decoding method of the present invention with respect to different values of Δ. In this experiment, we used a random image with 1000 different pixel values. In this image, the packet loss is set to 1/3 and the approximate decoding method according to the present invention is performed. The similarity factor is equal to the Δ value given in FIG. 4.

Referring to FIG. 4, it can be seen that better quality is obtained when Δ = ^2k (that is, a high 1 / MSE value). Also, the smaller the value of k, the higher the quality (low decoding error) is.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. It will be understood that variations and specific embodiments which may occur to those skilled in the art are included within the scope of the present invention.

Claims (5)

In a method for decoding data transmitted in a network system in which data having linear correlation is transmitted through a network coding technique,
Step S1, in which source data is transmitted to a network coding node;
Step S2 transmitted to the decoder by applying a network coding scheme to the source data transmitted in step S1; And
And a step S3 of performing approximate decoding on the basis of linear correlation when the packet of data transmitted to the decoder in the decoder in step S2 is insufficient or the network coding coefficient matrix causes a singular problem. Approximation decoding method of original data with corrected linear correlation. The method of claim 1,
Approximate decoding method of original data having network coded linear correlation, characterized in that the data transmitted from the network system has a linear correlation as shown in the following equation.

Where X _N is the Nth set of source data with n elements,

Is a vector of ones only,

Is a vector with similarity factor) The method of claim 2,
Where the similarity factor △ is

Approximate decoding method of original data with network coded linear correlation characterized in that it is a range. The method of claim 1,
Approximate decoding method of the original data having a network coded linear correlation, characterized in that the result of the approximate decoding is performed in the step S3.

(Where C is a coding coefficient matrix, D is a constraint matrix,

Is the product of matrices within a finite field, and 1 _(NK) is a vector with (NK) 1 values) 5. The method of claim 4,
Wherein the similarity factor Δ is in the form of 2 ^K , wherein k is in the range 0 ≦ k <M.

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