WO2015099266A1

WO2015099266A1 - Method for optimizing decomposed lt code degree distribution

Info

Publication number: WO2015099266A1
Application number: PCT/KR2014/008368
Authority: WO
Inventors: 허준; 서영길; 백종현
Original assignee: 포항공과대학교 산학협력단; 고려대학교 산학협력단
Priority date: 2013-12-24
Filing date: 2014-09-05
Publication date: 2015-07-02
Also published as: KR101643039B1; KR20150074887A

Abstract

Disclosed is a method for optimizing degree distribution of an LT code. A method for optimizing a degree distribution of the LT code, carried out by transmitting devices, comprises the steps of: sorting into a plurality of classes all messages including a message portion shared between a plurality of transmitting devices; calculating a symbol error probability for each of the sorted classes; and obtaining a degree distribution which can minimize the symbol error probability based on the calculated symbol error probability. As a result, the symbol recovery probability can be maximized in a decomposed LT code system including a shared message between multiple transmitting users.

Description

Order Distribution Optimization Method of Distributed LT Codes

The present invention relates to a channel coding technique, and more particularly, to a method of optimizing order distribution of distributed LT codes that can be applied to error correction of an application layer.

Generally, Automatic Repeat Request (ARQ) and Forward Error Correction (FEC) are used to compensate for performance degradation due to loss of packets or symbols in binary erasure channels. Correction) sign is used.

Since the late 1990s, the FEC code has been studied in the form of application to the application layer or network layer.Fountain code channel coding techniques such as LT (Luby-Transform) code and Raptor code have been studied. It became.

The fountain code is designed in consideration of transmission efficiency and low encoding and decoding operations in broadcasting and multicasting, in which a signal is transmitted to a large number on a network represented by a lost channel.

The key design element of the fountain code is the degree distribution, which determines the amount of encoding and decoding operations and decoding performance.

The LT code has a low complexity and is a representative channel loss error correcting code that can recover all information using a number of code symbols that are similar or slightly larger than the number of messages. The LT code is a code using Robust Soliton Distribution (RSD), and only a small amount of (1 + ε) k and ε are very small positive numbers are required to recover k message symbols.

However, when information is to be transmitted by multiple transmitters, RSD, an optimal order distribution method used in the existing LT code, does not guarantee optimal performance.

The LT code used to transmit information from multiple senders to a single receiver is defined as a distributed LT code. To date, many studies have been conducted for the design of distributed LT codes.

For example, M. Luby's "LT Codes" proposes the LT code, describes the coding and decoding processes in the binary loss channel, and describes the optimal RSD distribution. In addition, in "Analysis of random processes via and-or tree evaluation" by M. Luby, M. Mitzenmacher and A. Shokrollahi, a bipartite graph structure, which is a decoded graph of LT codes using an AND-OR tree, is used. It provides an analysis method that can calculate the recovery probability of the message symbol in asymptotic way (asymptotic). Meanwhile, S. Puducheri, J. Kliewer and T. Fuja's "The Design and Performance of Distributed LT Codes" defines the role of relays in a network of even senders, a single relay, and a single receiver, and accordingly deconvolution ( order distribution method through deconvolution. In addition, A. Liau, S. Yousefi, and I. M Kim's "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, and accordingly The performance of the designed order distribution is superior to that of the Distributed Luby Transform (DLT). Also, in D. Sejdinovic, R. Piechocki, A. Doufexi and M. Ismail, "Decentralized distributed fountain coding: asymptotic analysis and design" defines a generalized LT code that multiple senders can consider when passing information to a single receiver. Performance evaluation, and in some cases it is possible to design directly. In addition, M. Zeng, R. Calderbank and Suguang Cui's "On Design of Rateless Codes over Dying Binary Erasure Channel" assumes that the reception overhead of rate code is a certain random variable and the channel loss rate is a fixed constant. We propose a design method of order distribution that maximizes the average symbol reconstruction probability in the environment of randomly disconnected channels. The proposed scheme includes AND-OR tree analysis and sequential quadratic programming (SQP) algorithm.

However, the conventional LT code design methods described above are methods considering only the case where each transmitter transmits independently without information shared among multiple transmitters.

Therefore, there is a disadvantage that optimal performance cannot be achieved in a practical environment in which some information is shared among a plurality of senders.

SUMMARY OF THE INVENTION An object of the present invention for solving the above problems is to provide an order distribution optimization method of a distributed LT code that can obtain an optimal order distribution in all practical environments including an environment in which information is shared between a plurality of senders. will be.

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

In order to achieve the above object of the present invention, a method for optimizing the distribution of distributed LT codes according to an aspect of the present invention is a method for optimizing the distribution of orders of LT code performed by a transmitter, and a message common to a plurality of transmitters. Dividing the entire message including portions into a plurality of classes, calculating a symbol error probability for each classified class, and obtaining an order distribution that minimizes the symbol error probability based on the calculated symbol error probability It includes a step.

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

Here, the messages included in each of the plurality of classes may be asymmetrically selected for each class by the selection coefficient.

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

Here, the calculating of the symbol error probability for each classified class may be performed repeatedly, and the symbol error probability and l + obtained in the process of calculating the symbol error probability of the l (where l is a natural number of 2 or more) If the difference in the symbol error probability obtained during the first symbol error probability calculation is less than a preset threshold, the symbol error probability obtained in the lth symbol error probability calculation is set as the convergence value of the symbol error probability for each class. Can be.

Here, in calculating the symbol error probability for each of the classified classes, the sum of the convergence values of the symbol error probabilities for the respective classes may be obtained to obtain a total symbol error probability.

In the obtaining of the order distribution capable of minimizing the symbol error probability, the order distribution and the selection coefficient for minimizing the overall symbol error probability may be obtained using sequential binary programming.

The order distribution optimization method of a distributed LT code according to the present invention provides a method of designing an order distribution capable of minimizing a symbol error probability in a distributed LT coding system which is intended to transmit a message partially shared among multiple transmitters. Therefore, it is possible to maximize the symbol recovery probability in a distributed LT code system including a shared message among multiple senders.

In addition, we can define optimization problems 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, it is possible to design the LT code for maximizing the recovery performance of the specific message as well as the recovery performance for all messages received at the receiving end.

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

2 illustrates a decode graph considered in the method of order distribution optimization of distributed LT codes according to an embodiment of the present invention.

3 illustrates 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.

As the present invention allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the written description.

However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination 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. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

Hereinafter, with reference to the accompanying drawings, it will be described in detail a preferred embodiment of the present invention. In the following description of the present invention, the same reference numerals are used for the same elements in the drawings and redundant descriptions of the same elements will be omitted.

The LT code is a representative channel loss error correcting code widely used in the application layer. The code rate of the LT code is undefined and theoretically can generate an infinite number of code symbols.

When the transmitter determines the order by a given degree distribution, the transmitter generates a code symbol by performing an XOR operation on randomly selected message symbols by the number of orders. The receiver recovers the received code symbols using a message passing (MP) algorithm. Here, the success rate of restoration of the message is determined by the number of received code symbols. The ratio of the number of received code symbols to the number of messages is defined as reception overhead.

In case of LT code using RSD, it has the capability of minimizing the reception overhead required to recover all messages. In this case, 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.

LT codes are widely used in applications such as multimedia streaming because they can decode all messages with low complexity and low overhead. However, when multiple senders want to send a message to a single receiver at the same time, optimal performance cannot be guaranteed when multiple senders each use RSD. Therefore, a new order distribution considering multiple senders is needed.

Much research has been done on distributed LT codes to convey information from multiple senders, and the beginning was to define relay protocols and design the order distribution through deconvolution. Since then, we have tried to improve the performance of distributed LT codes and reduce the limitations in various situations. However, these studies have been conducted under the assumption that the messages of each transmitter are independent and have the same length, and there is a problem in that a proper solution cannot be provided for the case where a message is shared between senders. In addition, among the studies related to the conventional distributed LT codes, a linear programming based optimization method has been conducted in some limited situations by defining generalized distributed LT codes and performing theoretical performance analysis. However, this method also does not present a way to design the optimal order distribution in all possible situations. Therefore, a new optimization technique for generalized distributed LT code is needed.

In the order distribution optimization method of distributed LT codes according to an embodiment of the present invention, an optimization problem based on sequential quadratic programming is defined through theoretical performance analysis of generalized distributed LT codes, and a method of designing order distribution of LT codes is disclosed. To provide.

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

Referring to FIG. 1, the method of optimizing order distribution of distributed LT codes according to an embodiment of the present invention may be applied to a communication environment in which a plurality of senders 101 to 106 transmit a message to a single receiver 110. Here, the plurality of senders 101 to 106 transmit a message including a portion common to each other to a single receiver 110.

In FIG. 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 transmitters 101 to 106. In addition, N _s means the number of senders.

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

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

If there are messages that are shared in common between the senders 101 to 106, if multiple shared messages participate in the encoding process, the possibility of equal recovery of all messages is prevented.

Thus, by dividing the entire message into classes

It is defined as Here, A _j means the j th class, N _m means the number of classes.

The number of messages in each class

(here,

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

Is chosen asymmetrically by.

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. No selection factor was found.

In other words, in D. Sejdinovic, R. Piechocki, A. Doufexi and M. Ismail's "Decentralized distributed fountain coding: asymptotic analysis and design", linearity is based on theoretical performance in an environment where multiple senders send messages to a single receiver. Considering the programming-based optimization technique, the order distribution can be obtained only in a unique environment where all senders have the same message length and there is only one class of shared messages between senders. Therefore, when the message length of the sender considered in the present invention is different or when there are two or more common message classes, the linear programming based optimization method disclosed in the above study cannot be applied.

In the LT distribution order distribution optimization method according to an embodiment of the present invention, based on the theoretical performance analysis of each message class, an optimization scheme as shown in Equation 1 is applied to transmit a message in which a plurality of senders own a common part. It is possible to design the optimal LT code for all cases including

In Equation 1,

Is the lowest attainable symbol error probability and is calculated based on the theoretical performance analysis as shown in Equation 2.

Denotes a polynomial for generating an order distribution, and d _max denotes the maximum order.

That is, Equation 1 may be defined as a linear combination of error probabilities y _j for each class as shown in Equation 2. Here, y _j represents the numerically calculated error probability of the j-th class A _j and is theoretically assuming that infinite number of repetitive decoding and infinite length messages are assumed.

Thus, the LT code design method shown in Equation 1 can be understood as the problem of finding the order distribution and the selection coefficient that minimize the theoretically achievable performance for all K message symbols.

On the other hand, as found in the previous studies dealing with AND-OR tree analysis, the error probability y _{j, l} for each theoretical class in the iterative decoding step of l (where l is a natural number of 2 or more) is a decreasing function for l. Therefore, in order to apply the results of the performance analysis to the present invention, it is necessary to be able to calculate a convergence value of y _{j, l} . In the embodiment of the present invention, when the theoretical performance shows a difference smaller than the predetermined threshold y _Th preset in the convergence process, the optimization problem is defined to be regarded as a convergence value of error probability for each class.

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

In addition, the present invention solves the optimization problem defined in Equation 1 by using sequential quadratic programming (SQP).

Accordingly, the LT code designer for optimizing the order distribution of LT codes according to an embodiment of the present invention distributes message symbols.

Is taken as the optimal order distribution and selection coefficient

Will print

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

In FIG. 3, when the number of senders is 2 (that is, N _s = 2), the input variable

Shows the result of obtaining the selection coefficient and the order distribution for.

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 a transmitting device) in the communication environment as shown in FIG.

Referring to FIG. 4, first, a sender divides a message including a part shared among senders into N _m classes, and calculates a symbol error probability y _{j, l} of each classified class (S401). Here, the symbol error probability for the N _m classes can be theoretically calculated using the AND-OR tree analysis. In addition, in order to obtain a convergence value of the symbol error probability y _{j, l} of each class, the symbol error probability calculation process is repeated until y _{j, l} has a difference value smaller than a predetermined specific threshold y _Th .

That is, the sender calculates the symbol error probability y _{j, l} of each class in step S401, and then increases l by 1 (S402). The difference of the symbol error probability calculated in the step is calculated, and the calculated difference value is compared with a preset threshold y _Th (S403).

When the calculated difference value is smaller than the preset threshold y _{Th, the} sender sets the symbol error probability obtained in the first step as a convergence value of the symbol error probability, and adds the symbol error probability obtained for each class to add the entire symbol. An error probability y _total is obtained (S404).

The sender then uses an ordered binary programming (SQP) order distribution to minimize the _total symbol error probability y _total .

And selection coefficient

An optimization value is obtained (S405).

Although described with reference to the embodiments above, those skilled in the art will understand that the present invention can be variously modified and changed without departing from the spirit and scope of the invention as set forth in the claims below. Could be.

Claims

In the order distribution optimization method of the LT code performed in the transmitting device,

Dividing an entire message including a message part common to each other among a plurality of transmitters into a plurality of classes;

Calculating a symbol error probability for each classified class; And

And obtaining an order distribution capable of minimizing the symbol error probability based on the calculated symbol error probability.
The method according to claim 1,

And 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 message symbols set in each class.
The method according to claim 1,

And a message included in each of the plurality of classes is asymmetrically selected for each class by a selection coefficient.
The method according to claim 1,

Computing the symbol error probability for each of the divided classes,

An order optimization method of an LT code, characterized in that it is calculated using an AND-OR tree analysis.
The method according to claim 1,

Computing the symbol error probability for each of the divided classes,

An order optimization method of an LT code, characterized in that it is performed repeatedly.
The method according to claim 5,

Computing the symbol error probability for each of the divided classes,

where l is a natural number equal to or greater than 2, where the difference between the symbol error probability obtained during the symbol error probability calculation and the symbol error probability obtained during the l + 1 symbol error probability calculation is less than the predetermined threshold, l And a symbol error probability obtained during the second symbol error probability calculation process as a convergence value of symbol error probabilities for each class.
The method according to claim 6,

Computing the symbol error probability for each of the divided classes,

And a sum of convergence values of symbol error probabilities for each class to obtain a total symbol error probability.
The method according to claim 7,

Acquiring an order distribution capable of minimizing the symbol error probability,

And an order distribution and selection coefficient for minimizing the overall symbol error probability using sequential binary programming.