KR20100083731A - A method of dirty paper coding by using nested lattice codes - Google Patents

Abstract

PURPOSE: A DPC(Dirty Paper Coding) method using a nested lattice code is provided to reduce complexity of DPC. CONSTITUTION: A lattice is scaled so that interference of another receiver is located at a lattice point of a lattice of one receiver for one receiver among at least two different receivers(501). The Interference is reduced from a signal which will be transmitted to the one receiver(503). The reduced signal is mapped on a basic lattice of one receiver through a modulo operation(505). The mapped signal is transmitted(507).

Description

Dirty paper coding method using nested lattice codes {A METHOD OF DIRTY PAPER CODING BY USING NESTED LATTICE CODES}

The present invention relates to a coding method of a wireless communication system, and more particularly, to a dirty paper coding (DPC) method using nested lattice codes.

Broadcast channels are one of the most basic entities in multiuser information theory. For multi-antenna Gaussian broadcast channels, it is well known that dirty paper coding is obtained in all regions.

One of the biggest drawbacks of these channels is the difficulty of performing dirty paper coding. This is for two reasons. Firstly, dirty paper coding requires accurate grasping of channel state information for all channels at the transmitter, and second, even if the state is known, the encoding and decoding required for conventional dirty paper coding mechanisms. It is complicated to carry out the procedure. In addition, multiple papers are substantially written similar to dirty paper coding using other mechanisms such as Tomlinson-Harashima precoding, zero-forcing and MMSE coding. On the other hand, in cellular networks, it has been shown that dirty paper coding can obtain a large gain compared to approximation schemes, and most importantly, dirty paper coding can be performed by a mechanism of low complexity.

Knowing the channel conditions at the transmitter, dirty paper precoding can be implemented with a complexity that represents an approximate polynomial-time without approximation. This means that in a gentle fading environment for channel state feedback, dirty paper coding is in fact a low complexity technique and can be more real.

SUMMARY OF THE INVENTION An object of the present invention is to provide a method of coding duffy paper using a nested grating capable of reducing the complexity of dirty paper coding.

In accordance with a preferred embodiment of the present invention, a method of encoding a dirty paper using a nested grid of a transmitter for transmitting a signal to at least two different receivers may include any of the at least two different receivers. Scaling the grid so that interference of another receiver with respect to one receiver is located at a grid point of the grid of the receiver; and in the signal to be transmitted to the receiver to the basic grid of the grid of the receiver through modulo operation And a process of mapping the subtracted signal and transmitting the mapped signal.

The scaling is characterized in that to scale the grid of any one of the receiver and the other receiver.

및

중 적어도 하나에 따라 스케일링하며, 상기 N은 잡음이고, 상기

은 전력 제한이며,

,

,

이고,

및

는 상기 일 수신기 및 상기 타 수신기로부터 수신하는 채널 정보에 따라 결정되며, a 및 b는 벡터인 것을 특징으로 한다. In addition, the scaling is expressed by equation

And

Scaling according to at least one of, wherein N is noise,

Is the power limit,

,

,

ego,

And

Is determined according to channel information received from the one receiver and the other receiver, and a and b are vectors.

The mapping may be performed according to a modulo operation.

According to a preferred embodiment of the present invention for achieving the above object, a dirty paper decoding method using a nested grid of any one receiver for receiving a signal transmitted by a transmitter for transmitting a signal to at least two different receivers Receiving a signal transmitted by the transmitter, and decoding the signal through a modulo operation using a scaled grid.

The decoding may further include linear filtering and dither removing before the modulo operation.

The scaling is characterized by scaling the grid of any one of the at least two different receivers.

및

중 적어도 하나에 따라 스케일링하며, 상기 N은 잡음이고, 상기

은 전력 제한이며,

,

,

이고,

및

는 상기 일 수신기 및 상기 타 수신기로부터 수신하는 채널 정보에 따라 결정되며, a 및 b는 벡터인 것을 특징으로 한다. The scaling is equation

And

Scaling according to at least one of, wherein N is noise,

Is the power limit,

,

,

ego,

And

Is determined according to channel information received from the one receiver and the other receiver, and a and b are vectors.

The present invention proposes a nested lattice coding method that provides a concise approach to designing code for dirty paper coding of a broadcast channel. This simplicity is made possible by using nested gratings that allow linear time encoding and spherical decoding. With this approach, capacity for the MISO broadcast channel can be achieved.

1 is a diagram illustrating a MISO broadcast channel according to an embodiment of the present invention.
2 illustrates an example of a grating used for dirty paper coding according to an embodiment of the present invention.
3 is a view for explaining dirty paper coding using a nested grating according to the prior art.
4 is a view for explaining dirty paper coding using a nested grating according to an embodiment of the present invention.
5 is a view for explaining a dirty paper coding method using a nested grating according to an embodiment of the present invention.
6 is a view for explaining a dirty paper decoding method using a nested grid according to an embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that in the following description, only parts necessary for understanding the operation according to the present invention will be described, and descriptions of other parts will be omitted so as not to distract from the gist of the present invention. The present invention consists of dirty paper encoding using the nested grating of the encoder of the transmitter and dirty paper decoding using the nested grating of the decoder of the receiver.

1 is a diagram illustrating an MISO broadcast channel according to an embodiment of the present invention, and FIG. 2 is a diagram illustrating an example of a grid used for dirty paper coding according to an embodiment of the present invention. 3 is a diagram for explaining general dirty paper coding using a nested grating, and FIG. 4 is a diagram for describing dirty paper coding using a nested grating according to an embodiment of the present invention.

System model

The character used in the equation of the embodiment of the present invention means a column vector unless otherwise specified. T is the transposition that swaps the rows and columns of a column. Mod also refers to a modulo operation on the lattice . For example, sphere coding and decoding are examples of modulo operations.

In an embodiment of the present invention, it is assumed that the network system is a multiple input single output (MISO) broadcast channel shown in FIG. 1. To more clearly illustrate the invention, it is assumed that there are only two receivers 100, 200 in the system. When the signals Y1 and Y2 transmitted by the transmitter 300 to the first and second receivers 100 and 200 are considered, the channel states h1 and h2 and the noises N1 and N2, the following < It can be described as in Equation 1>.

All symbols here mean real values, but can be extended to complex numbers. In addition, the transmit power of the transmitter 300 is limited to P, and the additional noise takes the form of Gaussian with a deviation of N. In addition, it is assumed that both the transmitter 300, the first receiver 100, and the second receiver 200 know the channel states h1 and h2. It is well known that the capacitive region of this channel is obtained by Dirty Paper Coding (DPC).

In general, dirty paper coding can be implemented by Gel'fand-Pinsker-style binning. In recent research, grid codes have been used to perform this operation. In particular, Erez, Shamai, and Zamir have demonstrated that nested lattice codes can be used to perform dirty paper coding in point-to-point channels with additional Gaussian states. Continues to be generalized to apply to any other state classification. The encoding and decoding design will be described later. A point-to-point Gaussian channel with an additional Gaussian state is represented by Equation 2 below.

The transmission message X here has a power limit P, an additional Gaussian state S and noise deviation N that the transmitter 300 recognizes.

)를 나타내는 성근(coarse) 격자 L에 네스티드된다. In terms of channel coding, a good grating is chosen as the fine grating used to communicate the message,

Nested in a coarse lattice L,

Referring to FIG. 3, the fine lattice refers to each lattice indicated by reference numerals 1 to 9, and the perforated lattice refers to lattice that adds up to all reference numerals 1 to 9. Similarly, referring to FIG. 4, the fine lattice refers to each lattice indicated by 10 to 90, and the perforated lattice refers to the lattice that adds up to 10 to 90. As illustrated in FIGS. 3 and 4, the plurality of fine gratings are nested in the cochlear grating, and the colic gratings and the fine gratings may be interpreted as relative concepts.

In Fig. 3 and Fig. 4, each lattice is divided into 3 * 3 row and column elements, and the midpoint of each element is called lattice point. In FIG. 2 to FIG. 3, the lattice points are shown as a figure. For example, the same rows and columns of all microgrids have the same value. Therefore, the lattice points (marked with pentagons) of the first row and the first column of reference numeral 10 and the lattice points (pentagons) of all the first rows and first columns of the reference numerals 20 to 90 can be interpreted as the same value.

), 송신기(300)가 인식하고 있는 상태 S 및 α = P/(P + N)가 주어진다면, 송신기(300)의 송신 신호 부호화 과정은 다음의 <수학식 3>과 같다. When the signal to be transmitted by the transmitter is λ and the lattice point is Λ, the lattice point where the signal λ is located (

), Given a state S recognized by the transmitter 300 and α = P / (P + N), the transmission signal encoding process of the transmitter 300 is expressed by Equation 3 below.

or

Referring to FIG. 3, L denotes a lattice and mod denotes a modulo operation according to the DPC, as described above. X is the result of the dirty paper coded over the channel. That is, X maps a value 11 obtained by subtracting the interference S 15, which is an additional state recognized by the transmitter 300, from the signal λ to be transmitted to one of the fine gratings 1 constituting the sexual root grating. , Denotes a value 17 mapped to a good lattice 9 through a modulo operation. It is sequentially decoded using dirty paper decoding using a Lettis grid at the receiving end. Direct application of this grid-based decoding design on broadcast channels is still very complex and difficult to implement.

If the additional state S is generated from a Gaussian codebook or any codebook, the encoding process of Equation 3 becomes very difficult to perform. The main object of the present invention is as follows.

The first is to simplify the coding task with a linear complexity task using a grid structure.

Second, the grid decoding operation is simplified by using a sphere decoding algorithm having a POLINOMIAL time average complexity.

Therefore, the overall encoding and decoding operation has a POLINOMIAL complexity, which is actually easy to implement further.

Low Complex Dirty Paper Encoding Method

에서 전송 전력 P를 가지는 더티 페이퍼 인코딩된 코드 북(dirty-paper-encoded codebook)을 가진다고 가정한다. The first receiver 100 has a specific range,

Suppose we have a dirty-paper-encoded codebook with transmit power P at.

According to the prior art, the codebook for the second receiver 200 transmitted without dirty paper coding is configured first, and the codebook for the first receiver 100 transmitted with dirty paper coding is configured next. However, according to an embodiment of the present invention, the codebook is designed in the reverse order.

를 나타내는 성근 격자(coarse lattice)

에 네스티드 된다. First, the transmitter 300 selects the fine grating Λ in terms of channel coding for the first receiver 100. Selected fine grating is Power Constraint

Coarse lattice

Is nested in.

및

를 결합시킬 수 있다. MISO(Multi-Input Single-Output) 방송 채널에 대한 최적의

및

의 선택은 전체 용량 영역(Capacity region)에 대한 단위 랭크 매트릭스(unit rank matrices)이다. 이것은 다음의 <수학식 4>의 형태로 표현 할 수 있다. On the other hand, when dirty paper coding is used, each of the codebooks of the first and second receivers 200 is optimal covariance that satisfies power constraints.

And

Can be combined. Optimal for Multi-Input Single-Output (MIS) Broadcast Channels

And

The choice of is the unit rank matrices for the entire capacity region. This can be expressed as the following Equation 4.

이다. 본 발명의 실시 예에서는 다음의 <수학식 5>와 같은 표기법을 정의하도록 한다. In Equation 4, a and b each represent a specific vector,

to be. In an embodiment of the present invention, the following notation is defined as in Equation 5 below.

)는 기본 볼륨으로 존재하고, 평균적으로 간섭 없이 제1 수신기(100)에 대해 네스티드 격자 총체에 의해 획득되는 비율은 다음의 <수학식 6>과 같이 주어진다. Returning to the description of the lattice construction, the nested lattice ensemble (

) Is the fundamental volume, and on average, the ratio obtained by the nested grating total with respect to the first receiver 100 without interference is given by Equation 6 below.

을 사용하는 경우, 제1 수신기(100)에 의해 간섭 없이 보여지는 최대 비율이며,

을 적당히 선택하여 채널에 대한 용량 영역 경계에 놓인다. This is essentially a transmission covariance for codebook generation.

When using, the maximum ratio seen without interference by the first receiver 100,

Is appropriately selected and placed at the capacitive region boundary for the channel.

만큼 스케일링하여, 제2 수신기(200)에 대해

를 만족하는 격자를 획득한다. 용량 영역 경계에 놓이기 위해 제2 수신기(200)에 대해 요구되는 비율은 다음의 <수학식 7>과 같다는 점에 유의해야 한다. Next, the transmitter 300 generates a codebook for the second receiver 200. After acquiring the lattice Λ of the first receiver 100 as the lattice point, the obtained lattice (each element of the lattice) is obtained.

Scaling by, for the second receiver 200

Obtain a grid that satisfies It should be noted that the ratio required for the second receiver 200 to be placed at the capacitive region boundary is as shown in Equation 7 below.

Where β is a non-trivial value. The ratio required for the second receiver 200 expressed in Equation 7 is much smaller than the ratio for the first receiver 100.

을 나타내는 성근 격자 L2에 네스트된(nested) 경우, 임의의 양의 정수 M에 대해

를 만족하는

의 부격자(sublattice)를 찾을 수 있으며, 이러한 스케일링의 비율은 상기 <수학식 7>에서 보인 바와 같다. Thus, power constraints on the second receiver 200

For any positive integer M, when nested to

To satisfy

The sublattice of can be found, and the ratio of such scaling is as shown in Equation 7 above.

)와 제2 수신기(200)에 대한 네스티드 격자(

) 는 특유의 성질을 가지도록 설정된다. Thus, the nested lattice for the first receiver 100 (

) And the nested gratings for the second receiver 200 (

) Is set to have unique properties.

First of all, the gratings are good gratings for communication to ensure that they can be used for encoding and decoding in end-to-end communication. And the grids are, on average, derived from an ensemble with enough codebooks to ensure that the rate required in the broadcast channel can be achieved. The gratings are also associated with a scaling factor. This relationship ensures that dirty paper coding can be performed effectively.

)하고, 제1 송신기(100)가 전송하고자 하는 신호 λ가 격자점 Λ에 위치(

)한다고 가정한다. 그러면, 제2 수신기(200)에 대한 격자 코드 출력이 다음의 <수학식 8>과 같이 주어진다. According to the scaling as described above, the signal γ to be transmitted by the second transmitter 200 is located at the grid point Γ.

), And the signal λ to be transmitted by the first transmitter 100 is located at the lattice point Λ

Suppose Then, the grid code output for the second receiver 200 is given by Equation 8 below.

는 기본 영역(fundamental region) L2에 걸쳐 균일하게 분배된 랜덤 변수이다. 그러면 다음의 <수학식 9>에 의해 제1 수신기(100)에 대한 더티 페이퍼 코드 출력을 생성할 수 있다. here,

Is a random variable that is uniformly distributed over the fundamental region L2. Then, the dirty paper code output to the first receiver 100 may be generated by Equation 9 below.

는 기본 영역 L1에 걸쳐 균일하게 분배된 랜덤 변수이다. 여기서,

가 Λ의 요소(element)임을 주의해야 한다. 즉,

는 격자점에 위치한다. 그러므로,

는 Λ의 요소이다. 즉,

또한, 격자점에 위치한다. 따라서, 인코딩에 대한 상기 모듈로(modulo) 동작은 선형 시간에서 수행될 수 있다. 마지막으로 시간 'i'에서 전송된 벡터는 아래의 <수학식 10>과 같이 주어진다. here

Is a random variable uniformly distributed over the base region L1. here,

Note that is an element of Λ. In other words,

Is located at the grid point. therefore,

Is an element of Λ. In other words,

It is also located at the grid point. Thus, the modulo operation for encoding can be performed in linear time. Finally, the vector transmitted at time 'i' is given by Equation 10 below.

Decoding method ( Decoding Strategy )

When the block size is n, the signal received by the first receiver 100 is expressed by Equation 11 below.

에 따른 모듈로 연산에 의거하여 선형 필터링(linear filtering) 및 디더 제거(dither remoivng)에 따라 처리되며, 이러한 디코딩은 다음의 <수학식 12>와 같다. Dirty-paper decoding of the first receiver 100

Based on a modulo operation according to the linear filtering and dither remoivng, the decoding is performed as shown in Equation 12 below.

은

와 같이 표현될 수 있다. 또한, 노이즈의 변화(the variance of the effective noise)를 최소화하기 위해, 수신기는 선형 필터 팩터,

를 취한다. 예컨대,

은 MMSE 스캐일링 팩터에서 선택된다. 또한, MMSE 스캐일링 및 스피어 디코딩은 선형 시간 복잡에 의거하므로, 제1 수신기(100)의 디코딩은 선형 시간에 따라 수행된다. here,

silver

It can be expressed as Also, to minimize the variance of the effective noise, the receiver uses a linear filter factor,

Take for example,

Is selected from the MMSE scaling factor. In addition, since MMSE scaling and sphere decoding are based on linear time complexity, decoding of the first receiver 100 is performed according to linear time.

)에 따라, 제1 제1 수신기(100)의 인코딩된 아웃풋(u)은

의 기본 영역(fundamental region)에서 유니폼(uniform)하다. 따라서 아웃풋(u)는

에 독립(independent of

)이며, 디더(

)와 그 분포가 동일하다. Dither,

), The encoded output u of the first first receiver 100 is

Uniform in the fundamental region of. So the output (u)

Independent of

) And dither (

) And its distribution are the same.

의 EX²의 범위는 다음의 <수학식 13>과 같이 계산된다. <수학식 13>에서

의 EX²는 직교성에 따라 도출된다. Depending on these factors, the noise

The range of EX ² is calculated as shown in Equation 13 below. In Equation 13

EX ² is derived according to orthogonality.

)에 의해 나타낼 수 있다. 여기서, 임의의 변수는

의 기본 영역에서 균등하게 분포된다. In order to view the ratio obtained at the first receiver 100, a message is randomized.

Can be represented by Where any variable

Evenly distributed in the basic area of.

Then, the information rate satisfies Equation 14 below.

는 일반화된

의 두 번째 시간(second moment)이다. 두 번째 시간(second moment)에서, 화이트 가우시안 랜덤 벡터는 임의의 벡터 중 극대의 엔트로피를 가지므로, <수학식 13>에 따라 다음의 <수학식 15>를 얻을 수 있다. here,

Generalized

Is the second moment of. At the second moment, since the white Gaussian random vector has the maximum entropy of any vector, the following Equation 15 can be obtained according to Equation 13.

In addition, the following Equation 16 can be obtained.

및 충분히 큰 블록 사이즈 n을 가정하면, n 개로 분할된 격자 L은 다음의 <수학식 17>을 만족한다. Any positive value

And a sufficiently large block size n, n divided gratings satisfy the following equation (17).

및 충분히 큰 블록 사이즈에서,

과 같은 부격자(sublattice)를 가지는 격자를 선택하면, 다음의 <수학식 18>과 같이 나타낼 수 있다. Also, any positive value

And at a sufficiently large block size,

If a lattice having a sublattice as follows is selected, it can be expressed as Equation 18 below.

This indicates that the capacity can be approximated by appropriate selection of coarse lattice. This can be seen that the rate according to the dirty-paper coding of the first receiver 100 satisfies Equation 6.

The second receiver 200 performs grid decoding. Lattice decoding is performed according to sphere decoding in linear time. The signal received by the second receiver 200 is represented by Equation 19 below.

에 따른 모듈로 연산에 의거하여, 선형 필터링(linear filtering) 및 디터 제거(dither remoivng)에 따라 처리되며, 이러한 디코딩은 다음의 <수학식 20>과 같다.Dirty paper decoding of the second receiver 200

Based on a modulo operation according to, the process is performed according to linear filtering and dither remoivng, and the decoding is as shown in Equation 20 below.

는 MMSE 스케일링 팩터(the MMSE scaling factor)

에서 선택된 값이며,

는

이다. here,

Is the MMSE scaling factor

Is selected from

Is

to be.

)에 따라서, 격자 코딩의 출력(v)은

의 중요 지역에서 균등하다. 여기서,

는

에 독립적이다. 또한, u 및

는

에 독립적이다. <수학식 9>에 따라, 격자 코딩의 출력(v)은,

및 u가 독립적인 맥락에 따라, u에 독립적인

에서 유니폼하다. Dither (

According to the output of the grid coding (v)

Even in important areas of the here,

Is

Is independent. U and

Is

Is independent. According to Equation 9, the output v of the grid coding is

And u independent, depending on the independent context

Uniform in

는

와 그 배치가 균등하다. 또한,

는 다음의 <수학식 21>을 만족한다. Accordingly,

Is

And the arrangement is even. Also,

Satisfies Equation 21 below.

 In the same way, the following Equation 22 can be derived according to Equation 15.

)와 격자 디코딩 출력(

) 간의 정보율은 다음의 <수학식 23>을 만족한다. Then, the message (

) And grid decoded output (

), The information rate satisfies Equation 23 below.

로 선택할 경우, 다음의 <수학식 24>를 얻을 수 있다. At this time, a grid satisfying Equation 17 is obtained.

In this case, the following <Equation 24> can be obtained.

및 충분히 큰 블록 사이즈 n을 가지는 경우에 만족한다. 이에 따라, <수학식 7>을 만족함을 알 수 있다. Equation 24 is any random number

And a sufficiently large block size n. Accordingly, it can be seen that Equation 7 is satisfied.

Hereinafter, a dirty paper coding and decoding method according to an embodiment of the present invention will be described.

First, a dirty paper coding method using a nested grating according to an embodiment of the present invention will be described. 5 is a view for explaining a dirty paper encoding method using a nested grid according to an embodiment of the present invention.

)를 말한다. 3 and 4, each of the gratings 1 to 9, 10 to 90 is a fine grating, has unit units of 3 * 3, and unit units located in the same row and column have the same value. The lattice of the sum of all the fine lattices, that is, the lattice of the sum of all the reference numerals 1 to 9 and the lattice of the sum of all the reference numerals 10 to 90, is coarse. Here, the interference (S) is a signal that the first receiver 100 receives a signal to be transmitted to the second receiver 200 through another antenna provided by the transmitter 300 (

Say).

According to the prior art with reference to FIG. 3, reference numeral 15, which indicates a signal that the transmitter 300 receives by the second terminal, denotes interference S, and the interference S does not exactly match the grid point 13. Do not. On the other hand, according to an embodiment of the present invention, the transmitter 300 scales the grid such that the interference S 101 is located at the grid point in step 501.

As described above, scaling of the grating may scale the grating of the second terminal 200. In addition, the grid of the first terminal 100 may be scaled. In this case, the scaling ratio is based on Equation 6 or Equation 7.

)에서 간섭(S)을 뺀다. 이와 같이, 송신하고자 하는 데이터(

)에서 간섭(S)을 뺀 값(

)(103) 또한 도면 부호 10이 지시하는 격자의 격자점에 위치한다. 앞서 설명한 바와 같이, 모든 단위 격자 각각(10 내지 90)은 동일한 위치에서 동일한 값을 가진다. Next, the transmitter 300 transmits data to be transmitted in step 503.

) Subtract the interference (S). As such, the data to be transmitted (

) Minus interference (S) (

103 is also located at the lattice point of the grid indicated by 10. As described above, each of the unit grids 10 to 90 has the same value at the same location.

)에서 간섭(S)을 뺀 값(103)을 기본 격자(Fundamental Voronoi Region)(90)에 동일한 위치에 그 값(105)을 매핑시킨다. 이는 <수학식 9>에 따라 스케일링된 격자를 이용한 모듈로 연산을 통해 이루어진다. In this case, according to the DPC coding method, the transmitter 300 transmits data to be transmitted in step 505.

The value 103 minus the interference S is mapped to the value 105 at the same position in the fundamental lattice (Fundamental Voronoi Region) 90. This is achieved through a modulo operation using a scaled grid according to Equation (9).

)에서 간섭(101)을 뺀 값(103) 및 그 값(103)을 기본 격자(90)의 동일한 위치에 매핑시킨 값(105) 모두 격자점에 일치하게된다. Since the interference is scaled to exactly match the lattice point, the scaled interference 101 according to the lattice scaling, the signal to be transmitted to the first transmitter 100 (

), The value 103 minus the interference 101 and the value 105 that maps the value 103 to the same position of the base grating 90 coincide with the grid point.

Next, the transmitter 300 transmits the DPC signal to the first transmitter 100 as described above in operation 507.

)에서 간섭을 뺀 값(11) 및 데이터에서 간섭을 뺀 값을 기본 격자에 매핑시킨 값(17) 모두 격자점에 일치하지 않으므로, 종래기술은 DPC 코딩 방법의 복잡도가 증가한다. 반면, 본 발명의 실시 예에 따르면, 간섭(101)을 스케일링하여 격자점에 위치시킴으로써, 전송하고자 하는 신호에서 간섭을 뺀 값(103)과, 기본 격자에 매핑시킨 값(105) 모두 격자점에 정확히 일치되므로, 그 DPC 코딩의 복잡도를 줄일 수 있다. Comparing the present invention described above with FIG. 3, the prior art of FIG.

Since the subtracted interference (11) and the data obtained by subtracting the interference from the data (17) do not coincide with the lattice points, the complexity of the DPC coding method increases in the prior art. On the other hand, according to an exemplary embodiment of the present invention, by scaling the interference 101 at a grid point, both the value 103 obtained by subtracting the interference from the signal to be transmitted and the value 105 mapped to the basic grid are located at the grid point. Since it is an exact match, the complexity of the DPC coding can be reduced.

Next, a dirty paper decoding method according to an embodiment of the present invention will be described.

6 is a view for explaining a dirty paper decoding method using a nested grating according to an embodiment of the present invention.

As described above with reference to FIG. 5, since the data to be transmitted is transmitted without noise, it is to be noted that the signal received by the receiver becomes a signal with noise added again.

Referring to FIG. 6, the first receiver 100 receives a signal from the transmitter 300 in step S601. As described with reference to FIG. 5, the signal received by the first receiver 100 is a signal obtained by subtracting a signal to be transmitted to the second receiver 200 from a signal to be transmitted to the first receiver 100 by the transmitter 300. , A signal to be transmitted to the second receiver 200. Accordingly, the signals to be transmitted to the second receiver 300 by the transmitter 300 according to Equation 12 are canceled.

Accordingly, the first receiver 100 may easily recover its signal by performing a modulo operation using the scaled grid in step S603.

As described above, the scaling ratio is based on Equation 6 or Equation 7 and may scale any one of the gratings of the first or second transmitters 100 and 200.

As described above, the present invention proposes a nested lattice coding method that provides a concise approach for designing a code for dirty paper coding of a broadcast channel. This simplicity is made possible by using nested gratings that allow linear time encoding and spherical decoding. In this approach, capacity for the MISO broadcast channel can be achieved.

While the present invention has been described with reference to several preferred embodiments, these embodiments are illustrative and not restrictive. As such, those of ordinary skill in the art will appreciate that various changes and modifications can be made according to equivalents without departing from the spirit of the present invention and the scope of rights set forth in the appended claims.

Claims (8)

In the dirty paper encoding method using a nested grating of the transmitter for transmitting a signal to at least two different receivers,
Scaling a grid such that, for any one of the at least two different receivers, interference of another receiver is located at a grid point of the grid of the one receiver;
Mapping a signal obtained by subtracting the interference from a signal to be transmitted to the one receiver to a basic grid of the lattice of the one receiver through a modulo operation;
And transmitting the mapped signal to the dirty paper encoding method using a nested grating of the transmitter. The method of claim 1 wherein the scaling is
And scaling the grid of any one of the one receiver and the other receiver. The method of claim 2, wherein the scaling
Equation

And

Scaling according to at least one of, wherein N is noise,

Is the power limit,

,

,

ego,

And

Is determined according to channel information received from the one receiver and the other receiver, and a and b are vectors, characterized in that the dirty paper encoding method using a nested grid of the transmitter. The method of claim 2, wherein the mapping process
Dirty paper encoding method using a nested grating of the transmitter, characterized in that according to the modulo operation. In the dirty paper decoding method using a nested grid of any one receiver receiving a signal transmitted by a transmitter for transmitting a signal to at least two different receivers,
Receiving a signal transmitted by the transmitter;
And decoding the signal through a modulo operation using a scaled grating. The method of claim 5, wherein the decoding is performed.
And a linear filtering and dither removing process prior to the modulo operation. 6. The method of claim 5, wherein said scaling
And scaling the grid of any one of said at least two different receivers. 8. The method of claim 7, wherein said scaling is
Equation

And Scaling according to at least one of, wherein N is noise,

Is the power limit,

,

,

ego,

And

Is determined according to channel information received from the one receiver and the other receiver, and a and b are vectors, characterized in that the dirty paper decoding method using the nested grid of the receiver.

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