KR102535853B1 - Apparatus and method for low-complexity ldpc decoding for ofdm index modulation - Google Patents

Abstract

Disclosed is a low-complexity LDPC decoding apparatus and method for OFDM index modulation, and a low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present invention is an OFDM to which low density parity check coding is applied. - Obtaining a received signal corresponding to the IM-based transmission signal, calculating a first posterior probability for an index bit for selecting an activation pattern of a subcarrier based on the received signal, and activating the activation pattern based on the received signal and calculating a second posterior probability for data bits for selecting a QAM symbol transmitted by a subcarrier.

Description

Low-complexity LDPC decoding apparatus and method for OFDM index modulation

The present application relates to a low complexity LDPC decoding apparatus and method for OFDM index modulation.

Index Modulation (IM) is a promising technology for 5G and beyond wireless networks that can use the index of active resources to achieve additional data rates. Here, the resource can be any transmitting entity including transmit antenna, subcarrier, modulation type, precoder, time slot and channel condition. Regarding this index modulation (IM), it has been merged with an orthogonal frequency division multiplexing (OFDM) system to design a subcarrier IM method (SIM), and this technique is named OFDM-IM (Orthogonal Frequency Division Multiplexing Index Modulation). It became.

That is, OFDM-IM can increase spectral efficiency by delivering information bits through the index of active subcarriers in addition to those transmitted by data symbols. It has been proposed to apply Low Density Parity Check (LDPC) coding.

On the other hand, the low density parity check (LDPC) code can be applied to an OFDM-IM based in-vehicle power line communication system or to an MM-OFDM-IM system. However, although the formula for calculating the posterior probability can be applied to all subblock sizes and modulation orders, it is difficult to calculate the posterior probability and apply it to decoding due to the enormous computational complexity in the case of practically small subblock sizes and low modulation orders. was limited to Accordingly, it is required to develop a more efficient LDPC decoding approach for OFDM-IM that has low computational complexity and does not cause performance loss.

The background technology of the present application is disclosed in Korean Patent Registration No. 10-2231278.

The present invention is intended to solve the above-mentioned problems of the prior art, and implements complexity of LDPC decoding without performance loss by deriving the posterior probability of low density parity check (LDPC) coded bits for an Orthogonal Frequency Division Multiplexing Index Modulation (OFDM-IM) system. An object of the present invention is to provide a low-complexity LDPC decoding apparatus and method for OFDM index modulation capable of reducing .

However, the technical problem to be achieved by the embodiments of the present application is not limited to the technical problems described above, and other technical problems may exist.

As a technical means for achieving the above technical problem, a low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present invention is OFDM-IM-based transmission with Low Density Parity Check coding applied Obtaining a received signal corresponding to the signal, calculating a first posterior probability for an index bit for selecting an activation pattern of a subcarrier based on the received signal, and transmitting by an active subcarrier based on the received signal and calculating a second posterior probability for data bits for selecting a QAM symbol.

In the calculating of the first posterior probability, the first posterior probability may be calculated based on a predefined first log likelihood ratio function with respect to the index bit.

In the calculating of the second posterior probability, the second posterior probability may be calculated based on a predefined second log likelihood ratio function for the data bits.

Also, the received signal may be divided into a plurality of subblocks.

Also, the first log-likelihood ratio function and the second log-likelihood ratio function may be individually calculated corresponding to each of a plurality of subcarriers included in each of the plurality of subblocks.

In addition, the first log likelihood ratio function is a minimum value of a reference function calculated based on activation patterns matched with a sequence in which the target index bit for calculating the first posterior probability is 0 among a plurality of activation patterns and the plurality of It may be calculated based on a difference between minimum values of the reference function calculated based on activation patterns matched with a sequence in which the target index bit is 1 among activation patterns.

In addition, the first log ratio likelihood function may be defined by Equation 1 below.

In addition, the second log ratio likelihood function may be defined by Equation 2 below.

In addition, the low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present invention may include decoding the received signal based on the first posterior probability and the second posterior probability.

On the other hand, in the low complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present application, a receiving unit for obtaining a received signal corresponding to an OFDM-IM based transmission signal to which low density parity check coding is applied , a first operation unit for calculating a first posterior probability for an index bit for selecting an activation pattern of a subcarrier based on the received signal, and a data bit for selecting a QAM symbol transmitted by an active subcarrier based on the received signal It may include a second calculator for calculating a second posterior probability for .

Also, the first operator may calculate the first posterior probability based on a predefined first log-likelihood ratio function with respect to the index bit.

Also, the second operator may calculate the second posterior probability based on a predefined second log-likelihood ratio function for the data bits.

In addition, the low-complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present invention may include a decoding unit that decodes the received signal based on the first posterior probability and the second posterior probability.

The above-described problem solving means are merely exemplary and should not be construed as intended to limit the present disclosure. In addition to the exemplary embodiments described above, additional embodiments may exist in the drawings and detailed description of the invention.

According to the above-described problem solving means of the present application, the posterior probability of low density parity check (LDPC) coded bits is derived for an Orthogonal Frequency Division Multiplexing Index Modulation (OFDM-IM) system to reduce the implementation complexity of LDPC decoding without performance loss A low-complexity LDPC decoding apparatus and method for OFDM index modulation can be provided.

According to the above-described problem solving means of the present application, by modularizing the part for obtaining the posterior probability at the receiving end of the OFDM-IM system, scalability for various types of decoders that take the posterior probability associated with OFDM-IM as an input This can drastically reduce the complexity of the decoder.

According to the above-described means for solving the problems of the present application, it is possible to reduce the cost of constructing a system applying the LDPC code by reducing the implementation complexity of the LDPC decoder without deteriorating performance.

However, the effects obtainable herein are not limited to the effects described above, and other effects may exist.

1 is a diagram showing the structure of a transmitter applying an LDPC code to an OFDM-IM system by way of example.
2 is a conceptual diagram illustrating a low-complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present invention.
3 is a schematic configuration diagram of a low complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present invention.
4 shows the complexity of the conventional posterior probability calculation technique and the low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present application when an LDPC code is applied to OFDM-IM by reducing the number of CM (Complex Multiplication) This is a chart showing the results of the comparison.
5 is a graph showing a comparison of the complexity of a conventional a posteriori probability calculation technique and a low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present application based on DCRR when an LDPC code is applied to OFDM-IM. am.
6a and 6b show BER performance of a conventional a posteriori probability calculation technique, a low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present invention, and a conventional approach when an LDPC code is applied to OFDM-IM. It is a graph showing the evaluation of the LDPC-coded OFDM-IM system with a code rate of 0.5.
7 is an operation flowchart of a low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present invention.

Hereinafter, embodiments of the present application will be described in detail so that those skilled in the art can easily practice with reference to the accompanying drawings. However, the present disclosure may be implemented in many different forms and is not limited to the embodiments described herein. And in order to clearly describe the present application in the drawings, parts irrelevant to the description are omitted, and similar reference numerals are attached to similar parts throughout the specification.

Throughout the present specification, when a part is said to be “connected” to another part, it is not only “directly connected”, but also “electrically connected” or “indirectly connected” with another element in between. "Including cases where

Throughout the present specification, when a member is referred to as being “on,” “above,” “on top of,” “below,” “below,” or “below” another member, this means that a member is located in relation to another member. This includes not only the case of contact but also the case of another member between the two members.

Throughout the present specification, when a certain component is said to "include", it means that it may further include other components without excluding other components unless otherwise stated.

The present application relates to a low complexity LDPC decoding apparatus and method for OFDM index modulation.

The low-complexity LDPC decoding apparatus 100 for OFDM index modulation according to an embodiment of the present application (hereinafter referred to as 'decoding apparatus 100') converts the posterior probability of low density parity check (LDPC) coding bits to OFDM- This is to reduce the implementation complexity of LDPC decoding without performance loss by inducing the IM (Orthogonal Frequency Division Multiplexing Index Modulation) system. LDPC decoding by decomposing the posterior probability of coded bits into a plurality of possible probabilities It is characterized in that the complexity of is reduced, and at this time, each decomposed possibility probability can be obtained for each subcarrier in the corresponding OFDM-IM subblock.

1 is a diagram showing the structure of a transmitter applying an LDPC code to an OFDM-IM system by way of example.

정보 비트들로 구성되는 메시지

이 OFDM 색인 변조 시스템의 송신부(200)에 의해 LDPC 인코딩 되어,

비트들로 구성된

코드워드가 생성될 수 있다. 이 때 코드율은

이이며, LDPC 인코딩은 하기 식 1과 같이 표현될 수 있다.Referring to Figure 1,

A message made up of bits of information

LDPC-encoded by the transmitter 200 of this OFDM index modulation system,

made of bits

Codewords can be generated. In this case, the code rate is

In this case, LDPC encoding can be expressed as Equation 1 below.

[Equation 1]

는

크기를 갖는 코드 생성 행렬로서, sparse한 행렬인

에 대하여, systematic LDPC generator matrix

를 생성할 수 있다. 이와 관련하여, OFDM-IM 시스템의 수신단(수신기) 측인 디코딩 장치(100)에서는 추정한 코드워드

에 대한 검증을

임을 확인함으로써 수행할 수 있다. 또한,

를 인터리빙(interleaving)하여

를 얻을 수 있으며,

를

개 서브벡터로 나누어 하기 식 2와 같이 표현할 수 있다.here,

Is

A code generation matrix with size, which is a sparse matrix

For , systematic LDPC generator matrix

can create In this regard, the codeword estimated by the decoding apparatus 100, which is the receiving end (receiver) of the OFDM-IM system.

verification for

This can be done by confirming that also,

by interleaving

can be obtained,

cast

It can be divided into two subvectors and expressed as in Equation 2 below.

[Equation 2]

의 길이를 갖게 되며,

개의 비트들 중 앞쪽

개의 비트들은 인덱스 비트(index selecting bits, ISBs)로 지칭될 수 있으며, 이러한 복수의 인덱스 비트는 부반송파 활성화 패턴(subcarrier activation pattern, SAP)을 선택하는데 사용되는 비트일 수 있다.where each subvector is

will have the length of

the front of the bit

N bits may be referred to as index selecting bits (ISBs), and the plurality of index bits may be bits used to select a subcarrier activation pattern (SAP).

개의 비트들을 포함하는 인덱스로 이루어진 시퀀스는 ISB 시퀀스(11)로 지칭될 수 있으며, 각각의 ISB 시퀀스(11)에 대하여 매핑되는 부반송파 활성화 패턴의 시퀀스는 SAP 시퀀스(12)로 지칭될 수 있다.On the other hand, in the description of the embodiment of the present application

A sequence consisting of an index including N bits may be referred to as an ISB sequence 11, and a sequence of subcarrier activation patterns mapped to each ISB sequence 11 may be referred to as a SAP sequence 12.

개의 비트들 중 나머지

개의 비트들은 데이트 비트(symbol selecting bits)로 지칭될 수 있으며, 이러한 복수의 데이터 비트는

개의 활성 부반송파 상으로 전송되는

개의 M-ary QAM 심볼들을 선택하는데 사용되는 비트일 수 있다.also,

remainder of bits

The number of bits may be referred to as data bits (symbol selecting bits), and these plurality of data bits are

transmitted on active subcarriers.

It may be a bit used to select M-ary QAM symbols.

개의 1과

개의 0으로 나타낼 수 있으며, 1과 0은 각각 활성 부반송파와 불활성 부반송파를 나타낸다. 이에 따라, 가능한 모든 SAP 시퀀스(12)의 후보들은 모두

개가 존재할 수 있는데, 여기서

는

개 요소로 된 집합에서 선택하는

개 소소들에 대한 경우의 수를 나타낸다.On the other hand, one SAP sequence 12

department 1 of the dog

It can be represented by number of 0s, and 1 and 0 represent active subcarriers and inactive subcarriers, respectively. Accordingly, all candidates of all possible SAP sequences 12 are

Dogs may exist, where

Is

to choose from a set of elements

Indicates the number of cases for each location.

로 선택함으로써 주파수 효율을 극대화할 수 있다. 한편, 만일

일 경우, ISB 시퀀스(11)와 SAP 시퀀스(12)의 일대일 매핑을 위해서,

개의 가능한 SAP 시퀀스들 중에서

를 선택해 사용해야 한다. 이해를 돕기 위해 예시하면, ISB 시퀀스(11)와 SAP 시퀀스(12)의 일대일 매핑 방법으로서 combinational mapping 등이 활용될 수 있으나, 이에만 한정되는 것은 아니다.In addition, since each ISB sequence 11 corresponds to one separate SAP sequence 12, the number of index bits (p ₁ )

By selecting , the frequency efficiency can be maximized. On the other hand, if

In one case, for one-to-one mapping of the ISB sequence 11 and the SAP sequence 12,

out of the possible SAP sequences.

should be selected and used. For better understanding, combinational mapping may be used as a one-to-one mapping method of the ISB sequence 11 and the SAP sequence 12, but is not limited thereto.

번째 SAP 시퀀스(12)는

와 같이 표현될 수 있으며, 여기서,

에 대해

라 가정할 수 있다.At this time,

The second SAP sequence (12) is

It can be expressed as, where,

About

can be assumed

번째 SAP 시퀀스(12)의

개 활성 부반송파 인덱스들은 하기 식 3과 같이 정의될 수 있다.also,

of the th SAP sequence (12)

The active subcarrier indices may be defined as in Equation 3 below.

[Equation 3]

이며,

는

가 자연수 일 때

로 주어지는 집합을 의미하며, 전술한 combinational mapping에 의해,

이

에 순서대로 매핑됨으로써 송신 신호(1)인 OFDM블록은 하기 식 4와 같이 정의될 수 있다.here

is,

Is

when is a natural number

It means a set given by , and by the above-described combinational mapping,

this

The OFDM block, which is the transmission signal 1, can be defined as shown in Equation 4 below.

[Equation 4]

는 송신 신호(1)의

번째 서브블록을 나타내며, 이는 다시 하기 식 5로 표현될 수 있다.here,

is the transmission signal (1)

th subblock, which can be expressed by Equation 5 below.

[Equation 5]

는

번째 서브블록의

번째 심볼을 의미한다. here

Is

of the second subblock

means the second symbol.

, 1) 는 하기 식 6과 같이 뒤섞인 블록

를 생성한다.In addition, a transmission signal (which is an OFDM block) by a subcarrier level interleaver

, 1) is a scrambled block as shown in Equation 6 below

generate

[Equation 6]

2 is a conceptual diagram illustrating a low complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present invention, and FIG. 3 is a schematic diagram of a low complexity LDPC decoding apparatus for OFDM index modulation according to an embodiment of the present invention. It is a composition diagram.

Referring to FIGS. 2 and 3 , the decoding device 100 may include a receiving unit 110 , a posterior probability calculating unit 120 and a decoding unit 130 . In addition, referring to FIG. 3 , the posterior probability calculator 120 includes a first calculator 121 for deriving (calculating) a posterior probability for the index bit (b _i ) and the data bit (d _{i )} as will be described in detail below. ) may include a second operator 122 that derives (calculates) the posterior probability.

Referring to FIGS. 2 and 3, in the transmission unit 200 of the OFDM index modulation system, a block corresponding to the transmission signal 1 is IFFTed and a Cyclic Prefix is attached, and then the receiver 110 of the decoding device 100 from the transmitter antenna can propagate to the receiving side antenna of

번째 서브블록에 대하여 하기 식 7과 같은 수신 결과를 얻는다.In this regard, when the receiving unit 110 of the decoding apparatus 100 performs FFT on the received signal 2 from which the Cyclic Prefix has been removed, and then performs deinterleaving at the subcarrier level,

For the th subblock, the reception result shown in Equation 7 below is obtained.

[Equation 7]

는 주파수 도메인 채널 벡터를 의미하고,

는 잡음 벡터를 의미한다.here,

denotes a frequency domain channel vector,

denotes a noise vector.

는 평균이 0이고 분산이

인 가우시안 잡음을 의미한다. Signal-to-Noise ratio (SNR)은

로 주어지는데, 여기서

는 비트 당 평균 에너지를 의미한다.also,

has a mean of 0 and a variance of

means in Gaussian noise. Signal-to-Noise ratio (SNR) is

is given, where

is the average energy per beat.

를 획득할 수 있다.That is, the receiving unit 110 receives a received signal 2 corresponding to an OFDM-IM based transmission signal 1 to which low density parity check coding is applied.

can be obtained.

를 M-ary QAM 상의 모든 심볼들을 포함하는 집합이라 가정하면,

가

번째 SAP 시퀀스에 따라 형성되었다면,

는

일 경우

에 속하는 한 심볼이 될 것이고,

일 경우 0이 될 수 있고, 이 때

를 하기 식 8과 같이 표시할 수 있다. Meanwhile,

Assuming that is a set containing all symbols on M-ary QAM,

go

If it is formed according to the second SAP sequence,

Is

case

will be a symbol belonging to

In case of 1, it can be 0, in which case

can be expressed as in Equation 8 below.

[Equation 8]

일 수 있다.here,

can be

In addition, referring to FIG. 2, the decoding apparatus 100 disclosed herein separates the posterior probability estimator block corresponding to the posterior probability operator 120 from the LDPC decoder block corresponding to the decoding unit 130 inside the LDPC decoder block. By doing so, it can be understood as modularizing the entire LDPC decoding process.

In addition, due to the modular structure of the decoding device 100, the LDPC decoder block corresponding to the decoding unit 130 of FIG. 2 uses the LDPC code to apply other codes than the LDPC code under the condition that the decoder takes the posterior probability as an input. The decoder block can be replaced with various decoder blocks.

및

정보를 사용해 인덱스 비트(b_i) 및 데이터 비트(d_i)를 포함하는 LDPC 코딩된 비트들에 대한 사후 확률(posterior probability)들이 계산될 수 있으며, 이렇게 사후 확률 연산부(120)에 의해 계산된 사후 확률(posterior probability)들은 수신 신호(2)의 모든 블록에 대해 취합된 후 디인터리빙(deinterleaving)이 적용될 수 있다. 또한, 복호화부(130)는 디인터리빙(deinterleaving)이 적용된 사후 확률(posterior probability) 정보를 활용해 예시적으로 sum-product decoding algorithm(SPA) 등의 알고리즘을 기초로 하여 LDPC 코딩된 비트 벡터

를 추정할 수 있다.On the other hand, in the posterior probability calculator 120 in the LDPC decoder block

and

Posterior probabilities for LDPC-coded bits including the index bit (b _i ) and the data bit (d _i ) may be calculated using the information, and the posterior probabilities calculated by the posterior probability calculator 120 in this way may be calculated. After the posterior probabilities are aggregated for all blocks of the received signal 2, deinterleaving may be applied. In addition, the decoder 130 utilizes posterior probability information to which deinterleaving is applied, illustratively based on an algorithm such as a sum-product decoding algorithm (SPA) to generate an LDPC-coded bit vector

can be estimated.

를 반복적으로 수정하는 디코딩 루프를 수행하며, 디코딩 루프는

라는 조건이 만족되면 종료되어 상기 조건을 만족하는

가 LDPC 코딩된 비트 벡터로 추정된다. 만약 일정 회수의 디코딩 루프가 수행된 이후에도

조건이 만족되지 않으면 디코딩 실패(decoding failure)가 선언되고 이터레이션(iteration)과정은 종결된다.Here, the aforementioned SPA is temporarily determined

Performs a decoding loop that iteratively modifies , and the decoding loop is

When the condition is satisfied, it terminates and satisfies the condition

is estimated as an LDPC coded bit vector. Even after a certain number of decoding loops are performed,

If the condition is not satisfied, decoding failure is declared and the iteration process is terminated.

의 조건이 만족되는 경우, 디코딩 장치(100)로 전송된 메시지는 하기 식 9와 같이 주어질 수 있다.on the other way,

When the condition of is satisfied, the message transmitted to the decoding device 100 may be given as in Equation 9 below.

[Equation 9]

로부터 메시지

를 얻을 수 있는 이유는

가 systematic LDPC generator matrix이기 때문이다.On the other hand, like this

message from

why you can get

This is because is a systematic LDPC generator matrix.

Hereinafter, when LDPC codes are applied to an OFDM-IM system in contrast to the present invention, a conventional technique for obtaining a posterior probability for LDPC-coded bits at a receiving end and its limitations will be described.

When the LDPC code is applied to OFDM-IM, the core of the LDPC decoding block is the part for obtaining the posterior probability for the LDPC-coded binks. Since the symbols transmitted through IM have the effect of being bound together, in order to obtain the posterior probability of LDPC coded bits, all received signals within one subblock must be considered beforehand, and the posterior probability is specifically log likelihood ratio ( LLR) can be calculated as shown in Equation 10 below.

[Equation 10]

Therefore, in order to obtain the posterior probability of LDPC coded bits, the LLR must first be calculated. Conventional techniques calculate the LLR for the LDPC coded OFDM-IM index bits based on Equation 11 below, and based on Equation 12 below The LLR for the LDPC-coded OFDM-IM data bits was calculated with

[Equation 11]

[Equation 12]

However, the conventional operation method of calculating the LLR for the index bit and the data bit, which can be understood through Equations 11 and 12, considers all received signals in one subblock, and at the same time all possible SAP sequences. There is a disadvantage in that the implementation complexity becomes excessively large because the LLR must be calculated considering all possible M-ary QAM symbols.

In particular, the conventional technique causes a problem that the implementation complexity increases geometrically for a relatively large M-ary QAM order or a large subblock size, and in such cases, it is difficult to apply it practically due to implementation complexity and processing delay. cause problems Therefore, in order to reduce the implementation complexity of the entire LDPC decoding process, it is necessary to derive the posterior probability of LDPC coded bits as simply as possible in consideration of the binding effect of OFDM-IM, which is the decoding device 100 disclosed herein. This can be said to be the biggest difference between the calculation method and the conventional technique.

Hereinafter, when the LDPC code is applied to the OFDM-IM system performed by the decoding apparatus 100 disclosed herein, a specific method of inferring a posterior probability for LDPC coded bits at the receiving end will be described. let it do

The posterior probability calculator 120 may calculate a first posterior probability for the index bit (b _i ) of the received signal 2 and a second posterior probability for the data bit (d _i ) of the received signal 2 .

Specifically, the first operator 121 may calculate a first posterior probability for the index bit ( _bi ) for selecting an activation pattern of a subcarrier based on the received signal 2 . Also, the second operator 122 may calculate a second posterior probability for the data bit _di for selecting a QAM symbol transmitted by an active subcarrier based on the received signal 2 .

In addition, according to an embodiment of the present invention, the posterior probability calculator 120 decomposes the posterior probability of the encrypted bit in the received signal 2 into a plurality of probability probabilities to infer a first a posteriori probability and a second a posteriori probability. can do.

In particular, the posterior probability calculator 120 has a simplified LLR derivation formula that can more easily obtain the posterior probability for LDPC-coded bits compared to the conventional technique described above. In order to explain this, 4QAM will be described below as an example let it do However, the decoding apparatus 100 is not limited thereto and can be easily extended and applied to M-ary QAMs of various sizes.

First, a set of 4QAM symbols using gray mapping can be defined as shown in Equation 13 below.

[Equation 13]

개의

의 부분집합을 하기 식 14와 같이 정의할 수 있다.also

doggy

A subset of can be defined as in Equation 14 below.

[Equation 14]

이고,

이며,

이고,

는 한 M-ary 심볼을 통해 전송되는 데이터 비트수를 나타낸다. However, here

ego,

is,

ego,

represents the number of data bits transmitted through one M-ary symbol.

를

개의 활성 부반송파로 전송되는

개의

심볼들이라고 가정할 경우, 그러한 심볼들은 다음과 같이 결정된다고 가정할 수 있다(

).also,

cast

transmitted on active subcarriers.

doggy

Assuming that they are symbols, it can be assumed that such symbols are determined as follows (

).

이며, 만약

일 경우,

는

로 선택될 수 있는 모든 심볼들의 집합이라 해석할 수 있다. However, here

and if

In case of

Is

It can be interpreted as a set of all symbols that can be selected as

가 모든 SAP 시퀀스들 (즉,

) 의 집합이라고 가정하면,

가

에 대해

라는 조건을 만족하는 모든 SAP 시퀀스들의 집합이라고 가정한다.also,

is all SAP sequences (i.e.

) assuming that it is a set of

go

About

It is assumed that it is a set of all SAP sequences that satisfy the condition

Next, a process in which the first operator 121 calculates (infers) the first posterior probability for the index bit (bi ₎ will be described through a specific formula.

가 주어질 경우, 해당 서브 블록의 i번째 인덱스 비트(b_i)의

에 대한 사후 확률은 하기 식 15와 같이 정의할 수 있다.First, the βth subblock of the received signal (2)

When is given, the i th index bit (b _i ) of the corresponding subblock

The posterior probability for can be defined as in Equation 15 below.

[Equation 15]

를 하기 식 16과 같이 변형할 수 있다.In addition, according to Bayes' law, Equation 15

Can be transformed as shown in Equation 16 below.

[Equation 16]

이기 때문에

이고,

이고,

이므로, 상기 식 15는 하기 식 17과 같이 변형될 수 있다.here,

because it is

ego,

ego,

Therefore, Equation 15 may be modified as shown in Equation 17 below.

[Equation 17]

인 경우에 있어서,

가 주어질 때

의 요소들은 서로 독립이라 할 수 있으므로 상기 식 15는 하기 식 18과 같이 변형될 수 있다.also,

In case of

when given

Since the elements of can be said to be independent of each other, Equation 15 can be modified as shown in Equation 18 below.

[Equation 18]

인 경우에 있어서, 상기 식 18의

를 두 그룹으로 나눌 수 있으며, 첫 번째 그룹은

이고

인 경우,

가 주어질 때

에 대한 확률들의 집합이고, 두 번째 그룹은

이고

인 경우,

가 주어질 때

에 대한 확률들의 집합일 수 있다.In this regard,

In the case of Equation 18

can be divided into two groups, the first group is

ego

If

when given

is the set of probabilities for, and the second group is

ego

If

when given

It may be a set of probabilities for

를 하기 식 19와 같이 나눌 수 있다.Based on this grouping, Equation 18

can be divided as shown in Equation 19 below.

[Equation 19]

In other words, the first operation unit 121 selects a probability set corresponding to an active bit (ie, a bit corresponding to 1) among a plurality of bits constituting the SAP sequence 12 and an inactive bit among a plurality of bits constituting the SAP sequence 12 The process of calculating the first posterior probability can be simplified by dividing a probability set corresponding to (that is, a bit corresponding to 0) and calculating (independent operation).

는 베이스 법칙을 적용함에 따라 하기 식 20으로 도출될 수 있다.In addition, in Equation 19 above

Can be derived from Equation 20 below by applying Bayes' law.

[Equation 20]

이고

에 대해

이 성립함이 사용되었다.

이고

에 대해

와

이 주어진 경우

에 대한 이벤트는 하기 식 21과 같이 가우시안 분포를 따른다.In deriving Equation 20,

ego

About

This establishment was used.

ego

About

and

if given

Events for follow a Gaussian distribution as shown in Equation 21 below.

[Equation 21]

As a result, Equation 20 may be modified as shown in Equation 22 below.

[Equation 22]

일 경우

이라 할 수 있으므로

는 하기 식 23과 같이 도출될 수 있다.At this time,

case

so it can be

Can be derived as shown in Equation 23 below.

[Equation 23]

일 때

임을 이용하면, 하기 식 24가 도출될 수 있다.In addition, applying Bayes' law to Equation 23 above,

when

Using , Equation 24 below can be derived.

[Equation 24]

에 대해

와

이 주어진 경우

에 대한 이벤트는 하기 식 25와 같이 가우시안 분포를 따른다.also,

About

and

if given

Events for follow a Gaussian distribution as shown in Equation 25 below.

[Equation 25]

에 대해

이기 때문에 상기 식 25는 하기 식 26으로 도출될 수 있다.here,

About

Since Equation 25 can be derived as Equation 26 below.

[Equation 26]

In addition, when the result of Equation 26 is applied to Equation 24, the following Equation 27 can be obtained.

[Equation 27]

Accordingly, the first posterior probability can be derived as shown in Equation 28 below.

[Equation 28]

은

을 만족하는 정규화(normalization) 상수이고,

의 근사를 적용하면, 하기 식 29가 도출될 수 있다.here,

silver

is a normalization constant that satisfies

Applying the approximation of , the following Equation 29 can be derived.

[Equation 29]

에 대해 인덱스 비트(b_i)를 위한 제1로그 우도 비율 함수(LLR)가 하기 식 30과 같이 정의될 수 있다.Also, according to Equation 29 above

The first log likelihood ratio function (LLR) for the index bit (b _i ) may be defined as in Equation 30 below.

[Equation 30]

In conclusion, the LLR for the index bit is derived by Equation 31 below, and based on the LLR of Equation 31, the first posterior probability corresponding to the index bit can be finally derived as shown in Equation 32 below.

In other words, the first operator 121 calculates a first posterior probability based on a predefined first log-likelihood ratio function for index bits, and the first log-likelihood ratio function may be given based on Equation 31 below. . In this regard, in the description of the embodiments of the present application, Equation 31 below will be referred to as 'Equation 1' representing a first log likelihood ratio function for a first posterior probability operation.

[Equation 31] [Equation 1]

는 각각에 대응하는 복수 개의 활성화 패턴(달리 말해, SAP 시퀀스(12) 등) 각각을 나타내고,

는 대상 인덱스 비트가 0인 시퀀스와 매칭된 활성화 패턴들의 집합이고,

는 대상 인덱스 비트가 1인 시퀀스와 매칭된 활성화 패턴들의 집합이고,

은 각 부반송파를 나타내는 식별자이고,

는 각 QAM 심볼을 나타내는 식별자이고,

는 각 서브블록을 나타내는 식별자이고,

는 활성화 패턴의

번째 비트이고,

는 채널 벡터이고,

는 가우시안 잡음일 수 있다.In Equation 1 above,

Represents each of a plurality of activation patterns (in other words, SAP sequences 12, etc.) corresponding to each,

is a set of activation patterns matched with a sequence in which the target index bit is 0,

Is a set of activation patterns matched with a sequence in which the target index bit is 1,

is an identifier representing each subcarrier,

Is an identifier representing each QAM symbol,

is an identifier representing each subblock,

is the activation pattern

is the second bit,

is the channel vector,

may be Gaussian noise.

In addition, referring to Equation 1, the first operator 121 specifically means that a target index bit for calculating the first posterior probability among a plurality of activation patterns (that is, the SAP sequence 12) is 0. If the minimum value of the reference function calculated based on the activation patterns matched with the ISB sequence 11 (ie, satisfying b _i =0) and the target index bit among the plurality of activation patterns is 1 (ie, b _i =1) A first log-likelihood ratio function may be calculated based on the difference between the minimum values of the reference functions calculated based on the activation patterns matched with the ISB sequence 11 that satisfies .

텀을 의미하는 것일 수 있다. 한편, 이러한 기준 함수의 경우, M-ary QAM과 연계된 M개의 심볼 각각을 대입(달리 말해, 4 QAM의 경우 4개의 심볼만을 대입)하기만 하면 결과값이 도출될 수 있어 제1로그 우도 비율 함수의 전체적인 연산이 간략화될 수 있다.Here, the reference function is

It could mean a term. On the other hand, in the case of this reference function, the first log likelihood ratio can be obtained by simply substituting each of the M symbols associated with M-ary QAM (in other words, substituting only four symbols in the case of 4 QAM). The overall operation of the function can be simplified.

In addition, in the case of Equation 11 representing the log likelihood ratio function (LLR) according to the conventional technique described above, the parameters in the calculation formula are defined in a vector form and vector calculation between all SAP sequences and all M-ary QAM symbols that can be considered In contrast to the fact that the complexity is excessively high because it must be performed on the entire subblock, the first operation unit 121 of the decoding apparatus 100 disclosed in the present application, as can be seen in Equation 1 above, each of the subblocks It is individually calculated corresponding to each of a plurality of subcarriers included in, and the first log likelihood ratio function is derived based on the minimum value of the reference function sufficient by inputting only scalar-type parameters, so the complexity can be dramatically reduced compared to the conventional technique. .

[Equation 32]

Next, a process in which the second calculator 122 calculates (infers) the second posterior probability will be described.

가 주어질 경우, 해당 서브 블록의 i번째 데이터 비트(d_i)의

에 대한 사후 확률(제2사후 확률)은 하기 식 33으로 주어질 수 있다.βth subblock of received signal (2)

If is given, the i th data bit (d _i ) of the corresponding subblock

The posterior probability (second posterior probability) for can be given by Equation 33 below.

[Equation 33]

를 likelihood 확률인

의 함수로서 나타내면 하기 식 34가 도출될 수 있다.In addition, Bayes' law is applied to Equation 33 above, and the posterior probability

where is the likelihood probability

When expressed as a function of , the following Equation 34 can be derived.

[Equation 34]

이고

이므로, 하기 식 35가 도출될 수 있다.here,

ego

Therefore, the following Equation 35 can be derived.

[Equation 35]

와

가 주어질 때,

의 요소들은 서로 독립이기 때문에 하기 식 36이 도출될 수 있다.Also, here

and

When is given,

Since the elements of are independent of each other, the following Equation 36 can be derived.

[Equation 36]

와

가 주어질 때,

에 대한 이벤트는 하기 식 37과 같이 가우시안 분포를 따른다.also,

and

When is given,

Events for follow a Gaussian distribution as shown in Equation 37 below.

[Equation 37]

는 다음과 같이 정의된다.here,

is defined as

[Equation 38]

Accordingly, the following Equation 39 can be finally derived for the second posterior probability.

[Equation 39]

는

를 만족하는 상수로서, 제1사후 확률의 연산 과정에서와 마찬가지로, 데이터 비트에 대한 사후 확률(제2사후 확률)을 LLR을 정의함으로써 도출할 수 있으며, 데이터 비트에 대한 LLR은 하기 식 40과 같이 정의될 수 있다.here,

Is

As a constant that satisfies , as in the calculation process of the first posterior probability, the posterior probability (second posterior probability) for the data bit can be derived by defining the LLR, and the LLR for the data bit is as shown in Equation 40 below. can be defined

[Equation 40]

에 대한 LLR은 하기 식 41으로 도출될 수 있으며, 이에 따라 수신 신호

가 주어질 때의 데이터 비트

에 대한 제2사후 확률은 하기 식 42와 같이 LLR로부터 계산될 수 있다.Based on the above derivation results, the data bit

The LLR for can be derived by Equation 41 below, and thus the received signal

Data bits when given

The second posterior probability for can be calculated from the LLR as shown in Equation 42 below.

In other words, the second operator 122 calculates a second posterior probability based on a predefined second log likelihood ratio function for data bits, and the second log likelihood ratio function may be given based on Equation 41 below. . In this regard, in the description of the embodiments of the present application, Equation 41 below will be referred to as 'Equation 2' representing a second log likelihood ratio function for a second posterior probability operation.

[Equation 41] [Equation 2]

는 활성화 패턴에 포함되는 활성 부반송파(달리 말해, 값이 1인 부반송파)에 대한 인덱스(색인)일 수 있다.In Equation 2, p ₁ is the number of index bits (b _i ), D is the number of data bits (d _i ) included in each QAM symbol,

may be an index (index) for an active subcarrier (in other words, a subcarrier having a value of 1) included in the activation pattern.

[Equation 42]

In addition, in the case of Equation 12 representing the log likelihood ratio function (LLR) according to the conventional technique described above, the parameters in the calculation formula are defined in a vector form and vector calculation between all SAP sequences and all M-ary QAM symbols that can be considered In contrast to the fact that the complexity is excessively high because it must be performed on the entire subblock, the second operation unit 122 of the decoding apparatus 100 disclosed in the present application, as can be seen in Equation 2 above, each of the subblocks It is individually calculated corresponding to each of a plurality of subcarriers included in , and since the second log-likelihood ratio function is calculated using only scalar-type parameters as inputs, complexity can be drastically reduced compared to the conventional technique.

Also, the decoder 130 may decode the received signal 2 based on the first posterior probability and the second posterior probability derived from the received signal 2 through the above-described process. Illustratively, the decoder 130 may be an LDPC decoder, but is not limited thereto, and in the present disclosure, all types of decoder blocks using posterior probabilities as inputs may be applied to the decoder.

Hereinafter, performance levels such as computational complexity of the decoding device 100 and the conventional technique will be compared with reference to FIGS. 4 to 6B.

4 shows the complexity of the conventional posterior probability calculation technique and the low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present application when an LDPC code is applied to OFDM-IM by reducing the number of CM (Complex Multiplication) This is a chart showing the results of the comparison.

Referring to FIG. 4 , it can be seen that the decoding apparatus 100 has significantly lower computational complexity compared to the conventional technique in terms of the number of complex multiplications (CMs) required for calculating the posterior probability.

5 is a graph showing a comparison of the complexity of a conventional a posteriori probability calculation technique and a low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present application based on DCRR when an LDPC code is applied to OFDM-IM. am.

5 specifically shows decoding complexity reduction ratio (DCRR) results for three sub-block size and active subcarrier number pairs. Referring to FIG. 5, all RM-based DCRR in the three cases are greater than 77.4% and in the three cases It can be seen that all RA-based DCRRs are greater than 79.6%. In addition, both the RM-based and RA-based DCRR monotonically increase as the value of M increases. This means that the posterior probability calculation method of the decoding device 100 in higher order modulation can reduce the computational complexity of LDPC decoding more than the conventional approach.

Meanwhile, the aforementioned DCRR may be defined by Equation 43 below.

[Equation 43]

6a and 6b show BER performance of a conventional a posteriori probability calculation technique, a low-complexity LDPC decoding technique for OFDM index modulation according to an embodiment of the present invention, and a conventional approach when an LDPC code is applied to OFDM-IM. It is a graph showing the evaluation of the LDPC-coded OFDM-IM system with a code rate of 0.5.

및 4QAM을 가정하였고, 도 6b에서는

및 16QAM을 가정하였으며, LDPC 디코딩에 대한 ISB와 SAP 시퀀스 간의 매핑 효과를 조사하기 위해 조합 매핑과 효율적인 인덱스 매핑을 교대로 적용하였다. 참고로, 도 6a 및 도 6b에는 대략적으로 계산된 LLR을 보완하기 위해 소정의 보정 함수를 사용하여 얻은 비트 에러율(bit error rate, BER) 곡선이 표시되어 있다.In Figure 6a

and 4QAM were assumed, and in FIG. 6B

and 16QAM were assumed, and combinatorial mapping and efficient index mapping were alternately applied to investigate the mapping effect between ISB and SAP sequences on LDPC decoding. For reference, FIGS. 6A and 6B show bit error rate (BER) curves obtained using a predetermined correction function to complement the roughly calculated LLR.

Specifically, referring to FIGS. 6A and 6B, efficient index mapping simultaneously improves the performance of PROP and CONV compared to combinatorial mapping, while PROP has a bit error rate equal to that of CONV regardless of the mapping type between ISB and SAP sequences. (bit error rate, BER) performance, and the correction function simultaneously improves the performance of PROP and CONV, while PROP has the same bit error rate (BER) as CONV regardless of the use of the correction function. ) performance can be seen.

In conclusion, when the simulation results of FIGS. 4 to 6B are combined, it can be confirmed that implementation complexity can be greatly reduced without performance loss compared to the conventional technique when the technique by the decoding device 100 is applied.

Hereinafter, based on the details described above, the operation flow of the present application will be briefly reviewed.

7 is an operation flowchart of a low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present invention.

The low-complexity LDPC decoding method for OFDM index modulation shown in FIG. 7 can be performed by the decoding apparatus 100 described above. Therefore, even if omitted below, the description of the decoding device 100 can be equally applied to a description of a low-complexity LDPC decoding method for OFDM index modulation.

Referring to FIG. 7 , in step S11, the receiving unit 110 may obtain a received signal 2 corresponding to an OFDM-IM based transmission signal 1 to which low density parity check coding is applied.

Next, in step S12, the first calculator 121 may calculate a first posterior probability for the index bit (bi ₎ for selecting an activation pattern of a subcarrier based on the obtained received signal 2.

Specifically, in step S12 , the first operator 121 may calculate a first posterior probability based on a predefined first log likelihood ratio function for the index bit b _i .

According to an embodiment of the present application, in step S12, the first operator 121 performs a reference function that is calculated based on activation patterns matched with a sequence in which a target index bit to be calculated is 0, among a plurality of activation patterns. A first log-likelihood ratio function may be derived based on a difference between the minimum value of and the minimum value of a reference function calculated based on activation patterns matched with a sequence having a target index bit of 1 among a plurality of activation patterns.

Next, in step S13, the second operation unit 122 may calculate a second posterior probability for the data bit (d _i ) for selecting a QAM symbol transmitted by an active subcarrier based on the received signal (2). .

Specifically, in step S13 , the second calculator 122 may calculate a second posterior probability based on a predefined second log likelihood ratio function for the data bit d _i .

Next, in step S14, the decoder 130 may decode the received signal 2 based on the first and second posterior probabilities calculated through steps S12 and S13, respectively.

In the foregoing description, steps S11 to S14 may be further divided into additional steps or combined into fewer steps, depending on an embodiment of the present invention. Also, some steps may be omitted if necessary, and the order of steps may be changed.

The low-complexity LDPC decoding method for OFDM index modulation according to an embodiment of the present application may be implemented in the form of program instructions that can be executed by various computer means and recorded on a computer-readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination. Program instructions recorded on the medium may be those specially designed and configured for the present invention or those known and usable to those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. - includes hardware devices specially configured to store and execute program instructions, such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include high-level language codes that can be executed by a computer using an interpreter, as well as machine language codes such as those produced by a compiler. The hardware devices described above may be configured to act as one or more software modules to perform the operations of the present invention, and vice versa.

In addition, the low-complexity LDPC decoding method for OFDM index modulation described above may be implemented in the form of a computer program or application stored in a recording medium and executed by a computer.

The above description of the present application is for illustrative purposes, and those skilled in the art will understand that it can be easily modified into other specific forms without changing the technical spirit or essential features of the present application. Therefore, the embodiments described above should be understood as illustrative in all respects and not limiting. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present application is indicated by the following claims rather than the detailed description above, and all changes or modifications derived from the meaning and scope of the claims and equivalent concepts thereof should be construed as being included in the scope of the present application.

100: low complexity LDPC decoding device for OFDM index modulation
110: receiver
120: posterior probability calculator
121: first calculation unit
122: second calculation unit
130: decryption unit
200: transmitter of OFDM index modulation system
1: transmit signal
2: receive signal

Claims (15)

In the low complexity LDPC decoding method for OFDM index modulation,
obtaining a received signal corresponding to an OFDM-IM-based transmission signal to which low density parity check coding is applied;
calculating a first posterior probability for an index bit for selecting an activation pattern of a subcarrier based on the received signal; and
Calculating a second posterior probability for data bits for selecting a QAM symbol transmitted by an active subcarrier based on the received signal;
including,
In the step of calculating the first posterior probability,
Calculate the first posterior probability based on a predefined first log likelihood ratio function for the index bit;
In the step of calculating the second posterior probability,
Calculating the second posterior probability based on a predefined second log likelihood ratio function for the data bits;
The received signal is divided into a plurality of subblocks;
The first log-likelihood ratio function and the second log-likelihood ratio function are individually calculated in correspondence with each of a plurality of subcarriers included in each of the plurality of subblocks,
The first log likelihood ratio function,
The minimum value of the reference function calculated based on activation patterns matched with a sequence in which the target index bit for calculating the first posterior probability is 0 among a plurality of activation patterns and a sequence in which the target index bit is 1 among the plurality of activation patterns Decoding method that is calculated based on the difference between the minimum values of the criterion function calculated based on activation patterns matched with . delete delete delete According to claim 1,
The first log likelihood ratio function is defined by Equation 1 below,
[Equation 1]

here,

represents each of the plurality of activation patterns,

Is a set of activation patterns matched with a sequence in which the target index bit is 0,

Is a set of activation patterns matched with a sequence in which the target index bit is 1,

is an identifier representing each subcarrier,

Is an identifier representing each QAM symbol,

is an identifier representing each subblock,

is the activation pattern

is the second bit,

is the channel vector,

Is the Gaussian noise, the decoding method. According to claim 5,
The second log likelihood ratio function is defined by Equation 2 below,
[Equation 2]

here,

is the number of bits of the index bits,

Is the number of data bits included in each of the QAM symbols,

Is an index of an active subcarrier included in the activation pattern, the decoding method. According to claim 1,
decoding the received signal based on the first a posteriori probability and the second a posteriori probability;
To further include, the decoding method. In the low complexity LDPC decoding apparatus for OFDM index modulation,
a receiving unit for acquiring a received signal corresponding to an OFDM-IM-based transmission signal to which low density parity check coding is applied;
a first calculator configured to calculate a first posterior probability for an index bit for selecting an activation pattern of a subcarrier based on the received signal; and
a second calculator for calculating a second posterior probability for data bits for selecting a QAM symbol transmitted by an active subcarrier based on the received signal;
including,
The first operation unit,
Calculate the first posterior probability based on a predefined first log likelihood ratio function for the index bit;
The second operation unit,
Calculating the second posterior probability based on a predefined second log likelihood ratio function for the data bits;
The received signal is divided into a plurality of subblocks;
The first log-likelihood ratio function and the second log-likelihood ratio function are individually calculated in correspondence with each of a plurality of subcarriers included in each of the plurality of subblocks,
The first log likelihood ratio function,
The minimum value of the reference function calculated based on activation patterns matched with a sequence in which the target index bit for calculating the first posterior probability is 0 among a plurality of activation patterns and a sequence in which the target index bit is 1 among the plurality of activation patterns Which is calculated based on the difference between the minimum value of the reference function calculated based on the activation patterns matched with , the decoding device. delete delete delete According to claim 8,
The first log likelihood ratio function is defined by Equation 1 below,
[Equation 1]

here,

represents each of the plurality of activation patterns,

Is a set of activation patterns matched with a sequence in which the target index bit is 0,

Is a set of activation patterns matched with a sequence in which the target index bit is 1,

is an identifier representing each subcarrier,

Is an identifier representing each QAM symbol,

is an identifier representing each subblock,

is the activation pattern

is the second bit,

is the channel vector,

is Gaussian noise, the decoding device. According to claim 12,
The second log likelihood ratio function is defined by Equation 2 below,
[Equation 2]

here,

is the number of bits of the index bits,

Is the number of data bits included in each of the QAM symbols,

Is an index of an active subcarrier included in the activation pattern, the decoding device. According to claim 8,
a decoding unit to decode the received signal based on the first a posteriori probability and the second a posteriori probability;
Which further comprises a decoding device. A computer-readable recording medium recording a program for executing the method of any one of claims 1, 5 to 7 on a computer.

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