KR20060105416A - Method for soft-demodulation and soft-modulation of multi-antenna system - Google Patents

Abstract

The present invention relates to a method for soft demodulation and soft modulation of a multi-antenna system. More specifically, a method for quickly implementing soft demodulation and soft modulation among high-level quadrature amplitude modulation is a high-speed modulation using high-level QAM (orthogonal amplitude modulation). The present invention relates to a data transmission mobile communication method.

According to the present invention, the method for implementing soft demodulation uses a fast lookup table method, which first generates and stores a lookup table used for soft demodulation, and compares a received signal and noise variance based on a channel coefficient. A normalization process is performed, the normalized processed signal is quantized, and a method of combining interpolation with a lookup table or a lookup table for the signal after quantization is performed to normalize values obtained after the lookup table. Multiplying the noise variance to obtain the likelihood ratio (LR) of the required bits, wherein the soft modulation method of the high-level quadrature amplitude modulation is calculated by switching the bit likelihood ratio according to the linear relationship between the code and the bit being mapped to the natural QAM. Calculating the mean and variance of the sign based on the mean and variance of the bits.

Orthogonal Frequency Multiplexing (OFDM), Synchronization Method, Block Transmission System

Description

Soft demodulation and soft modulation method for multi-antenna systems {Method for Soft-Demodulation and Soft-Modulation of Multi-Antenna System}

1 is a basic block diagram for implementing soft demodulation with a lookup table.

2 is a basic block diagram for implementing soft demodulation by combining linear interpolation with a lookup table.

3 is a gray mapping soft modulation block diagram.

The present invention relates to a method for soft demodulation and soft modulation of a multi-antenna system. More specifically, a method for quickly implementing soft demodulation and soft modulation among high-level quadrature amplitude modulation is a high-speed modulation using high-level QAM (orthogonal amplitude modulation). The present invention relates to a data transmission mobile communication method.

Future wireless communication systems not only require high speed data transmission, but also require high frequency spectrum utilization. High level modulation is a kind of effective means for wireless communication systems to realize high frequency spectrum utilization. Powerful error control codes, such as Turbo codes and LDPC codes, also greatly enhance the anti-interference capabilities of communication systems. Bit interleaved code modulation has therefore become an important baseband processing method in wireless communication systems. Of these systems, decoders require bit likelihood ratios from detectors (demodulators), and demodulation is still a relatively complex process, especially in high level modulated situations.

Such communication systems include wired communication systems and wireless communication systems, and adaptive code modulation is an important technique for improving the working efficiency of the system. The principle of adaptive code modulation is to improve the power efficiency and frequency spectrum efficiency of the system by adjusting the modulation and code schemes to adapt to channel conditions. However, since the demodulation methods of the various modulations are not exactly the same and the complexity is also different, it is disadvantageous to implement smooth adaptive demodulation with the conventional demodulation method. The present invention aims to quickly implement soft demodulation and effectively reduce complexity by using a lookup table or a method that combines a lookup table with multi-phase interpolation.

In systems that repeatedly detect a large number of decoding, it is necessary to reconstruct an average variance of a signal based on soft information fed back by a decoder, so that MMSE detection or interference cancellation with advance information can be detected. However, when the number of modulation levels is too high, the complexity of reconstructing the mean variance of the signal from the bit likelihood ratio is still high.

Accordingly, the present inventors have completed the present invention as a result of diligent efforts to overcome the above problems.

After all, an object of the present invention is to calculate soft demodulation (i.e., calculate the bit likelihood ratio based on signal detection and noise variance) and soft modulation (i.e., calculate the code statistic based on bit likelihood ratio). It is to provide a method of realizing a low complexity of the, to be applied to the in-phase / quadrature QAM modulation scheme.

In order to achieve the above object, the present invention provides a method for soft demodulation and soft modulation of a multi-antenna system, wherein the method for implementing soft demodulation adopts a fast lookup table implementation method, and (a) a lookup table used for soft demodulation. Generating and storing; (b) normalizing the received signal and the noise variance based on the channel coefficients; (c) quantizing the normalized received signal; And (d) combining the lookup table or the lookup table with the interpolation with respect to the signal after quantization, and multiplying the value obtained after the lookup table by the normalized noise variance to obtain the likelihood ratio of the required bits; The soft modulation method comprises the steps of: (e) calculating by switching the bit likelihood ratio; And (f) calculating, based on the linear relationship between the natural QAM mapped code and the bit, the mean and variance of the code based on the mean and variance of the bits, if the QAM mapping scheme is natural mapping (d) Provides a method which can be omitted.

In the present invention, the normalization process comprises: (a) normalizing a signal: dividing a received signal value by a channel increase coefficient; And (b) normalizing variance: dividing the noise variance value by the channel increase coefficient.

In the present invention, a fast implementation method for combining interpolation with the soft demodulation lookup table includes the steps of: (a) normalizing a received signal and noise variance based on a channel coefficient; (b) quantizing the normalized received signal and simultaneously estimating a quantization error; (c) performing a lookup table on the signal after quantization and obtaining error term coefficients and then correcting it using an interpolation method; And (d) multiplying the normalized noise variance by the value after calibration to obtain the required bit likelihood ratio.

In the present invention, when the lookup table is performed on the signal after quantization, an error term coefficient is obtained at the same time, and the interpolation method during the correction process using the interpolation method includes linear interpolation, or secondary interpolation, and higher level interpolation. It may be characterized by using.

Hereinafter, the present invention will be described in detail.

In the fast implementation method of soft demodulation and soft modulation in the high level quadrature amplitude modulation of the present invention, the implementation method of the soft demodulation adopts a fast lookup table implementation method, which includes the following steps.

(a) First, a lookup table used for soft demodulation is created and stored.

(b) The normalization process is performed based on the channel coefficients for the received signal and the noise variance.

(c) Quantize the normalized received signal.

(d) A lookup table is performed on the signal after quantization or interpolation is combined with the lookup table, and the value obtained after the lookup table is multiplied by a normalized noise variance to obtain the likelihood ratio of the required bits.

The soft modulation method during high level quadrature amplitude modulation includes the following steps.

(d) Calculate by switching the bit likelihood ratio.

(e) calculating an average value and a variance of the code based on the average value and the variance of the bit based on the linear relationship between the natural QAM mapped code and the bit, and if the QAM mapping method is natural mapping, step (d) Can be omitted.

The normalization process includes the following steps.

(a) Normalization of the signal: Divides the received signal value by the channel increase coefficient.

(b) Normalization of variance: The noise variance is divided by the channel increase coefficient.

A fast implementation method for combining interpolation with a soft demodulation lookup table includes the following steps.

(1) The normalization process is performed based on the channel coefficients for the received signal and noise variance.

(2) Quantize the normalized received signal and at the same time estimate the quantization error.

(3) While the lookup table is performed on the quantized signal, the error term coefficient is obtained and corrected using the interpolation method.

(4) Multiply the normalized noise variance by the value after calibration to obtain the required bit likelihood ratio.

An error term coefficient is obtained while the lookup table is processed for the signal after quantization, and the interpolation method during the correction process using the interpolation method uses a linear interface or a secondary interpolation and a higher level interpolation.

1. High Level QAM Modulation Soft Demodulation

를 복부호 s로 맵핑하는데, 통상적으로 우리가 사용하는 동위상/직교 QAM 변조는 즉 s의 실부 s _R 와 허부 s _I 를 각각 비트 a ₀ a ₁ L a _{n -1} 과 a _n L a _{2n -1} 로 맵핑하여 이루어진 것이다. 신호가 통신 시스템의 전송 과 채널(각종 전송방식과 각종 채널 포함)을 지나, 수신단에서 채널 균형 또는 간섭 상쇄 신호 검측 등을 거치게 되는데, 신호의 동치(equivalant) 전송 채널은 다음과 같이 표시할 수 있다.Modulation is a group of bit data

The mapping to a bokbuho s, typically in-phase / quadrature modulation QAM we use that is the real part s of s _R And huh Map s _I to bits a ₀ a ₁ L a _{n -1} and a _n L a _{2n -1} , respectively. The signal passes through the transmission system and communication channel (including various transmission methods and various channels) of the communication system, and the receiving end undergoes channel balance or interference cancellation signal detection. The equivalent transmission channel of the signal can be expressed as follows. .

[1]

[One]

는 실 부호항의 증가 계수를 나타내고,

은 잉여의 간섭과 노이즈를 나타낸다. 통상적으로 에러컨트롤코딩 디코더는 복조기의 비트 우도비를 입력으로 한다. 우리는 신호의 실부와 허부를 분리할 수 있는데, 이럴 경우 공식[1]은 다음과 같이 변한다.among them,

Represents the coefficient of increase of the real code term

Denotes surplus interference and noise. Typically, the error control coding decoder takes as input the bit likelihood ratio of the demodulator. We can separate the real and the false of the signal, in which case the formula [1] changes as follows.

[2]

[2]

을 실부호

에 맵핑하고, 상응하는 실 수신 신호를

로, 증가계수는

로, 제곱 노이즈 분산은

으로 설정한다. 복조기가 출력하는 우도비는 다음과 같이 정의된다.According to the above formula, we can demodulate the likelihood ratios for the signals of both paths independently. We can derive the process of demodulation by taking an in-phase component as an example. beat

The symbol

To the corresponding real received signal

, The increase factor is

Squared noise variance

Set to. The likelihood ratio output by the demodulator is defined as

[3]

[3]

과

는 각각 비트

의 사전정보와 사전 확률을 나타낸다. 일반성을 잃지 않고, 비트를 0과 1 등 확률로 가설하면, 노이즈의 가우스 가설로부터 다음을 얻을 수 있다:Of the above formula

and

Each bit

It shows the dictionary information and the probability of the dictionary. Without losing generality, hypothesizing bits with 0 and 1 probabilities gives the following from the Gaussian hypothesis of noise:

[4]

[4]

를 근거로

Based on

[5]

[5]

In general, we complete the function of demodulation by calculating the likelihood ratio of every bit by the formula [5].

2. Fast Implementation of Lookup Table of High Level QAM Modulation Soft Demodulation

를 이용하여 공식[5]를 단축시켜 다음을 얻을 수 있다.We can calculate that the bit likelihood ratio using Equation [5] shows that the complexity increases with the exponent according to the number of modulation levels, and the amount of computation is very large. We are

By shortening Formula [5], we can get

[6]

[6]

는 룩업테이블 방법으로 구현할 수 있으며, 각기 다른 변조방 식의 소프트 복조를 다른 테이블로 만들 수 있다. 만약 우리가 정상화된 수신 신호

를

비트에 따라 양자화하면,

는 룩업테이블로

길이를 만들어야 하는 테이블을 구현할 수 있다. 다른 변조방식은 사전에 다른 테이블을 만들어 메모리에 저장하기만 하면 되는데, 발송신호의 각기 다른 변조양식에 따라 상응하는 테이블에서 상응하는 값을 얻으면 다른 변조방식의 소프트 복조를 구현할 수 있다. 도 1은 고레벨 변조 소프트복조의 기본 과정을 설명해주고 있는데, 우선 수신신호를 정상화하고 이를 양자화한 후 룩업테이블을 진행한 후, 다시 상응하는 계수를 곱하면 비트 우도비를 얻을 수 있다.among them,

Can be implemented using the lookup table method, and soft modulation of different modulations can be made into different tables. If we normalize the received signal

To

If you quantize according to bits,

Is a lookup table

You can implement a table whose length needs to be created. Different modulation schemes only need to create different tables in advance and store them in memory. Soft modulation of different modulation schemes can be implemented by obtaining corresponding values from the corresponding tables according to different modulation patterns of the outgoing signal. 1 illustrates the basic process of high level modulation soft demodulation. First, normalize a received signal, quantize it, proceed with a lookup table, and then multiply corresponding coefficients to obtain a bit likelihood ratio.

의 양자화 레벨 수가 비교적 높을 경우, 테이블의 크기는 대폭으로 증가하게 되어 복잡도가 높아진다. 만약 비교적 정확한

에 대하여 저레벨 양자화 룩업테이블을 진행할 경우에는 성능의 손실을 초래하게 된다. 낮은 복잡도로 우수한 성능을 얻으려면, 우리는 룩업테이블에 다항식 인터폴레이션을 결합하는 방법으로 소프트 복조 방법을 개선할 수 있는데, 그것의 기본 원리는

에 대하여 룩업테이블의 정밀도에 따라 양자화를 진행하고, 룩업테이블을 진행한 후 다항식 인터폴레이션을 이용하여 갱신 후의 값을 얻는 것이다.We can see here that the size of the table and the number of quantization levels represent an exponential increase. if

If the number of quantization levels is relatively high, the size of the table is greatly increased, which increases the complexity. If relatively accurate

Performing a low level quantization lookup table with respect to the WB causes a loss of performance. To achieve good performance with low complexity, we can improve the soft demodulation method by combining polynomial interpolation with a lookup table.

The quantization is performed according to the precision of the lookup table, the lookup table is performed, and the updated value is obtained using polynomial interpolation.

의 정밀도가 양자화 레벨수보다 높고 서로 이웃한 두 개의 양자화 지점 사이에 놓일 경우, 리니어 인터폴레이 션

으로 더욱 정확한 값을 얻을 수 있다. 이와 유사하게, 2 레벨 또는 더욱 높은 레벨의 인터폴레이션을 진행할 수도 있다. 양자화기는 논리니어(non-linear) 양자화의 방법을 이용하여 테이블 크기를 더욱 축소할 수 있다.2 is a basic block diagram for implementing soft demodulation by combining linear interpolation with a lookup table. The main principle is as follows. if

Linear interpolation when the precision of is higher than the number of quantization levels and lies between two neighboring quantization points

You can get more accurate values with Similarly, two or higher levels of interpolation may proceed. The quantizer can further reduce the table size by using a method of non-linear quantization.

3. High Level QAM Modulation Soft Demodulation

Some methods of iteratively detecting decoding typically require reconstruction of the mean and variance according to the bit likelihood ratios that the decoder feeds back to. In other words, based on the probability that each bit is +1 or -1, the transmission signal is calculated as the probability of each code in the code set, thereby calculating the average value and the variance of the signal. The average variance of the signal is calculated using the bit likelihood ratio as follows.

[7]

[7]

[8]

[8]

를 비트 d _{0 ,} d ₁ 로 설정하고, L d _{MC -1} 을 맵핑하여 구성하면, 즉:sign

Bit d _{0 ,} If you set d ₁ , and you configure L d _{MC -1} by mapping:

[9]

[9]

는

를 부호

로 표시할 때 상기 비트가 상응되는 값 이다.Becomes among them

Is

Sign

The bit is the corresponding value when denoted by.

In the high-level modulation situation, it is possible to reconstruct the mean and variance of the signal only by calculating the probability of each code, and it can be seen that the complexity increases exponentially with the number of bits of each code. When the number of modulation levels is high, the complexity increases significantly, and the difficulty in constructing hardware greatly increases.

The present invention seeks to provide a low complexity mean variance algorithm for QAM modulation of natural mapping or gray mapping. The method regards general QAM modulation as two stages, and the first stage is a process of dividing linear or nonlinear groups of bit sequences by encoding, for example, identity transform, gray code, etc., and the second stage is linear mapping. In other words, the modulation code can be represented linearly by the bit sequence obtained in the first step. Correspondingly, the soft modulation process can also be divided into two stages: in the first stage, the bit likelihood ratio conversion is performed according to the transformed rule, and in the second stage, the bit likelihood ratio after switching is performed. Obtain the mean and variance of the constructed signal based on the linear mapped relationship. This method can effectively reduce the complexity of calculating the mean variance by omitting the step of calculating the probability of all codes based on the bit log likelihood ratio.

The implementation of soft demodulation adopts a fast lookup table implementation, which includes the following steps;

(a) Calculate first based on Equation [6], and create and store a lookup table for soft demodulation according to certain quantization bits.

이 우선적으로 채널증가계수

에 의해 정상화되면 정상화된 수신신호

과 정상화된 노이즈 분산의 역수

를 얻는다.(b) Normalize the received signal and the noise variance based on the channel coefficients. As shown in Figure 1, the received signal

Preferentially the channel growth factor

Normalized received signal by

And the inverse of normalized noise variance

Get

(c) Quantize the normalized received signal, and quantization may use uniform quantization and non-uniform quantization.

에 대하여 룩업테이블을 진행하고, 룩업테이블 후 얻은 값에 정상화된 노이즈 분산의 역수를 곱하면 소프트 복조와 상응하는 비트의 대수 우도비를 얻을 수 있으며, 디코더로 판별 또는 전송하여 디코딩한다.(d) signal after quantization

Proceeding the lookup table for, multiplying the value obtained after the lookup table by the inverse of the normalized noise variance to obtain the soft likelihood ratio and the logarithm likelihood ratio of the corresponding bits.

A fast implementation method for combining interpolation with a soft demodulation lookup table includes the following steps.

(1) The normalization process is performed on the received signal and noise variance based on the channel coefficient.

(2) Quantize the normalized received signal and estimate the quantization error.

(3) A lookup table is performed on the signal after quantization, and at the same time, an error term coefficient is obtained and corrected by using an interpolation method.

(4) The required bit likelihood ratio can be obtained by multiplying the normalized noise variance by the value after calibration.

When the lookup table is performed on the signal after quantization, the error term coefficients are simultaneously acquired, and the interpolation method in the process of correcting the interpolation method is linear interpolation or second order interpolation and higher level interpolation.

은 먼저 채널 증가계수

에 의해 정상화되어 정상화된 수신 계수

를 얻은 다음, 이에 대한 양자화를 진행한다. 양자화는 균일 양자화와 비균일 양자화를 사용할 수 있다. 양자화 후의 값

은 룩업테이블에서 상응하는 값을 찾은 후, 양자화 오차

를 계산하고, 아울러 별도의 룩업테이블에서 상응계수

를 찾아, 상기 계수

와 양자화 오차를 이용하여

값을 교정한다.An apparatus for quickly implementing a high level QAM soft demodulation lookup table / interpolation is illustrated in FIG.

Is the channel growth factor

Receive coefficient normalized by and normalized by

Then, the quantization is performed. Quantization can use uniform quantization and non-uniform quantization. Value after quantization

Finds the corresponding value in the lookup table, and then

, And the corresponding coefficients in a separate lookup table

Find the coefficient

And quantization error

Correct the value.

When implemented in real hardware, data generally exists in hardware in the form of quantized data. If the valid bits of the received signal and the corresponding coefficient itself are relatively low (close to each other with the lookup table quantization bits), the lookup table is never large. Therefore, the first scheme is relatively suitable, and if the valid bits of the received signal and the corresponding coefficients themselves are relatively high (much larger than the lookup table quantization bits), forcing quantization may cause loss of data precision. In such a situation, a lookup table / interpolation method can be used to overcome the above-described drawbacks and achieve high precision performance with relatively low complexity.

The soft demodulation method during high level quadrature amplitude modulation includes the following steps:

(d) Calculate by switching the bit likelihood ratio.

(e) calculating the mean and variance of the code based on the linear relationship between the natural QAM mapped code and the bit, and calculating the mean and variance of the code based on the mean and variance of the bits. Can be omitted.

The working steps of the soft demodulation (i.e., calculating the code statistic with bit likelihood ratio) apparatus will now be described in detail using natural mapping and gray mapping as examples.

1. Nature Mapping

(±1을 취함)와 부호

사이의 관계는 하나의 리니어 표현식으로 다음과 같이 설명할 수 있다. Normally natural mapping bit

(Takes ± 1) and sign

The relationship between can be described as a linear expression as follows.

[10]

[10]

In other words, by the independence between bits, the mean value and the variance of the sign are expressed as

[11]

[11]

[12]

[12]

이고,

이다.among them

ego,

to be.

2. Gray Mapping

Gray mapping cannot describe the relationship between bits and signs as a linear relationship, but since we can separate it into one gray encoder and one natural mapper, we switch the likelihood ratio through the gray encoder and again natural The mapping allows the average and variance of the sign to be calculated.

3 illustrates a process of calculating the average variance of gray mapping, which is mainly divided into two parts. First, it converts its bit likelihood ratio based on gray code, and then formulas [10], [11], and [12]. Compute the natural mapped mean and variance.

Typically, bit sequence gray codes can be represented by the following formula:

[13]

[13]

는 그레이 코드 전의 비트를 나타내고,

는 그레이 코드 후의 비트를 나타낸다. 이러한 관계를 근거로, 우리는 우도비 사이의 관계를 계산할 수 있다.During a meal

Represents the bits before the gray code,

Denotes the bit after the gray code. Based on this relationship, we can calculate the relationship between the likelihood ratios.

[14]

[14]

이며,

를 이용하여 근접할 수 있다. 수학함수

는 프로그램에서 통상 룩업테이블의 방식으로 구현된다.During a meal

Is,

It can be approached using. Math Function

Is usually implemented in the manner of a lookup table in a program.

The rapid implementation of high level QAM soft modulation in the present invention can significantly reduce the complexity of reconstructing the mean and variance of the code based on the bit likelihood ratio, especially when the number of modulation levels is high or linear mapping is used. The performance is close to or equal to the best calculation method.

The fast lookup table implementation of high level QAM soft demodulation in the present invention is applicable to various systems using high level QAM modulation, and is suitable for use in various high level QAM mapping communication systems including wired communication systems and wireless communication systems. It is suitable for communication systems of various transmission methods including transmission systems such as multi-antennas, single carriers, and multiple carriers, and can be used not only for regular maps but also for irregular maps.

The rapid implementation of high level QAM soft modulation in the present invention is based on MMSE Turbo balance with pre-information, multi-user detectors that match the interference cancellation of MMSE or filtering in CDMA systems, and iterative detection using linear detectors in multi-antenna systems. It can be applied to systems that are modulated with high level QAM and need to calculate the mean and variance of the sign, such as decoding.

As described above, according to the present invention, the rapid implementation of the quantization / lookup table can greatly reduce the complexity without reducing the performance, especially in the situation of high level modulation. In addition, since the corresponding values in the table need to be changed for different modulation schemes, the usability is greatly increased. Soft demodulation can be split into two processes, bit likelihood ratio conversion and statistics calculation, to effectively reduce the complexity of computing sign statistics.

In addition, when implementing the fast lookup table of the high level QAM soft demodulation of the present invention, the complexity of the QAM modulation soft demodulation can be greatly reduced in the situation of high level QAM modulation, and the performance is hardly damaged, and it is different from the calling party. In the case of using the modulation scheme, since the soft demodulation of the receiver is performed in the same frame and has the same complexity, it is advantageous to implement the reception of the adaptive modulation, and the very complicated irregular QAM mapping is the same complexity as the QAM mapping of the same rule. By having, the selection of the mapping method can be further diversified.

In addition, when implementing the low complexity of calculating the average variance of the high level QAM equal sign of the present invention, the complexity of the average variance calculation process can be greatly reduced, and the complexity of the natural mapping QAM can be lowered from the exponential increase to the linear increase according to the number of bits. .

Soft demodulation of the present invention can be implemented quickly by the quantization / lookup table method, thereby effectively lowering the complexity and flexibly implementing adaptive modulation since other modulation schemes only need to change the mapping table. The method is suitable for communication systems using any QAM modulation scheme, in particular for in-phase / quadrature QAM systems. The soft modulation of the present invention divides the calculation of the sign statistic (which typically includes the mean and variance of the sign) into two stages: bit likelihood ratio conversion and mean variance calculation, and this method effectively reduces the complexity and reduces in-phase / It is suitable for use in quadrature QAM modulation.

Claims (4)

In a soft demodulation and soft modulation method of a multiple antenna system, The soft demodulation method adopts a fast lookup table implementation method. (a) generating and storing a lookup table for soft demodulation; (b) normalizing the received signal and the noise variance based on the channel coefficients; (c) quantizing the normalized received signal; And (d) performing interpolation of the lookup table or the lookup table with respect to the signal after quantization, and multiplying the value obtained after the lookup table by the normalized noise variance to obtain the likelihood ratio of the required bits; The soft modulation method (e) converting and calculating the bit likelihood ratios; And (f) calculating, based on the linear relationship between the natural QAM mapped code and the bit, the average and variance of the code based on the mean and variance of the bits, if the QAM mapping scheme is natural mapping. Method which can be omitted. The method of claim 1, wherein the normalization treatment (a) normalizing the signal: dividing the received signal value by the channel increase coefficient; And (b) normalizing variance: dividing the noise variance value by the channel increase coefficient. 2. The method of claim 1, wherein the fast implementation method for combining interpolation with the soft demodulation lookup table comprises the following steps; (a) normalizing the received signal and the noise variance based on the channel coefficients; (b) quantizing the normalized received signal and simultaneously estimating a quantization error; (c) performing a lookup table on the signal after quantization and obtaining error term coefficients and then correcting it using an interpolation method; And (d) multiplying the value after calibration by the normalized noise variance to obtain the required bit likelihood ratio. 4. The method of claim 3, wherein when the lookup table is performed on the signal after quantization, an error term coefficient is obtained at the same time, and the interpolation method during the correction process using the interpolation method is linear interpolation, or second-order interpolation, and higher level interpolation. Method for using the.

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