KR101976315B1 - Method for constructing polar codes on binary symmetric channel and apparatus therefor - Google Patents

Abstract

Disclosed are a method of polar code design in a binary symmetric channel and an apparatus therefor. According to an embodiment of the present invention, a method of polar code design comprises the following steps: calculating an error rate of a polarized channel generated through channel merging and splitting using density evolution; and selecting an information transmission channel based on the calculated error rate of the polarized channel. The calculating step calculates a channel density of the polarized channel by applying at least one of a minimum value calculation and an addition calculation from a channel density of the binary symmetric channel, and can calculate the error rate of the polarized channel based on the calculated density of the polarized channel.

Description

Field of the Invention < RTI ID = 0.0 > [0001] < / RTI > The present invention relates to a method of designing polar marks in discrete symmetric channels,

Field of the Invention [0002] The present invention relates to a polar code designing technique, and more particularly, to a pole code designing method and apparatus that can improve reliability while reducing a calculation amount in a discrete symmetric channel.

The polarity sign is a code that has received much attention since it is known to achieve the Shannon capacity, the limit of information transmission efficiency, in a binary-input memoryless symmetric channel.

The design of the polarity code is achieved through a process of generating a virtual channel from a given physical channel through a polarization operation. In this case, there are two kinds of polarization operations, and it is possible to generate virtual channels different in length by N according to the application order of operations. Then, the error rate of the virtual channels is calculated and the polar code is designed by using k virtual channels with low error rates as information transmission channels. However, in order to design a polarity code in a channel other than a binary erasure channel, it is impossible to implement it because it requires an exponentially increasing operation and a memory complexity with respect to a code length.

Although a method of designing codes by an approximate method has been proposed, a high computation amount is still required for channels other than the Gaussian noise channel, and the performance of the design code deteriorates as the length of the code increases.

The discrete symmetric channel is a channel dealt with in theoretical and practical fields, along with a discrete cancellation channel, a Gaussian noise channel. In polar code design studies, efficient discrete symmetric channel design methods have important locations in common channels.

Therefore, there is a need for a method of designing a polar code capable of improving the reliability while reducing the amount of computation.

Embodiments of the present invention provide a polar code design method and apparatus capable of improving reliability while reducing the amount of computation in a discrete symmetric channel.

Specifically, the embodiments of the present invention can improve the reliability of the polar code design by approximating an operation used for density evolution with a minimum value operation and performing only a small number of operations and a small memory in a discrete symmetric channel, Lt; / RTI >

A method of designing a polar code according to an embodiment of the present invention includes: calculating error rates of polarized channels generated through channel merging and demultiplexing using density evolution; And selecting an information transmission channel based on the calculated error rate of the polarized channel.

Calculating the channel density of the polarized channel by applying at least one of a minimum value operation and an addition operation from the channel density of the discrete symmetric channel, The error rate of the polarized channel can be calculated.

The calculating step may calculate an error rate of the polarized channel by adding a probability value of a point having a log likelihood ratio to the calculated density of the polarized channel.

The calculating step may recursively calculate the distribution of the channel density of the polarized channel on the binary tree.

The error rate of the polarized channel may be calculated by applying a minimum value operation and an addition operation to a channel log likelihood ratio distribution when each channel of two child nodes is generated from a channel of an upper node.

The selecting may select a channel having a certain number of low error rates as the information transmission channel after aligning error rates of the calculated polarized channels.

An apparatus for designing a polar code according to an embodiment of the present invention includes an operation unit for calculating an error rate of a polarized channel generated through channel merging and demultiplexing using density evolution; And a selection unit for selecting an information transmission channel based on the calculated error rate of the polarized channel.

Wherein the operation unit calculates a channel density of the polarized channel by applying at least one of a minimum value operation and an addition operation from a channel density of a discrete symmetric channel, and calculates the polarized channel density based on the calculated density of the polarized channel. The error rate of the channel can be calculated.

The operation unit may calculate an error rate of the polarized channel by adding a probability value of a point having a logarithmic likelihood ratio to the calculated density of the polarized channel.

The operation unit may recursively calculate the distribution of channel densities of the polarized channels on the binary tree.

The operation unit may calculate the error rate of the polarized channel by applying a minimum value operation and an addition operation to the channel log likelihood ratio distribution, respectively, when generating channels of two child nodes from a channel of an upper node.

The selecting unit may sort the error rate of the calculated polarized channel and then select a channel having a certain number of error rates as the information transmission channel.

According to embodiments of the present invention, by approximating the operations used for density evolution in designing the polar sign by the minimum value operation, the reliability of the polar sign design can be improved with fewer operations in the discrete symmetric channel and less memory .

According to the embodiments of the present invention, it is possible to design the polar sign with a shorter time than before, and to reduce the size and cost of the device by requiring less memory when implementing a device using a polar sign.

In other words, the present invention simplifies the operation of density evolution to use only addition and minimum value operations, and thus, it is possible to design a polar sign with linear memory and computational complexity, unlike the conventional method requiring exponential memory and computational complexity.

The technology according to the present invention can be applied to all industries that require error correction codes such as 5G next generation mobile communication, object Internet, data center, semiconductor storage device, and the like.

FIG. 1 illustrates an example of a channel merging process.
FIG. 2 is a flowchart illustrating a method of designing a polar code according to an embodiment of the present invention.
FIG. 3 illustrates an example of a process of obtaining a polarized channel through a binary tree.
FIG. 4 shows an example of a log-likelihood probability distribution of a discrete symmetric channel with an error rate p.
FIG. 5 is a diagram illustrating an exemplary process for recursively obtaining a log-likelihood ratio probability distribution in a binary tree.
FIG. 6 shows a structure of a polar code designing apparatus according to an embodiment of the present invention.

Hereinafter, embodiments according to the present invention will be described in detail with reference to the accompanying drawings. However, the present invention is not limited to or limited by the embodiments. In addition, the same reference numerals shown in the drawings denote the same members.

Embodiments of the present invention are intended to improve the reliability of the polar code design by approximating the operations used for density evolution with a minimum value operation, with fewer operations in the discrete symmetric channel and less memory.

The present invention simplifies the operation of density evolution to use only addition and minimum value operations, and thus it is possible to design a polarity code with only linear memory and computational complexity, unlike existing systems requiring exponential memory and computational complexity.

The polarity code was found to achieve the channel capacity when the length of the code was infinitely increased with the error correcting code proposed by Arkan. The polarizations are designed based on the channel polarization phenomenon, and the channel polarization phenomenon occurs through two processes of channel merging and channel separation.

을 얻는 과정으로, 채널 병합은 다음과 같이 재귀적으로 진행된다. The channel merging is performed through N physical channels W through a channel having N input / output alphabets

The channel merging is recursively performed as follows.

를 생성한다.FIG. 1 illustrates an example of a channel merging process. As shown in FIG. 1,

.

과

사이에는 아래 <수학식 1>과 같은 관계가 성립된다.Channel I / O

and

The following relationship is established as shown in Equation (1) below.

[Equation 1]

If it is recursively repeated with respect to Equation (1), the length N can be generalized as Equation (2) below.

&Quot; (2) &quot;

는 크로네커 지수를 의미할 수 있다.here,

May refer to the Kronecker index.

을 통해 가상의 채널

를 생성하는 과정으로 아래 <수학식 3>과 같이 정의될 수 있다.The channel separation process includes

Through a virtual channel

And can be defined as Equation (3) below.

&Quot; (3) &quot;

는 물리적 채널로부터의 출력 값

과 이전에 복호된 메시지의 값

을 알고 있을 때

의 값을 추정하기 위해 사용한다. 상술한 두 과정을 합하여 재귀적으로 표현하면 아래 <수학식 4>와 같이 나타낼 수 있다.The virtual channel

Lt; RTI ID = 0.0 &gt; physical channel

And the value of the previously decrypted message

When you know

Is used to estimate the value of. The above two processes may be recursively expressed as Equation (4) below.

&Quot; (4) &quot;

의 오류율을 구하고 오류율이 낮은 미리 설정된 개수 예를 들어, k개의 채널을 찾는 과정을 통해 이루어진다.The design of the polarity code is given by using the recursive equation of Equation (4)

And finding a predetermined number of channels having a low error rate, for example, k channels.

의 지수적 복잡도를 요구하기 때문에 실용적으로 불가능하다.However, in order to store the channel's transition matrix and calculate the error rate

It is practically impossible because it requires an exponential complexity of.

In order to solve the problems of the present invention, the present invention will be described with reference to Figs. 2 to 6. Fig.

FIG. 2 is a flowchart illustrating a method of designing a polar code according to an embodiment of the present invention.

Referring to FIG. 2, the polar code designing method of the present invention includes calculating (S210) an error rate of a polarized channel generated through channel merging and separation using density evolution (S210) And selecting an information transmission channel based on the error rate (S220).

In step S210, a channel density of a virtual channel, that is, a polarized channel is obtained by applying a minimum value operation or an addition operation from the channel density of the discrete symmetric channel, and the error rate of the polarized channel is calculated based on the density of the polarized channel .

Here, in step S210, the channel density for all the polarized channels is obtained, and the error rate of the polarized channel can be calculated by adding the log likelihood ratio, for example, the probability values of the points having the negative log likelihood ratios.

In addition, the step S210 can recursively calculate the channel density distribution of the channel polarized on the binary tree. When generating the channel of the two child nodes from the channel of the upper node, the channel log likelihood ratio distribution is subjected to the minimum value calculation and addition The error rate of the polarized channel can be calculated by applying only the operation.

In step S220, an information transmission channel is selected by providing an index of a channel having an error rate lower than the reference error rate or a predetermined number of channels having a low error rate, as output values, in the error rate of the polarized channel calculated in step S210.

Here, in step S220, the information transmission channel can be selected by selecting the k smallest polarized channels after aligning the N error rates.

The present invention will now be described in detail with reference to FIGS. 3 to 5. FIG.

In order to solve this problem, the present invention uses a method of recursively tracking the channel density distribution on the binary tree as shown in FIG. 3, since it is impossible to obtain the channel error rate by obtaining the channel's transition matrix.

로 표현할 수 있으며, 다시

에 재귀식을 적용하여

이를

단계만큼 반복하여 최종적으로 잎사귀 노드(leaf node)에는 분극화된 채널

들이 생성될 수 있다.In this case, the root of the binary tree is the given discrete symmetric channel W and the two channels generated from W through the recursive equation are

Can be expressed as

By applying a recursive

This

And finally a leaf node is provided with a polarized channel

Lt; / RTI &gt;

를 계산한다.In the binary tree shown in FIG. 3, each node stores a probability distribution of log likelihood ratios. To calculate the probability distribution of channels, a log likelihood ratio

.

이 된다. 이를 확률 변수 D로 표현하면 도 4와 같이 나타낼 수 있다.If the error rate of the channel is p, the log-likelihood ratio distribution for y values 0 and 1 is

. This can be expressed as a random variable D as shown in FIG.

과

의 로그 우도비 확률변수

은 아래 <수학식 5>와 같은 밀도 진화식을 이용하여 계산할 수 있다.For example, given the log-likelihood ratio non-random variable D of the parent node,

and

Log-likelihood ratio random variable

Can be calculated using the density evolution equation as shown in Equation (5) below.

&Quot; (5) &quot;

와

는 D와 같은 분포를 따르는 서로 독립인 확률변수를 의미할 수 있다.here,

Wow

Can be a random variable that is independent of each other following a distribution such as D.

5, when the density evolution equation of Equation 5 is repeated on the binary tree, the probability distribution of the log likelihood ratio can be calculated for each node as shown in FIG. 5. FIG. 5 shows the log likelihood non- This is a recursive process.

의 등간격으로 분포하기 때문에 덧셈과 최소값 연산으로 생성된 자식 노드들의 로그 우도비 또한 같은 간격으로 분포할 수 있다. j 단계에서 로그 우도비 분포를 저장하기 위해서 M개의 메모리가 필요하다면 j+1 단계에서는 최대 (2M-1)의 메모리만 있으면 로그 우도비 분포를 저장할 수 있다. 이는 기존 방식을 이용했을 때 필요한 최대 메모리 량인

보다 획기적으로 줄어든 값이다.In this case, in the case of discrete symmetric channels,

The log likelihood ratios of child nodes generated by addition and minimum operation can also be distributed at the same interval. If M memories are needed to store the log-likelihood ratio distribution in j-th stage, the log-likelihood ratio distribution can be stored if there is only a maximum memory (2M-1) in j + 1step. This is the maximum amount of memory

This is a dramatically reduced value.

From the log likelihood ratio distribution of the finally polarized channel, the error rate of the channel can be calculated using Equation (6) below.

&Quot; (6) &quot;

After calculating errors for each of the polarized channels using Equation (6), k sets of indexes having a low error rate are output (or selected), and a channel corresponding to the index set thus outputted is selected as an information transmission channel, The design can be completed.

As described above, according to the method of the present invention, the error rate of a polarized channel generated through channel merging and separation is calculated, and an index of a channel having a low error rate is selected as an output value to select an information transmission channel. It is possible to design the polar sign with shortened time, and it is possible to reduce the size and cost of the device by requiring less memory when implementing the device using the polar sign.

That is, the method according to the embodiment of the present invention approximates the operation used for density evolution in the design of the polar sign by the minimum value operation, thereby achieving the reliability of the polar sign design with fewer operations in the discrete symmetric channel and less memory Can be improved.

Also, the method according to the embodiment of the present invention simplifies the operation of the density evolution to use only the addition and the minimum value operation, thereby designing the polar sign with linear memory and computational complexity unlike the conventional method requiring the exponential memory and the computational complexity .

Also, the method according to an embodiment of the present invention recursively calculates the probability distribution of the log likelihood ratios of channels in a binary tree using density evolution, and can design the polar codes using the recursive calculation.

In the present invention, given a channel error rate p, a log likelihood ratio for channel outputs 0 and 1 is obtained, and each probability distribution is obtained and stored in a memory. tree.

이므로 최종적으로 하나의 가상 채널의 오류를 구하는 장치를 위해서

개의 메모리만 있으면 된다.Here, a root node is a given discrete symmetric channel, and a leaf node can be represented by N virtual channels. When a channel of two child nodes is generated from a channel of an upper node, a minimum value operation and an addition operation are applied to the channel log likelihood ratio distribution, respectively. Since the log likelihood ratio is distributed equidistantly, it is sufficient to store only the information of the starting point and the interval length in the memory, and the probability distribution of the log likelihood ratio also doubles every time the child channel is generated. +1 memory is needed. The depth of the binary tree is

For the device that finally finds error of one virtual channel

All you need is memory.

FIG. 6 shows a structure of a polar code designing apparatus according to an embodiment of the present invention, and shows a structure of an apparatus for performing the methods of FIGS. 2 to 5 described above.

Referring to FIG. 6, an apparatus 600 according to an embodiment of the present invention includes an operation unit 610 and a selection unit 620.

The operation unit 610 calculates the error rate of the polarized channel generated through channel merging and demultiplexing using density evolution.

At this time, the operation unit 610 calculates the channel density of the virtual channel, that is, the polarized channel, by applying a minimum value operation or an addition operation from the channel density of the discrete symmetric channel, and performs polarization based on the density of the polarized channel The error rate of the channel can be calculated.

Further, the operation unit 610 may calculate the channel density for all the polarized channels, and then calculate the error rate of the polarized channel by adding the log likelihood ratio, for example, the probability values of the points having the negative logarithmic likelihood ratios.

The operation unit 610 can recursively calculate the distribution of the channel densities of the channels polarized on the binary tree. When generating the channels of the two child nodes from the channels of the ancestor nodes, The error rate of the polarized channel can be calculated by applying only the operation.

The selection unit 620 selects an information transmission channel based on the calculated error rate of the polarized channel.

In this case, the selection unit 620 selects an information transmission channel by providing an index for a channel having an error rate lower than the reference error rate or a predetermined number of channels having a low error rate, as an output value, from the calculated error rate of the polarized channel .

The selection unit 620 may select an information transmission channel by selecting the smallest number of polarized channels after arranging error rates of the polarized channels.

Although the description has been omitted in the pole code designing apparatus shown in Fig. 6, it will be understood by those skilled in the art that the pole designing apparatus according to the present invention can include all the contents described in Figs. 1 to 5 It is obvious.

The system or apparatus described above may be implemented as a hardware component, a software component, and / or a combination of hardware components and software components. For example, the systems, devices, and components described in the embodiments may be implemented in various forms such as, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array ), A programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For ease of understanding, the processing apparatus may be described as being used singly, but those skilled in the art will recognize that the processing apparatus may have a plurality of processing elements and / As shown in FIG. For example, the processing unit may comprise a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of the foregoing, and may be configured to configure the processing device to operate as desired or to process it collectively or collectively Device can be commanded. The software and / or data may be in the form of any type of machine, component, physical device, virtual equipment, computer storage media, or device , Or may be permanently or temporarily embodied in a transmitted signal wave. The software may be distributed over a networked computer system and stored or executed in a distributed manner. The software and data may be stored on one or more computer readable recording media.

The method according to embodiments may be implemented in the form of a program instruction that may be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

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. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI &gt; or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (12)

Calculating an error rate of a polarized channel generated through channel merging and demultiplexing using density evolution; And
Selecting an information transmission channel based on the calculated error rate of the polarized channel
Lt; / RTI &gt;
The step of calculating
Calculating a channel density of the polarized channel from a channel density of a discrete symmetric channel by approximating an operation used for the density evolution by a minimum value operation and calculating a channel density of the polarized channel based on the calculated channel density of the polarized channel, Calculates the error rate of the channel,
The step of calculating
Wherein a distribution of the channel density of the polarized channel is recursively calculated using a channel density of the discrete symmetric channel and a recursive equation defined on a binary tree having the discrete symmetric channel as a root.
delete delete delete delete The method according to claim 1,
The step of selecting
Arranging error rates of the calculated polarized channels, and selecting a certain number of channels having an error rate lower than a reference error rate as the information transmission channels.
An operation unit for calculating an error rate of a polarized channel generated through channel merging and demultiplexing using density evolution; And
And a selection unit for selecting an information transmission channel based on the calculated error rate of the polarized channel,
Lt; / RTI &gt;
The operation unit
Calculating a channel density of the polarized channel from a channel density of a discrete symmetric channel by approximating an operation used for the density evolution by a minimum value operation and calculating a channel density of the polarized channel based on the calculated channel density of the polarized channel, Calculates the error rate of the channel,
The operation unit
And a distribution of channel density of the polarized channel is recursively calculated using a channel density of the discrete symmetric channel and a recursive equation defined on a binary tree having the discrete symmetric channel as a root.
delete delete delete delete 8. The method of claim 7,
The selecting unit
And arranges a predetermined number of channels having an error rate lower than a reference error rate as the information transmission channel after arranging error rates of the calculated polarized channels.

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