KR20150074887A - Methods for optimizing degree distribution of luby-transform code - Google Patents

Abstract

Disclosed is a method for optimizing degree distribution of an LT code. The method, which is performed in a transmission device, comprises the steps of: classifying a total message including a common message part among a plurality of transmission devices, into a plurality of classes; calculating a symbol error possibility about each divided class; and obtaining degree distribution capable of minimizing a symbol error possibility based on the calculated symbol error possibility. Accordingly, in a dispersion LT code system including a sharing message between multiple transmitters, a symbol restoring possibility can be maximized.

Description

METHODS FOR OPTIMIZING DEGREE DISTRIBUTION OF LUBY-TRANSFORM CODE

The present invention relates to a channel coding technique, and more particularly, to a method for optimizing a degree distribution of a distributed LT code applicable to error correction in an application layer.

In general, a method for compensating performance deterioration due to loss of a packet or a symbol occurring in a binary erasure channel includes Automatic Repeat Request (ARQ) and Forward Error Correction (FEC) Correction code is used.

Since the late 1990s, FEC codes have been studied in a form applicable to the application layer or the network layer, and fountain code channel coding techniques such as LT (Luby-Transform) codes and Raptor codes have been studied .

Fuzzy codes are designed in consideration of transmission efficiency and low encoding and decoding operations in broadcasting and multicasting that transmit signals to a large number on a network represented by lost channels.

The key design element of the fountain code is the degree distribution, which determines the coding and decoding computation volume and decoding performance.

The LT code has a low complexity and is a typical channel loss error correction code capable of recovering all information using a number of code symbols which is similar to or slightly larger than the number of messages. The LT code is a code using RSD (Robust Soliton Distribution), and it is advantageous that only a small amount ((1 + ε) k, ε is a very small positive number) code symbol is required to recover k message symbols.

However, in case of transmitting information by multiple senders, RSD, which is an optimal order distribution method used in existing LT codes, can not guarantee optimal performance.

A LT code used when transmitting information from a multiple sender to a single receiver is defined as a distributed LT code. To date, much research has been done to design distributed LT codes.

For example, M. Luby's "LT Codes" proposes a LT code, describes the coding and decoding process on a binary loss channel, and describes the optimal RSD distribution. In addition, M. Luby, M. Mitzenmacher, and A. Shokrollahi in "Analysis of random processes via and-or-tree evaluation", using an AND-OR tree, show the bipartite graph structure (Asymptotic) probability of recovery of a message symbol. In S. Puducheri, J. Kliewer and T. Fuja, "The Design and Performance of Distributed LT Codes" defines the role of relays in a network consisting of even number of senders, a single relay, and a single receiver, deconvolution). In A. Liau, S. Yousefi, and I. M Kim, "Binary Soliton-Like Rateless Coding for the Y-Network" defines the role of a relay in a network consisting of two senders, a single relay and a single receiver, It describes that the designed order distribution performance is better than DLT (Distributed Luby Transform). In addition, D. Sejdinovic, R. Piechocki, A. Doufexi, and M. Ismail, "Decentralized distributed fountain coding and design", defines a generalized LT code that can be considered when multiple senders transmit information to a single recipient And evaluates performance, and in some cases, direct design is possible. In addition, M. Zeng, R. Calderbank and Suguang Cui, "On Design of Rateless Codes Over Dying Binary Erasure Channel", assume that the reception overhead of rateless codes is a specific random variable, , We propose a method of order distribution that maximizes the average symbol recovery probability in an environment where the channel is disconnected randomly. Here, the proposed design method includes an AND-OR tree analysis method and a sequential quadratic programming (SQP) algorithm.

However, the conventional LT code designing methods as described above are considered only when each sender independently transmits information without sharing information among a plurality of senders.

Therefore, there is a disadvantage that optimum performance can not be achieved in a practical environment in which a part of information is shared among a plurality of senders.

It is an object of the present invention to solve the above problems and provide a method of optimizing a degree distribution of a distributed LT code capable of obtaining an optimum degree distribution in all practical environments including an environment in which information among a plurality of senders is shared will be.

Other objects and advantages of the present invention will be apparent from the following description taken in conjunction with the accompanying drawings, in which: FIG.

According to an aspect of the present invention, there is provided a method for optimizing order distribution of a distributed LT code, the method comprising: Dividing an entire message including a part into a plurality of classes, calculating a symbol error probability for each class, and obtaining a degree distribution capable of minimizing a symbol error probability based on the calculated symbol error probability .

Here, the number of messages included in each of the plurality of classes may be determined by multiplying the total message length by the distribution coefficient of the message symbols set for each class.

Here, the messages included in each of the plurality of classes can be selected asymmetrically for each class according to the selection coefficient.

Here, the step of calculating the symbol error probability for each class may be calculated using an AND-OR tree analysis method.

Here, the step of calculating the symbol error probability for each of the classified classes may be repeatedly performed, and the symbol error probability obtained in the calculation process of l (where l is a natural number of 2 or more) When the difference of the symbol error probability acquired in the first symbol error probability calculation process is less than the preset threshold value, the symbol error probability acquired in the l < th > symbol error probability calculation process is set as the convergence value of the symbol error probability for each class .

Here, the step of calculating the symbol error probability for each class may sum up the convergence values of the symbol error probabilities for the respective classes to obtain the total symbol error probability.

Here, the step of obtaining a degree distribution that minimizes the symbol error probability may obtain a degree distribution and a selection coefficient that minimize the overall symbol error probability using a sequential binary programming method.

The present invention provides a method for designing a degree distribution that minimizes a symbol error probability in a distributed LT code system in which a message partially shared among multiple senders is transmitted. Therefore, it is possible to maximize the symbol restoration probability in a distributed LT code system including a shared message between multiple senders.

In addition, optimization problems can be defined for all possible cases by numerically computing the objective function regardless of the theoretical performance of the independent message class.

In addition, when applying the order distribution optimization method of the distributed LT code according to the present invention, the LT code for maximizing the restoration performance for a specific message as well as the restoration performance for all messages received at the receiver can be designed.

1 is a conceptual diagram illustrating a communication environment to which a method of optimizing the degree distribution of a distributed LT code according to an embodiment of the present invention is applied.
FIG. 2 shows a decoding graph considered in a method for optimizing order distribution of a distributed LT code according to an embodiment of the present invention.
FIG. 3 shows a result obtained by applying the order distribution optimization method of the LT code according to an embodiment of the present invention.
4 is a flowchart illustrating a method of optimizing order distribution of LT codes according to an embodiment of the present invention.

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 terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with the meaning in the context of the relevant art and are to be interpreted in an ideal or overly formal sense unless explicitly defined in the present application Do not.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In order to facilitate the understanding of the present invention, 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 LT code is a typical channel loss error correction code widely used in the application layer. The code rate of the LT code is not defined and it is theoretically capable of generating infinite number of code symbols.

When a degree is determined by a given degree distribution, a transmitter symbolically generates a code symbol by XORing selected message symbols randomly. At the receiving end, received symbol symbols are recovered using a message passing (MP) algorithm. Here, the message restoration success rate is determined by the number of received code symbols. The ratio between the number of received code symbols and the number of messages is defined as the reception overhead.

In case of LT code using RSD, it has performance that minimizes the reception overhead required to recover all messages. At this time, it is assumed that the reception overhead exceeds 1, which means that the number of received code symbols should be larger than the number of messages.

Since all messages can be decoded from low complexity to low overhead, the LT code is widely used in applications such as multimedia streaming. However, when multiple senders attempt to transmit messages to a single receiver at the same time, optimal performance can not be guaranteed when multiple senders use RSDs, respectively. Therefore, a new degree distribution considering multiple senders is needed.

 A number of studies have been carried out on distributed LT codes to transmit information from multiple transmitters. The origin of the research was to define the relay protocol and to design the order distribution through deconvolution. It has been studied to improve the performance of distributed LT codes and to reduce the limitations in various situations. However, such studies have been carried out under the assumption that the messages of the respective transmitting terminals are independent and have the same length, and there is a problem in that an appropriate solution can not be presented when there is a shared message among the senders. In addition, among the studies related to the conventional distributed LT code, the generalized distributed LT code was defined and the optimization process based on the linear programming was performed in some limited situations through the theoretical performance analysis. However, this method also does not provide a way to design an optimal order distribution in all possible situations. Therefore, a new optimization technique for generalized distributed LT code is needed.

 In order to optimize the order distribution of the distributed LT code according to an embodiment of the present invention, sequential quadratic programming based optimization problem is defined through the theoretical performance analysis of the generalized distributed LT code, .

Hereinafter, a method for optimizing the degree distribution of a distributed LT code according to an embodiment of the present invention will be described in more detail with reference to the drawings.

1 is a conceptual diagram illustrating a communication environment to which a method of optimizing the degree distribution of a distributed LT code according to an embodiment of the present invention is applied.

Referring to FIG. 1, a method for optimizing the degree distribution of a distributed LT code according to an embodiment of the present invention can be applied to a communication environment in which a plurality of senders 101 to 106 transmit messages to a single receiver 110. Here, a plurality of senders 101 to 106 transmit a message including a common part to a single receiver 110.

1, K denotes a length of a message to be restored by the receiver 110, and S _i denotes an i-th sender of the plurality of senders 101 to 106. Also, N _s means the number of senders.

In FIG. 1, it is assumed that N _s senders 101 to 106 transmit code symbols at the same transmission rate, and the messages of the respective senders may have different lengths.

FIG. 2 shows a decoding graph considered in a method for optimizing order distribution of a distributed LT code according to an embodiment of the present invention.

2 is a graph illustrating a case where the receiver 110 attempts to recover all K messages using one BP (Belief Propagation) decoder.

If there is a message shared by the senders 101 to 106 in common, the possibility of restoring all messages equally can be prevented if the shared messages are multiplexed in the encoding process.

로 정의한다. 여기서, A_j는 j번째 클래스를 의미하고, N_m은 클래스의 개수를 의미한다. Therefore, you can divide the entire message into classes

. Here, A _j denotes the j-th class, and N _m denotes the number of classes.

(여기서,

는 메시지 심볼의 분포 계수를 의미함) 이며, 각 송신자의 부호화 과정에서 각각의 클래스에 소속된 메시지는 선택 계수

에 의해 비대칭적으로 선택된다. The number of messages contained in each class is

(here,

Is a distribution coefficient of a message symbol), and a message belonging to each class in the encoding process of each sender is a selection coefficient

Asymmetrically.

In the study that defined the graph model as described above, the theoretical symbol error probability of each class was calculated using the AND-OR tree analysis method, but the optimized order distribution for all situations that can be considered through the graph shown in FIG. 2 The selection coefficient could not be obtained.

In D. Sejdinovic, R. Piechocki, A. Doufexi, and M. Ismail, "Decentralized distributed fountain coding", in the environment where multiple senders send messages to a single recipient, In this study, we can obtain the order distribution only in a specific environment where all the senders have the same message length and the shared messages between senders have only one class. Therefore, when the message lengths of the senders considered in the present invention are different from each other or the number of common message classes is two or more, the optimization method based on the linear programming method disclosed in the above study can not be applied.

In the method of optimizing the degree distribution of the LT code according to the embodiment of the present invention, the optimization technique as shown in Equation (1) is applied based on the theoretical performance analysis of each message class to transmit a message The optimum LT code can be designed for all cases including the case where the LT code is used.

은 달성 가능한 최저의 심볼 오류 확률을 의미하며, 수학식 2와 같은 이론적 성능 분석을 바탕으로 계산된다.

는 차수 분포 생성을 위한 다항식을 의미하며, d_max는 최대 차수를 나타낸다.In Equation (1)

Denotes the lowest achievable symbol error probability, and is calculated based on the theoretical performance analysis as shown in Equation (2).

Denotes a polynomial for generating a degree distribution, and d _max denotes a maximum degree.

That is, Equation (1) can be defined as a linear combination of error probability y _j for each class as shown in Equation (2). Here, y _j denotes the error probability of the numerically calculated jth class A _j , and is the performance when assuming an infinite number of iterative decoding and an infinite length message.

Therefore, the LT code designing method shown in Equation (1) can understand the problem of finding a degree distribution and a selection coefficient that minimize the theoretically achievable performance for all K message symbols.

On the other hand, the error probability y _{j, l per} the theoretical class in the l-th iterative decoding step is a decreasing function for l as disclosed in the existing study on AND-OR tree analysis. Therefore, in order to apply the performance analysis result to the present invention, the convergence value of y _{j , l} should be calculated. In the embodiment of the present invention, the theoretical performance is determined by a predetermined threshold value y _Th If a smaller difference is found, the optimization problem is solved by considering the convergence value of class-specific error probability.

That is, the decoding step is stopped at l that satisfies the condition shown in Equation (3).

Also, in the present invention, the solution of the optimization problem defined in Equation (1) is obtained by using Sequential Quadratic Programming (SQP).

를 입력으로 받아 최적의 차수 분포와 선택 계수인

를 출력하게 된다.
Therefore, the LT code designing unit for optimizing the degree distribution of the LT code according to an embodiment of the present invention includes a distribution of message symbols

And the optimal order distribution and the selection coefficient

.

FIG. 3 shows a result obtained by applying the order distribution optimization method of the LT code according to an embodiment of the present invention.

에 대한 선택계수 및 차수분포를 획득한 결과를 나타낸다.
In Figure 3 when the number of the originator 2 (i.e., N _s = 2), the input variables

And the result is obtained.

4 is a flowchart illustrating a method of optimizing order distribution of LT codes according to an embodiment of the present invention. The order distribution optimization method of the LT code shown in Fig. 4 can be performed by each sender (or transmission apparatus) in a communication environment as shown in Fig.

Referring to FIG. 4, first, a sender divides a message including a part commonly shared among senders into N _m classes, and calculates a symbol error probability y _{j, l} of each class (S 401). Here, the symbol error probability for N _m classes can be calculated theoretically using an AND-OR tree analysis method. In order to obtain the convergence value of the symbol error probability y _{j , l} of each class, y _{j , l} is set to a predetermined threshold value y _Th The symbol error probability calculation process is repeated until a smaller difference value is obtained.

That is, the sender computes the symbol error probability y _{j , l} of each class in step S401 and increments l by 1 (S402). Then, as shown in Equation (3), the symbol error probability calculated in the current step, Calculates the difference of the symbol error probability calculated in the step, and compares the calculated difference value with a predetermined threshold value y _Th (S403).

If the calculated difference value is smaller than the preset threshold value y _{Th, the} transmitter sets the symbol error probability acquired in the first step as a convergence value of the symbol error probability, adds the symbol error probability acquired for each class, The error probability y _total is obtained (S404).

와, 선택 계수

최적화 값을 획득한다(S405).
Thereafter, the sender uses a sequential binary scheme (SQP) to minimize the _total symbol error probability, y _total ,

And a selection coefficient

And obtains the optimization value (S405).

It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined in the appended claims. It will be possible.

101 ~ 106: sender
110: Recipient

Claims (8)

A method for optimizing order distribution of LT codes performed in a transmitter,
Classifying an entire message including a message part common to a plurality of transmission devices into a plurality of classes;
Calculating a symbol error probability for each of the classified classes; And
And obtaining a degree distribution that minimizes a symbol error probability based on the calculated symbol error probability. The method according to claim 1,
Wherein the number of messages included in each of the plurality of classes is determined by multiplying the total message length by a distribution coefficient of a message symbol set for each class. The method according to claim 1,
Wherein a message included in each of the plurality of classes is selected asymmetrically for each class according to a selection coefficient. The method according to claim 1,
Wherein the step of calculating a symbol error probability for each class comprises:
And calculating an optimal order of the LT code using an AND-OR tree analysis method. The method according to claim 1,
Wherein the step of calculating a symbol error probability for each class comprises:
Wherein the step of estimating the order of the LT codes is performed repeatedly. The method of claim 5,
Wherein the step of calculating a symbol error probability for each class comprises:
th symbol error probability calculation process and the symbol error probability obtained in the (l + 1) th symbol error probability calculation process are less than a preset threshold value, l Th symbol error probability is set as a convergence value of a symbol error probability for each class. The method of claim 6,
Wherein the step of calculating a symbol error probability for each class comprises:
And summing the convergence values of the symbol error probability for each class to obtain the total symbol error probability. The method of claim 7,
Wherein the step of obtaining a degree distribution capable of minimizing the symbol error probability comprises:
And a degree distribution and a selection coefficient for minimizing the total symbol error probability are obtained by using a sequential binary programming method.

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