KR20090012189A

KR20090012189A - Apparatus and method for decoding using performance enhancement algorithm for ldpc codes with scaling based min-sum iterative decoding

Info

Publication number: KR20090012189A
Application number: KR1020080073655A
Authority: KR
Inventors: 허준
Original assignee: 고려대학교 산학협력단
Priority date: 2007-07-27
Filing date: 2008-07-28
Publication date: 2009-02-02

Abstract

The present invention provides a decoding apparatus and method using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of an LDPC code. A variable node updating unit which receives L _c and updates the LLR of the variable node; An iterative comparison unit which receives the result of the variable node update unit and determines whether the variable node update unit has a predetermined number of iterations or more; A scaling factor multiplier receiving the determination result of the iterative comparison unit and multiplying a scaling factor; A check node update unit for updating the L _v multiplied by the scaling factor in the scaling factor multiplier; A vector optimizer configured to receive an update result of the test node updater and obtain a scaling factor; A density development unit for performing a density development on a scaling factor obtained by the vector optimizer to obtain a limit value; A comparison unit which receives the result of the density development unit and compares the limit value in the current iteration with a previously obtained limit value; Determining unit for determining the output by receiving the result of the iterative comparison unit; by comprising a scaling-based improved MIN-SUM iterative decoding algorithm for improving the performance of the LDPC code compared to the SUM-PRODUCT algorithm The deterioration can be reduced while the complexity is reduced, so the hardware can be implemented with a simple structure.

Description

Apparatus and method for decoding using performance enhancement algorithm for LDPC codes with scaling based MIN-SUM iterative decoding}

The present invention relates to a decoding apparatus using the MIN-SUM iterative decoding algorithm and a method thereof, and more particularly, to the performance of the performance compared to the SUM-PRODUCT algorithm using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of the LDPC code. The present invention relates to a decoding apparatus and a method using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of an LDPC code, which is suitable for hardware implementation with a simple structure since the deterioration can be reduced while reducing complexity.

The present invention is a technology used to effectively recover data errors in the process of transmitting information. In the field where data errors can occur frequently, such as a mobile environment, wireless LAN, etc. Can be used.

In general, Low Density Parity Check Codes (LDPC codes) were first proposed by Gallager in 1962 and have been the most advanced channel coding technologies since Mackay and Neal rediscovered them in 1996. A big advantage of LDPC codes over other channel coding techniques is the excellent performance at high code rates required for high speed data transmission. Turbo code technology, one of the advanced channel coding technology, is one of the reasons that LDPC code is favored in future mobile communication in that it shows performance degradation such as error floor due to puncturing required to make high code rate. Can be. In addition, the BP (Belief Propagation) algorithm, which is used to decode LDPC codes, is considered as an advantage in high-speed data transmission because of parallel processing in hardware implementation as a whole. The disadvantage of LDPC code technology, which has many of these advantages, is that it has a large amount of computation in encoding. To compensate for this drawback, one of the ways to reduce the amount of encoding calculation is to represent the parity bit of the parity check matrix H in the form of dual-diagram, so that the parity generation block can be represented as an accumulator. Irregularly determined portions of systematic data can be represented by a combination of repetition code, interleaver and puncturing. In other words, the LDPC code group that reduces the encoding computation amount by limiting the H matrix structure among the LDPC codes is called structured-LDPC. Up to now, the repetition code and accumulator block are connected through a single interleaver, and the RA (Repeat Accumulate) code, which enables simple encoding, and the parity check matrix H of the LDPC code are assigned to Hd and parity bits corresponding to information bits. Semi-random LDPC codes that consist of Hd part by dividing the corresponding Hp into certain rules, and CZZ (Concatenated Zigzag) codes using several Zigzag codes proposed by Li Ping are introduced as structured-LDPC codes.

In addition, the MIN-SUM algorithm used to decode the LDPC code can reduce the complexity of the SUM-PRODUCT algorithm, which is advantageous to implement in hardware, but performance deteriorates. In order to improve performance degradation, the MIN-SUM algorithm using a scaling factor, which is a fixed constant at each iterative decoding, also causes a significant performance degradation compared to the SUM-PRODUCT algorithm.

FIG. 1 shows the thresholds of the SUM-PRODUCT and MIN-SUM algorithms according to various code rates of the LDPC code using a Density Evolution (DE) method using Gaussian approximation.

In FIG. 4, reference numeral 21 is a variable node (also called a variable node), 22 is a check node (also called a check node, or check node), and 23 is an edge.

LDPC codes are well illustrated by bipartite graphs, often referred to as Tanner graphs, such as the graph shown in FIG. The variable nodes 21 in the tanner graphs of a set of nodes correspond to the bits of the codeword. Check nodes 22 in other sets of nodes, also called constraint nodes, correspond to the parity-check set that defines the code. Edges 23 connect the variable nodes 21 to the check nodes 22 in the graph. Variable node 21 and check node 22 are referred to as neighbors if they are connected by edge 23 in the graph. It is typically assumed that node pairs are connected at most by one edge. LDPC codes may be equivalently represented using a parity check matrix.

Each variable node 21 is associated with one bit of the codeword. In some cases, some of these bits may be punctured. The punctured bits may be advantageous in certain code structures and are excluded from the codeword being transmitted.

The bit sequence one-to-one associated with the sequence of variable nodes 21 is equal to zero modulo 2, with the sum of the bits (through association with their variable nodes) neighboring the constraints for test node 22, respectively. Is the codeword of the code, i.e., only if they contain an even number of ones.

Decoder and decoding algorithms used to decode LDPC codewords operate by exchanging messages in a graph along edge 23 and by updating these messages by performing calculations at nodes based on incoming messages. Such algorithms will generally be referred to as message passing algorithms.

The number of edges 22 given to a node, ie variable node 21 or check node 22, is referred to as the node's degree. The regular graph or code is that all variable nodes 21 have the same class j and also all constraint nodes have the same class k. In this case, the code is referred to as the (j, k) rule code. These are the codes originally considered by Gallager (1961). In contrast to "regular" codes, irregular codes have variable classes 21 and / or check nodes 22 of different grades. For example, some variable nodes 21 may be grade 4, other variable nodes 21 may be grade 3, and another variable node 21 may be grade 2.

In the case of (a) of FIG. 4, the number of edges of the variable node 21 from the top becomes 2, 3, 1, 1, 1, and 2 respectively from above. In addition, the number of edges of the inspection node 22 becomes 4, 3, and 3 from the top, respectively.

In addition, in FIG. 1, d _v represents the variable node 21 in FIG. 4, and the number of connected edges 23 becomes a number of d _v . In addition, in FIG. 1, d _c represents the test node 22 in FIG. 4, and the number of the edges 23 connected is a number of d _c .

In addition, parity is attached to the data to be sent using an LDPC code. Through the channel, data with parity is sent, and the receiving end performs LDPC decoding to find the original data. Thus, in FIG. 1, rate represents a ratio of original data to data sent through a channel. For example, if you send 10 data and 1 parity, the rate is 10/11. Among the characteristics of the LDPC code, rate is defined as rate = 1-dv / dc.

Also in Figure 1

sum-product and

min-sum represents the threshold of the LDPC code when the sum-product and min-sum algorithms are used. The threshold represents the minimum power that the LDPC code can correct for errors. That is, below the threshold, LDPC cannot correct errors, and above the threshold, error correction is possible.

Also

Is

The value is converted to dB.

=

Becomes

Thus, referring to FIG. 1, when the code rate is 0.75, only 0.18 dB (= 2.44 dB-2.26 dB) is found, but when 0.33, the difference is 1.31 dB (= 3.04 dB-1.73 dB).

This has the advantage that the MIN-SUM algorithm reduces the complexity, but there is a problem that performance deterioration may be large in some cases.

In order to improve this, the decoding algorithm of LDPC code is designed based on the MIN-SUM algorithm, and in this case, multiplying the soft information delivered to a certain constant value improves the performance. The inventor's paper has been published. However, there is a need for a MIN-SUM algorithm for improved performance.

Accordingly, the present invention has been proposed to solve the above-mentioned general problems, and an object of the present invention is to further improve performance by multiplying a different constant value every repetition number, and for each repetition number (Iteration). Scaling base to improve the performance of LDPC code that can improve performance up to the part close to SUM-PRODUCT algorithm that MIN-SUM algorithm with the most suitable scaling factor is applied. The present invention provides a decoding apparatus and method using the improved MIN-SUM iterative decoding algorithm.

In addition, another object of the present invention is to provide a decoding apparatus and method using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of the LDPC code, which can find the best scaling factor for each iteration number. To provide.

2 is a block diagram of a decoding apparatus using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of an LDPC code according to an embodiment of the present invention.

As shown in the drawing, when the iteration is 0, the received symbol is received, and when iteration proceeds, L _c is received to update the Log Likelihood Ratio (LRL) of the variable node 21. A variable node update block 11; An iteration compare block 12 receiving the result of the variable node updater 11 and determining whether the variable node updater 11 is equal to or greater than a predetermined iteration number; A scaling factor multiplier 13 receiving the determination result of the iterative comparison unit 12 and multiplying a scaling factor; A check node update block (14) for performing an update on the L _v multiplied by the scaling factor in the scaling factor multiplier (13); A vector optimization block 15 receiving the update result of the check node updater 14 and obtaining a scaling factor; A density evolution block (16) for obtaining a threshold by performing density evolution (DE) on the scaling factor obtained by the vector optimizer (15); A comparator block 17 which receives the result of the density development section 16 and compares a threshold with a previously obtained threshold in a current iteration; And a decision block 18 for determining the output by receiving the result of the iterative comparison unit 12.

The iterative comparison unit 12 receives a result of the variable node updater 11, and if it is greater than or equal to a predetermined iteration, a decision block for finishing decoding and determining an output. (18), and if the iteration is not finished, L _v is transmitted to the scaling factor multiplier 13 to update the check node.

The comparison unit 17 causes the variable node update unit 11 to be performed if the threshold is less than a previously obtained threshold in the current iteration, otherwise the threshold is set. It is characterized by returning to the vector optimizer 15 so as to have the smallest scaling factor.

3 is a flowchart illustrating a decoding method using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of an LDPC code according to an embodiment of the present invention.

As shown in the drawing, when the iteration is 0, the received symbol is received, and when iteration proceeds, L _c is received to update the Log Likelihood Ratio (LRL) of the variable node 21. A variable node updating step ST1; An iterative comparison step (ST2) of receiving a result of the variable node updating step and determining whether the variable node is equal to or greater than a predetermined iteration number; A scaling factor multiplication step (ST3) for multiplying a scaling factor if it is determined to continue in the iterative comparison step; A check node update step (ST4) of performing an update on the L _v multiplied by the scaling factor in the scaling factor multiplication step; A vector optimization step (ST5) of receiving the update result of the check node update step and obtaining a scaling factor; A density development step (ST6) of obtaining a threshold value by performing density expansion (Density Evolution, DE) on the scaling factor obtained in the vector optimization step; A comparison step (ST7) of receiving a result of the density development step and comparing a threshold at a current iteration with a previously obtained threshold; If it is determined that the repetition in the iterative comparison step is finished, the determination step (ST8, ST9) for determining the output; characterized in that it comprises.

In the iterative comparison step (ST2), the result of the variable node update step is received, and if a predetermined number of iterations is greater than or equal to the iteration, the decoding step is terminated and a decision step for determining the output is performed. If iteration is not completed, the scaling factor multiplication step may be performed.

The comparing step ST7 causes the variable node updating step to be performed if the threshold is less than the previously obtained threshold in the current iteration, otherwise scaling is performed with the smallest threshold. The method may return to the vector optimization step to have a scaling factor.

Decoding apparatus using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of LDPC code according to the present invention and scaling method for multiplying each iterative decoding to reduce performance degradation when MIN-SUM algorithm is used By varying the factors, it is possible to derive results close to the performance of the SUM-PRODUCT algorithm.

Referring to the accompanying drawings and a preferred embodiment of the decoding apparatus using the scaling-based improved MIN-SUM iterative decoding algorithm for improving the performance of the LDPC code according to the present invention configured as described above in detail as follows. In the following description of the present invention, when it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted. In addition, terms to be described below are terms defined in consideration of functions in the present invention, which may vary according to intention or precedent of a user or an operator, and thus, the meaning of each term should be interpreted based on the contents throughout the present specification. will be.

First, the present invention uses a scaling-based improved MIN-SUM iterative decoding algorithm to improve the performance of LDPC codes, and thus, complexity can be reduced while the performance is reduced, compared to the SUM-PRODUCT algorithm. It would be.

4 is a bipartite graph of an LDPC code showing the most suitable scaling factor used for every iteration in accordance with a preferred embodiment of the present invention.

Referring to FIG. 4, reference numeral 21 denotes a variable node (also called a variable node) and reference numeral 22 denotes a check node (also referred to as a check node). The decoding method of LDPC code (Low Density Party Check code) is basically iterative process.

Repeated appearance of the same picture represents each iteration of each decoding. During decoding, Log Likelihood Ratio (LLR) information is exchanged between a variable node and a check node for each iteration, and a scaling factor of any size is used for this LLR information. Multiply by) to adjust the value. The reason that can improve performance through this is as follows.

The Log Likelihood Ratio (LLR) value compares only the logarithm of the size when decoding LDPC codes, so the performance difference between the SUM-PRODUCT algorithm and the MIN-SUM algorithm is substantially dependent on the difference between min * and min. Occurs. Where min * -sum is the logarithm of the sum-product. The size of the log changes, but the interest in LDPC decoding is not the size of the LLR, but the size of the two LLRs, so taking the log has no effect on performance. After all, comparing the sum-product and min-sum algorithms is equivalent to comparing min * -sum and min-sum.

Equation 1 below shows the relationship between min * and min according to a preferred embodiment of the present invention.

Where x and y are arbitrary variables and min (x, y) represents a function representing the minimum value among x and y. In addition, min * is a function defined by -ln (e ^-x + e ^-y ), which shows the relationship between min * and min in FIG. Also, appending -log to the sum-product (the LLR is a comparison of the sizes, appends log or -log but does not affect performance) results in min * -sum, max Adding -log to -product (max-product) yields min-sum. max-product represents an algorithm when the sum-product algorithm performs an operation that takes the maximum value instead of the sum operation.

In Equation 1

Eventually represents the difference. It is good to calculate and decode Equation 1, but since the complexity of the operation increases, the meaning of the complexity of the MIN-SUM algorithm is lost.

Therefore, the most appropriate constant for the value

, the value is adjusted by multiplying by scaling factor. At this time, min is a negative operation

Ranges from 0 to 1.

5 schematically illustrates a check node operation in the decoding algorithm of an LDPC code according to a preferred embodiment of the present invention.

In FIG. 5, (a) shows the edge 23 connected to the check node 22 and the LLR value coming into the edge, and (b) shows the MIN-SUM algorithm operation at that time. It is represented by an equation.

Is the LLR value of edge i transmitted from the check node 22 to the variable node 21,

Is the LLR value of the edge j transmitted from the variable node 21 to the check node 22.

And d _c represents the degree of the check node. In this operation

on

Multiply by to get closer to the value of min *.

Figure 6 shows that each scaling value is multiplied in the decoding algorithm of the LDPC code according to a preferred embodiment of the present invention.

In Figure 6 L represents LLR,

Denotes an LLR input from the variable node 21 to the test node 22,

,

Represents LLR from 1st to jth, respectively.

At this time, the present invention uses the following equation (2) for the min-sum algorithm.

In addition, the present invention uses the equation (3) of Figure 5 and the following for the min-sum algorithm.

here

Is the sign (+ or-) of the LLR of the j-th variable node 21,

Is the smallest of each absolute value of all inputs. in this case

That is, when j and I are not equal when calculating the LLR of the I th check node 22 (

) Only.

So in the calculation of equation (3)

To

Multiply by to get closer to the value of min *. In other words,

Is the LLR value coming from the variable node 21 to the check node 22, instead of this value.

on

Multiply by new

If you make and use it in Equation 3, the min-sum algorithm is close to the min * -sum algorithm performance.

As described above, the present invention uses a scaling-based improved MIN-SUM iterative decoding algorithm to improve the performance of LDPC codes, while reducing the complexity while reducing the performance degradation compared to the SUM-PRODUCT algorithm. Will be.

Although the above has been described as being limited to the preferred embodiment of the present invention, the present invention is not limited thereto and various changes, modifications, and equivalents may be used. Therefore, the present invention can be applied by appropriately modifying the above embodiments, it will be obvious that such application also belongs to the scope of the present invention based on the technical idea described in the claims below.

Explanation of symbols on the main parts of the drawings

11: variable node update unit

12: iterative comparison unit

13; Scaling Factor Multiplier

14: Inspection node update unit

15: vector optimizer

16: density development

17: comparison unit

18: decision part

21: variable node

22: inspection node

23: edge

Claims

A variable node updating unit which receives the received symbol when the number of repetitions is 0 and receives L _c and updates the LLR of the variable node when the repetition proceeds;

An iterative comparison unit which receives the result of the variable node update unit and determines whether the variable node update unit is equal to or greater than a predetermined number of iterations;

A scaling factor multiplier receiving the determination result of the iterative comparison unit and multiplying a scaling factor;

A check node update unit for updating the L _v multiplied by the scaling factor in the scaling factor multiplier;

A vector optimizer configured to receive an update result of the test node updater and obtain a scaling factor;

A density development unit for performing a density development on a scaling factor obtained by the vector optimizer to obtain a limit value;

A comparison unit which receives the result of the density development unit and compares the limit value in the current iteration with a previously obtained limit value;

A decision unit which receives the result of the iterative comparison unit and determines an output;

Decoding apparatus using the scaling-based improved MIN-SUM iterative decoding algorithm for improving the performance of the LDPC code comprising a.

The method according to claim 1,

The repeat comparison unit,

Receiving forward the variable node update negative result, the L _v parts of the scaling factor multiplied is above predetermined number of iterations to end the decoding gives send the value part determined for determining the output, if the iteration is not over so as to proceed with the update of the check node A decoding apparatus using an improved MIN-SUM iterative decoding algorithm based on scaling to improve the performance of an LDPC code.

The method according to claim 1 or 2,

The comparison unit,

In the current iteration, if the threshold is less than the previously obtained threshold, the variable node updater is performed. Otherwise, the performance of the LDPC code is returned to the vector optimizer so that the threshold has the smallest scaling factor. Decoder Using Scaling-based Improved MIN-SUM Iterative Decoding Algorithm

A variable node updating step of receiving a received symbol when the number of repetitions is 0 and receiving L _c and updating the LLR of the variable node when the repetition is performed;

An iterative comparison step of receiving a result of the variable node update step and determining whether the variable node is updated or more;

A scaling factor multiplication step of multiplying a scaling factor if determined to continue in the iterative comparison step;

A check node updating step of updating the L _v multiplied by the scaling factor in the scaling factor multiplication step;

A vector optimization step of receiving the update result of the check node update step and obtaining a scaling factor;

A density development step of obtaining a limit value by performing density development on the scaling factor obtained in the vector optimization step;

A comparison step of receiving a result of the density development step and comparing a limit value at a current iteration with a previously obtained limit value;

A determination step of determining an output if it is determined in the iterative comparison step that the iteration is finished;

Decoding method using an improved MIN-SUM iterative decoding algorithm based on scaling for the performance improvement of the LDPC code, characterized in that performed.

The method according to claim 4,

The iterative comparison step,

Receiving the result of the variable node update step, and if it is equal to or greater than a predetermined number of iterations, an LDPC step of determining decoding and determining an output is performed; and if the iteration is not completed, the scaling factor multiplication step is performed. Decoding Method Using Scaling-based Improved MIN-SUM Iterative Decoding Algorithm for Improving Code Performance.

The method according to claim 4 or 5,

The comparing step,

In the current iteration, if the threshold is less than the previously obtained threshold, the variable node updating step is performed, otherwise the performance of the LDPC code is returned to the vector optimization step so that the threshold has the smallest scaling factor. Decoding method using an improved MIN-SUM iterative decoding algorithm based on scaling for improvement.