KR101415584B1 - Apparatus and method for optimal approximate decoding of network coded data using source data statistic - Google Patents

Abstract

An optimal approximate decoding method of a network coded data in an ad-hoc network composed of a source node, an intermediate node, and a reception node according to embodiments of the present invention comprises the steps of: enabling the reception node to receive similarity information (SI) composed of the statistic information of difference values of successive symbols and symbols; determining a reverse matrix of a full-rank coding coefficient matrix from the received T number of the symbols when the T number of the symbols which are sufficient to decode is received, and restoring an original symbol from the reverse matrix and the received symbols; and generating the K×T number of the coding coefficient matrix from the received K (K<T) number of the symbols when the T number of the symbols which are sufficient to decode is not received, and restoring the original symbols by generating the T-K length of an addition restriction condition respectively from the correlation information related to the T-K number of the omitted symbols and the (T-K)×T number of the addition restriction condition related to the T-K number of the omitted coding coefficient.

Description

[0001] APPARATUS AND METHOD FOR OPTIMAL APPROXIMATE DECODING OF NETWORK CODED DATA USING SOURCE DATA STATISTIC [0002]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to network coding, and more particularly, to an approximate decoding technique for network coded data.

As mobile devices with wireless networking capabilities are routinely used, the importance of the technology to transmit information in a timely manner within such a dynamic network is becoming more and more dynamic as the wireless network continues to change by a number of different types of devices It is gradually getting higher.

Network coding is increasingly being used as a methodology for constructing an efficient distributed transmission algorithm in dynamic networks with various paths and sources. The existing routing-based network scheme simply forwards the data to point-to-point, so if the network configuration changes in the middle, the existing routing path is cut off or the speed is lowered to affect the quality of service and to maintain the routing path There is not much overhead.

On the other hand, network coding is a process by which neighboring nodes in the network repeatedly receive and output packets, thereby allowing data to flow to a destination without a predetermined routing path. Therefore, network coding can efficiently use bandwidth, power resources, And shows robustness to network fluctuations. As the source and path vary, that is, the number of nodes having the same information and the number of nodes requesting, the performance of such network coding can be maximized.

However, since the information transmitted through network coding is not transmitted as it is in the original data, but the network node modulates it through proper operation, there is a problem that the data can not be reconstructed when the symbols are incompletely received within a predetermined time have.

In particular, in the case of time delay sensitive data such as multimedia data, if the packet does not arrive within the allowable delay time, data decoding can not be performed by the conventional decoding methodologies, which is pointed out as a big limitation of network coding.

To cope with these problems, the proposed approximate decoding method is a technique that approximates lost data by using correlation of received data when receiving network coded data. For example, since the temperature or voltage measured in the real world has a high correlation between measurement data close in time, even when the data received by the data collection device is not sufficient for network decoding, Can be restored.

[1] Ho, T., M'edard, M., Shi, J., Effros, M. and Karger, D.R., "On randomized network coding, in Proc. Allerton Annual Conf. Commun., Control, and Comput., Oct. 2003 [2] H. Park, N. Thomos, and P. Frossard, Approximate decoding approaches for network coded correlated data, Signal Processing (Elsevier), vol. 93, no. 1, pp. 109 to 213, Jan. 2013

SUMMARY OF THE INVENTION It is an object of the present invention to provide an optimal approximate decoding method of network coded data using source data statistics in order to provide a near approximate decoding of delay sensitive data.

An optimal approximate decoding method of network coded data in an ad hoc network composed of a source node, an intermediate node and a receiving node according to an aspect of the present invention includes:

Receiving the similarity information (SI) comprising statistical information of differences between symbols and consecutive symbols;

로부터 풀-랭크 코딩 계수 행렬

의 역행렬

을 결정하고, 역행렬

및 수신 심볼들

로부터 원본 심볼

을 복원하는 단계; 및If enough T symbols are received to decode, the receiving node receives the received T symbols

Rank coding matrix

Inverse of

, And the inverse matrix

And received symbols

The original symbol

; And

로부터 K×T의 코딩 계수 행렬

를 생성하고, T-K 개의 누락된 코딩 계수에 관하여 (T-K)×T의 추가 제한 조건

및 T-K 개의 누락된 심볼들에 관하여 상기 유사도 정보로부터 T-K 길이의 추가 제한 조건

을 각각 생성하여 원본 심볼들

을 복원하는 단계를 포함할 수 있다.If not enough T symbols have been received to decode, the receiving node receives the received K (K < T) symbols

A coding coefficient matrix of K x T from

(TK) × T with respect to the TK missing coding coefficients,

And an additional constraint condition of the TK length from the similarity information with respect to the TK missing symbols

To generate original symbols

And a step of reconstructing the image.

의 역행렬

을 고유하게 결정할 수 있도록 T 개의 선형 비종속적인 심볼들이 수신되었는지 판정하는 단계를 더 포함할 수 있다.In one embodiment, prior to the step of recovering the original symbols, the receiving node may use a coding coefficient matrix

Inverse of

Lt; RTI ID = 0.0 &gt; T &lt; / RTI &gt;

In one embodiment, the data received by the receiving node may be delay sensitive data that must be provided to a user by decoding symbols within a predetermined time limit.

In one embodiment, the difference values of the consecutive symbols may be in accordance with a bilaterally symmetric distribution.

In one embodiment, the similarity information SI may be an average value of difference values of consecutive symbols.

을 복원하는 단계는,In one embodiment, if there are not enough T symbols received to decode,

Wherein:

The following equation

Lt; / RTI &gt;

는 수신된 심볼들

의 유사도 모델에 기초하여 생성될 수 있고, T-K 길이의 추가 제한 조건

은 소스 노드에서 전송되는 연속하는 심볼들의 차이 값들의 평균 값들으로부터 생성될 수 있다.Where (TK) x T additional constraints

Lt; RTI ID = 0.0 &gt; received symbols

Lt; RTI ID = 0.0 &gt; TK &lt; / RTI &gt; length,

May be generated from the mean values of the difference values of consecutive symbols transmitted at the source node.

According to the optimal approximate decoding method of network coded data using the source data statistics of the present invention, the receiving node can perform optimal approximate decoding using the statistical information of the source or source data.

According to the optimal approximate decoding method of the network coded data using the source data statistics of the present invention, only the average value of the statistical information of the source data is provided, and even if the correlation of the data is not yet determined, The received data can be decoded.

1 is a diagram conceptually illustrating a distributed data transmission system to which the present invention can be applied.
2 is a flowchart illustrating an optimal approximate decoding method of network coded data using source data statistics according to an embodiment of the present invention.
FIG. 3 is a graph illustrating a change in error performance according to a value of similarity information SI in an optimal approximate decoding method of network coded data using source data statistics according to an embodiment of the present invention. Referring to FIG.

For the embodiments of the invention disclosed herein, specific structural and functional descriptions are set forth for the purpose of describing an embodiment of the invention only, and it is to be understood that the embodiments of the invention may be practiced in various forms, The present invention should not be construed as limited to the embodiments described in Figs.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The same reference numerals are used for the same constituent elements in the drawings and redundant explanations for the same constituent elements are omitted.

The following description is largely divided into three sections, Sections 1 and 2, which illustrate the basic principles of approximate decoding along with an introduction to a distributed data transmission system to which the present invention may be applied, The decoding method will be explained. Note that some of the notations for vector or variable appearing in Section 3 may differ from those shown in Section 1 and Section 2.

1. Random linear network coding

1 is a diagram conceptually illustrating a distributed data transmission system to which the present invention can be applied. And the source data is transmitted to the decoder (decoder) through the network coding node. The data transmitted in this system has a correlation with each other. The correlated data may have external correlation, such as data measured over the sensor network, or may be highly correlated data, such as images within a video sequence.

Research on the transmission of such correlation data has been widely performed in distributed systems. Network coding techniques have been studied as a technique for transmitting correlation data over a network.

In FIG. 1, an overlay ad hoc network is composed of source nodes, intermediate nodes, and receiving nodes, and the source data is transmitted from the source node to the receiving node through intermediate nodes responsible for network coding operations do. The intermediate node may transmit the received data as it is, but may combine and output the data received from the other source nodes.

Random Linear Network Coding (RLNC) techniques used in the present invention among various network coding schemes are described in 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.

내의 L 개의 소스 심볼들은 라고 표시되며, 각각 이산(discrete)이면서 상관되어(correlated) 있고, 1≤i≤L일 때에

이다.

는

의 알파벳 집합(alphabet set)이고 |

|는

의 크기를 의미한다. 네트워크 코딩 연산은 갈로와 필드(GF: Galois Field) 내에서 수행되기 때문에, 각각의

은 GF 내의 원소로 고려되어야 한다.

가 실수 필드(

, field of real numbers)에 있는 수인지 아니면 GF에 있는 수인지 여부를 명확하게 특정하기 위해서, 수학식 1과 같은 식별 함수(identity function)을 정의할 수 있다.Source set

Lt; RTI ID = 0.0 &gt; L & And are respectively discrete and correlated, and when 1? I? L

to be.

The

Of the alphabet set (alphabet set) and |

| Is

. Since the network coding operation is performed in a Galois Field (GF), each

Should be considered as elements in the GF.

Is a real field (

, field of real numbers, or the number in GF, it is possible to define an identity function as shown in equation (1).

가

을 의미하는 GF 내의 원소임을 의미한다.

인 경우에,

는 L 개의 요소를 가지는 N 번째 소스 데이터 집합이다.

는

의 알파벳 세트를 의미한다. 또한 본 명세서에서 행렬 또는 벡터의 위 첨자로 쓰이는 T는 행렬 또는 벡터의 전치(transpose)를 의미하며, 실수값 T 또는 아래 첨자로 쓰이는 T와 구별됨을 유의한다.this is

end

Which means that it is an element in GF.

in case of,

Is the Nth source dataset with L elements.

The

&Lt; / RTI &gt; Also note that T, used as a superscript of a matrix or vector herein, is a transpose of a matrix or vector, and is distinguished from a real value T or a T used as a subscript.

기호는 생략된다.

와

연산자들은 각각 GF 내에서 정의되는 합산 연산과 승산 연산을 의미한다.In the formula describing with the operation symbols in the GF, it implies that all operations occur in the GF,

The symbol is omitted.

Wow

The operators refer to summation and multiplication operations defined in GF, respectively.

The intermediate node k using the RLNC generates and transmits a packet according to Equation (2).

와 코딩 계수

의 GF에서의 선형 결합(linear combination in GF)을 의미한다. i는 1≤i≤L인 임의의 정수이고, T는 하나의 패킷 내에 결합된 데이터의 개수이다.

와

는 항상 GF 내의 원소로 간주될 수 있다. 코딩 계수들은 크기 2^M을 가지고 GF로부터 균일하고 랜덤하게 선정되는데, 이를

라고 한다. 이는 GF 크기가 M에 의해 결정되며,

임을 의미한다.Equation (2)

And a coding coefficient

Means a linear combination in the GF. i is any integer with 1? i? L, and T is the number of pieces of data combined in one packet.

Wow

Can always be regarded as an element in the GF. The coding coefficients are chosen uniformly and randomly from GF with size 2 ^M ,

. This is because the GF size is determined by M,

.

에서 합산 연산은 XOR 연산으로 수행될 수 있다. GF의 크기는 소스 심볼에 관하여 수행될 수 있는 코딩 연산들의 집합을 결정한다. 따라서 입력 알파벳의 크기가

라고 가정할 수 있다. 만약

인 경우에는 입력 집합은 예를 들어 소스 결합(source binning) 또는 양자화 등을 이용하여 축소되고 그럼으로써 입력 집합은 GF 크기, 즉 2^M을 초과하지 않게 된다.In the present invention, in particular, a GF having a characteristic value of 2

The summation operation can be performed by an XOR operation. The size of GF determines the set of coding operations that can be performed with respect to the source symbol. Therefore, the size of the input alphabet is

. if

The input set is reduced using, for example, source binning or quantization, so that the input set does not exceed the GF size, i.e. 2 ^M.

이 수신되어 연산에 쓰일 수 있다면, 선형 시스템

는 다음 수학식 3과 같이 표현될 수 있다.The packets generated at each node are transmitted to neighboring nodes and finally to the receiving nodes. If at the decoder of the receiving node there are K innovative or linearly independent symbols or packets,

Lt; / RTI &gt; can be received and used in an operation,

Can be expressed by the following equation (3).

연산자는 유한 필드(finite field)에서 행렬들 사이의 승산 연산을 의미한다. here

The operator denotes a multiplication operation between matrices in a finite field.

는 코딩 계수 행렬(coding coefficient matrix)이라고 하는데, 컬럼 벡터들

로 구성되며, 수신된 심볼들의 유사도 모델에 기초하여 생성된다. 코딩 계수 행렬

를 유사도 모델에 기초하여 생성하는 방법은 네트워크 코딩의 복호화 기법에 숙련된 자들에게 주지된 방법이므로 설명을 생략한다.K × T matrix

Is called a coding coefficient matrix, and column vectors &lt; RTI ID = 0.0 &gt;

And is generated based on the similarity model of the received symbols. Coding coefficient matrix

Based on the degree-of-similarity model is a method well known to those skilled in the network coding decoding technique, and thus a description thereof will be omitted.

가 풀-랭크(full-rank), 즉 K=T인 경우, 다시 말해 수신된 심볼들의 개수 K가 송신된 심볼들의 개수 T와 같아 복호화하기에 충분한 T 개의 심볼들이 수신된 경우에, 수학식 3의 선형 시스템의 해(solution)인

는, 코딩 계수 행렬

의 역행렬

가 고유하게 결정되고 또한 이에 상응하여

이기 때문에, 다음 수학식 4와 같이 고유하게 결정될 수 있다.If such a coding coefficient matrix

That is, if the number of received symbols K is equal to the number of transmitted symbols T, and T symbols sufficient to decode are received, the following equation (3) is obtained: &lt; EMI ID = Of the linear system of

, A coding coefficient matrix

Inverse of

Is uniquely determined and correspondingly

, It can be uniquely determined as shown in the following equation (4).

The inverse matrix of the coding coefficient matrix can be easily obtained by a known method such as performing a Gaussian elimination on GF.

을 결정하기에 충분하지 않은 수의 심볼들만 수신된 경우에, 즉 K<T인 경우, 다시 말해, 수신된 심볼들의 개수 K가 송신된 심볼들의 개수 T보다 적어 복호화하기에 충분한 T 개의 심볼들이 수신되지 않은 경우에, 코딩 계수 행렬

가 풀-랭크가 아니기 때문에 수학식 3의 선형 시스템의 해

는 유일하게 결정되지 못할 뿐 아니라, 무한한 개수로 얻어질 수 있다. The problem is, if a unique inverse matrix

That is, K < T, that is, if the number K of received symbols is less than the number T of transmitted symbols and T symbols sufficient to decode are received If not, the coding coefficient matrix

Is not a full-rank, the solution of the linear system of equation (3)

Not only can not be determined uniquely, but can be obtained in an infinite number.

The approximate decoding method is introduced to solve this problem, and the approximately determined source symbols are reconstructed with insufficiently received data.

2. Approximate decoding method

이 특이 행렬(singular matrix)인 경우에는, 코딩 계수 행렬

의 역행렬

은 얻어질 수 없고 수학식 3의 선형 시스템에서 해가 유일하지 않을 수 있다.The decoder can recover the source data upon receipt of the symbol set y. If there are external factors such as packet delay or loss during the transmission procedure, or a randomly selected coding coefficient matrix

In the case of this singular matrix, the coding coefficient matrix

Inverse of

Can not be obtained and the solution may not be unique in the linear system of equation (3).

To solve this problem, the approximate decoding method can make the coding coefficient matrix full-rank using additional constraints.

와

를 구축하는 데에 이용될 수 있다. 추가 제한 조건들

및

의 모든 요소들(elements) 역시 GF 내의 값이다.The additional constraints that the correlation of the input data adds in the decryption procedure

Wow

Can be used for constructing. Additional Restrictions

And

All the elements of GF are also values in GF.

및

을 추가함으로써 선형 시스템은 유일한 해를 가질 수 있게 되고 유일한 해

는 다음 수학식 5와 같이 표현될 수 있다.Additional Restrictions

And

By adding the linear system can be the only solution and the only solution

Can be expressed by the following equation (5).

및

내의 계수들은 소스의 모델들에 기초하여 결정될 수 있다.

가 결정되면, 원본 데이터의 근사 심볼

은 수학식 1의 식별 함수들에 의해

과 같이 얻어질 수 있다. Additional Restrictions

And

The coefficients in the matrix can be determined based on the models of the source.

Is determined, an approximate symbol of the original data

Is determined by the identification functions of Equation (1)

Can be obtained.

H. Park, N. Thomos, and P. Frossard, Approximate decoding approaches for network coded correlated data, Signal Processing (Elsevier), vol. 93, no. 1, pp. 109 to 213, Jan. 2013 thesis can be referred to.

는 유사도 모델에 기초하여 생성될 수 있는데, 예를 들어 가장 유사한 데이터

및

의 위치에 상응하는 자리에 값 "1" 및 "1"을 가지는 두 개의 요소들을 제외하고 각 행이 0으로 구성되도록 생성된다. 또한

은 T-K 길이를 가지는 벡터로서 결정되는데, 예를 들어 모든 값이 0일 수 있다(

).(TK) x T matrix

May be generated based on the similarity model, for example, the most similar data

And

Quot; 1 "and" 1 "in the place corresponding to the position of " 1 &quot; Also

Is determined as a vector having a TK length, e.g., all values may be zero (

).

은 다음의 수학식 6과 같이 얻어질 수 있다.Thus, an approximate symbol of the original data

Can be obtained by the following Equation (6).

This allows the decoder to approximate the original symbols even though some symbols are insufficient for complete decoding.

를 가역적으로(invertible) 만든다는 점이다. 이는 네트워크 코딩된 데이터에 관하여 데이터 복원 방법론의 새로운 패러다임을 제시한다. The core idea of these existing algorithms is to add a surplus equation based on the source correlation,

To make it invertible. This presents a new paradigm of data restoration methodology for network coded data.

와

가 경험론적 방법론(heuristic approach)에 의존하는 경우가 대부분이어서 소스 유사성을 제대로 재현하지 못하였고, 이는 제한된 성능으로 이어졌다.
However, the above-described approximate decoding methodologies are not limited to the additional constraint matrix

Wow

Is largely dependent on the heuristic approach, which does not reproduce the source similarity well, leading to limited performance.

3. An approximate decoding method of data having a correlation of the present invention

3.1 Distribution model of source data

The optimal approximate decoding method of the network coded data using the source data statistics of the present invention considers statistical analysis of the correlation of the sources in order to get improved performance through a more objective methodology and away from the conventional empirical methodology.

내에서 나타나는 통계적으로 특징지어질 수 있다.The source correlation is the difference set of consecutive source data

Can be statistically characterized.

For statistical analysis, during the network coding procedure, prior to performing the combining, the data sets may be sorted in size order in the buffer.

라고 할 수 있다.The sequence can be denoted by the subscript N. Thus, x _{N + 1} is not less than x _N ,

.

이라 하면, N 번째 차이 집합

의 i 번째 요소는

이다.A difference set of L elements representing the difference between the _Nth source data x _N and the (N + 1) th source data x _{N + 1}

, The Nth difference set

The i-th element of

to be.

의 각 요소

은 각자의 평균 Δ과 분산 σ²를 가지는 종형 유니모달 대칭 분포 함수(bell-shaped unimodal symmetric distribution) Ψ(Δ, σ²)를 따른다고 가정할 수 있다. 유니모달 대칭 분포 함수는 어떤 데이터 그룹을 모델링하는 데에 널리 사용되며, 예를 들어 가우시안 분포나 라플라시안 분포와 같은 주지의 분포 함수들이 있다.At this time,

Each element of

Can be assumed to follow a bell-shaped unimodal symmetric distribution Ψ (Δ, σ ² ) with an average Δ and a variance σ ² of each. The Unimodulus symmetric distribution function is widely used to model any data group, for example, well known distribution functions such as Gaussian distribution or Laplacian distribution.

Therefore, the (N + 1) -th source data x _{N + 1} can be expressed by Equation (7).

이므로, N+1 번째 소스 데이터 x_N+1 내의 데이터

는 N 번째 소스 데이터 x_N 내의

와 차이 집합

내의

을 이용하여 수학식 8과 같이 표현될 수 있다.At this time,

, The data in the (N + 1) -th source data x _{N + 1}

Th _&gt; source data x _N

And the difference set

undergarment

Can be expressed as Equation (8).

In this model, the average difference between two consecutive source data can be denoted by the mean?. In this specification, the average? May also be referred to as similarity information (SI).

It is noted that in the approximate decoding method, the source correlation can be expressed using a similarity model, and the source similarity can be measured by the distance between the data.

Therefore, in view of this distance measurement, if the average? Of the distances between the source data is large, the correlation is reduced. On the contrary, if the average? Of the distances between the source data is small, the correlation becomes large.

내의 요소들의 값과 SI의 값은 GF(2^M) 공간 내에서 결정될 수 있다.
On the other hand, if the values of the source data do not exceed the GF size,

The values of the elements in the GF and the values of SI can be determined in the GF (2 ^M ) space.

3.2 Approximate Decoding of Symmetrically Distributed Source Data

는 T-K 데이터의 통계적 특성에 기초하여 결정된다.For the approximate decoding of symmetrically distributed source data, the equation of Equation (5) should be appropriately constructed. In other words, for every Nth source data, an additional constraint consisting of TK elements

Is determined based on the statistical characteristics of the TK data.

와 N+1 번째 시간 슬롯의 소스 데이터 x_N+1 내의 i 번째 데이터 요소

의 차이인

값들이 각각 종형 유니모달 대칭 분포 Ψ(Δ, σ²)를 따를 경우에, 전송 중에 데이터가 손실되거나 수신되지 않아 추가되어야 하는 T-K 길이의 추가 제한 조건

의 제한 조건의 요소들은 손실된 데이터 요소의 차이 평균들 Δ 값로 구성된다. For example, the i-th data element of the source data x _N of the _Nth time slot

And the i-th data element in the source data x _{N + 1} of the ( _{N + 1)}

Difference of

When the values follow the vertical symmetric distribution Ψ (Δ, σ ² ), respectively, the additional constraints of TK length, which must be added because data is lost or not received during transmission

The elements of the constraint are composed of the difference mean values of the missing data elements.

의 분포 Ψ(Δ, σ²)를 지속적으로 추적하며,

의 분포 Ψ(Δ, σ²)에 기초한 유사도 정보를 수신 노드에 전송한다.To this end, the source node may use a different set of data elements

(&Amp;thetas; ² ) continuously,

To the receiving node, similarity information based on the distribution? (?,? ² ).

의 평균 Δ을 수신하고, 만약 수신된 데이터에 누락, 손실된 데이터 요소가 있다면, 수신된 유사도 정보, 특히 평균들 Δ에 기초하여 추가 제한 조건

을 생성하여 근사 복호화할 수 있다.The receiving node may store similarity information,

And if there is a missing or missing data element in the received data, the received similarity information, in particular the additional constraints &lt; RTI ID = 0.0 &gt;

And approximate decoding can be performed.

2 is a flowchart illustrating an optimal approximate decoding method of network coded data using source data statistics according to an embodiment of the present invention.

Referring to FIG. 2, the optimal approximate decoding method of the present invention receives, in step S21, similarity information SI composed of statistical information of symbols and difference values of consecutive symbols for decoding from an intermediate node &Lt; / RTI &gt;

Depending on the embodiment, the difference values of consecutive symbols follow a bilaterally symmetric distribution, and the similarity information SI may be an average value of the difference values of consecutive symbols, or may be an average value and a variance value.

Then, in step S22, the receiving node determines whether sufficient symbols have been received for decryption.

의 역행렬

을 고유하게 결정할 수 있도록 T 개의 선형 비종속적인 심볼들이 수신되었는지 판정할 수 있다.In particular, the receiving node uses a coding coefficient matrix &lt; RTI ID = 0.0 &gt;

Inverse of

Lt; RTI ID = 0.0 &gt; T &lt; / RTI &gt;

According to an exemplary embodiment, the data received by the receiving node may be delay sensitive data that must be provided to a user by decoding symbols within a predetermined time limit.

If K symbols with K = T are received and it is determined in step S22 that sufficient symbols have been received, the flow proceeds to step S23.

로부터 풀-랭크 코딩 계수 행렬

의 역행렬

을 결정하고, 역행렬

및 수신 심볼들

로부터 원본 심볼

을 복원한다.In step S23, the receiving node receives the received T symbols

Rank coding matrix

Inverse of

, And the inverse matrix

And received symbols

The original symbol

.

If only K symbols of K < T are received and it is determined in step S22 that sufficient symbols have not been received, the process proceeds to step S24.

로부터 K×T의 코딩 계수 행렬

를 생성하고, T-K 개의 누락된 코딩 계수에 관하여 (T-K)×T의 추가 제한 조건

및 T-K 개의 누락된 심볼들에 관하여 유사도 정보로부터 T-K 길이의 추가 제한 조건

을 각각 생성하여 다음의 수학식 9를 통해 원본 심볼들

을 복원한다.In step S24, the receiving node receives the received K symbols

A coding coefficient matrix of K x T from

(TK) × T with respect to the TK missing coding coefficients,

And additional constraints of the TK length from the similarity information with respect to the TK missing symbols

And generates the original symbols &lt; RTI ID = 0.0 &gt;

.

는 수신된 심볼들

의 유사도 모델에 기초하여 생성될 수 있고, T-K 길이의 추가 제한 조건

은 소스 노드에서 전송되는 연속하는 심볼들의 차이 값들의 평균 값들으로부터 생성될 수 있다.
Specifically, the additional constraint (TK) x T

Lt; RTI ID = 0.0 &gt; received symbols

Lt; RTI ID = 0.0 &gt; TK &lt; / RTI &gt; length,

May be generated from the mean values of the difference values of consecutive symbols transmitted at the source node.

3.3 Performance Evaluation

를

라 표시하고,

중 n 번째 요소를

라 하며,

이 가장 좋은 복호 성능을 보여준다고 가정할 경우에,

대신에

이 적용되어 디코딩되었을 때의 오차

에 따른 기대 오차 함수는 다음 수학식 10과 같이 표현될 수 있다.For simplicity of expression

To

Respectively,

The nth element of

And,

Assuming that this shows the best decoding performance,

Instead of

And the error when decoding is applied

Can be expressed as Equation (10). &Quot; (10) &quot;

는

가 선택될 확률이고

는

가 선택될 확률이며,

는 근사 복호화 알고리즘에 기초한 오차를 모델링한 함수이다.here,

The

Is the probability of being selected

The

Is the probability of being selected,

Is a function modeling an error based on an approximate decoding algorithm.

=Δ=16으로 정해놓고 소스 데이터들을 생성하면서, 다양한

값들에 관하여 디코딩을 1000 회에 걸쳐 실시한 결과가 도 3에 나타나 있다.Based on Equation ( ¹⁰ ), within GF (2 ¹⁰ )

= [Delta] = 16 and generating the source data,

The results of decoding 1000 times over the values are shown in FIG.

를 변경하면서 실험한 결과를 참조하면, 평균 제곱 오차(MSE)는

≠

인 한 대동소이하게 매우 큰 값을 보이며,

=

인 때에만 급격하게 줄어든다.In Figure 3, from 1 to 35

, The mean square error (MSE) is

≠

The value is very large,

=

It is sharply reduced only when it is.

는 실질적으로 유사도 정보 SI가 전송 중에 소실되었거나 변조된 경우와 같다.
In the optimal approximation decoding method of the present invention, distribution information of the difference set, that is, similarity information (SI) is transmitted from the source node to the decoding node,

Is substantially the same as when the similarity information SI is lost or modulated during transmission.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, Modification is possible. Accordingly, the spirit of the present invention should be understood only in accordance with the following claims, and all of the equivalent or equivalent variations will fall within the scope of the present invention.

In addition, the method according to the present invention can be implemented as a computer-readable code on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of the recording medium include a ROM, a RAM, an optical disk, a magnetic tape, a floppy disk, a hard disk, a nonvolatile memory, and the like, and a carrier wave (for example, transmission via the Internet). The computer-readable recording medium may also be distributed over a networked computer system so that computer readable code can be stored and executed in a distributed manner.

Claims (7)

CLAIMS What is claimed is: 1. A method for optimal approximate decoding of network coded data in an ad hoc network consisting of a source node, an intermediate node and a receiving node,
Receiving the similarity information (SI) comprising statistical information of differences between symbols and consecutive symbols;
If enough T symbols are received to decode, the receiving node receives the received T symbols

Rank coding matrix

Inverse of

, And the inverse matrix

And received symbols

The original symbol

; And
If not enough T symbols have been received to decode, the receiving node receives the received K (K < T) symbols

A coding coefficient matrix of K x T from

(TK) × T with respect to the TK missing coding coefficients,

And an additional constraint condition of the TK length from the similarity information with respect to the TK missing symbols

To generate original symbols

The method comprising the steps of:
If the number of symbols transmitted by the source node and the number of symbols to be decoded by the receiving node are T, the number of symbols received by the receiving node is K, and K = T, T symbols sufficient to decode Where T < T &gt; symbols are not received sufficient to decode if K &lt; T. 2. The method of claim 1, wherein, prior to the step of recovering the original symbols,

Inverse of

Lt; RTI ID = 0.0 &gt; T &lt; / RTI &gt; linearly unconventional symbols have been received so as to uniquely determine the T &lt; th &gt; 2. The method of claim 1, wherein the data received by the receiving node is delay sensitive data that must be provided to a user by decoding symbols within a predetermined time limit. 2. The method of claim 1, wherein the difference values of the consecutive symbols follow a vertical unimodal symmetric distribution. 5. The method of claim 4, wherein the similarity information (SI) is an average value of difference values of consecutive symbols. The method of claim 1, wherein if T symbols are not received sufficient to decode,

Wherein:
The following equation

Lt; / RTI &gt;
Where (TK) x T additional constraints

Lt; RTI ID = 0.0 &gt; received symbols

Lt; RTI ID = 0.0 &gt; TK &lt; / RTI &gt; length,

Is generated from the mean values of the difference values of consecutive symbols transmitted at the source node. A computer-readable recording medium on which a program for implementing an optimal approximate decoding method of network coded data according to any one of claims 1 to 6 is recorded in a computer.

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