KR101126975B1 - Decoding method and device using nonbinary belief propagation algorithm including new stopping criteria - Google Patents

Abstract

Provided is a decoding method or apparatus to which a new stop criterion applied to a non-binary reliable spreading decoder of a weighted non-binary repeat-accumulate (RA) code on a finite field GF (q). The weighted non-binary RA code on GF (q) increases the decoding complexity as q increases. To reduce this decoding complexity, the message vectors of the non-binary trust-propagation decoder used in the weighted non-binary RA code are reduced. I use it. The message vectors in the non-binary confidence spread decoder are updated every iteration, and the updated message vectors tend to grow larger than other elements each time the iteration proceeds. In the first iteration, the number of elements having elements above the given threshold among the elements of each vector is defined as T (m), and when m≥2, D (m) is defined as T (m) -T (m- It is defined as 1). At this time, the iteration can be stopped when D (m) becomes zero or when the absolute value of D (m) is within the predetermined difference threshold value and continues for the iteration of the predetermined vibration number threshold value. By using the decoding stop criterion, it is possible to perform only the iterations smaller than the fixed iterations when performing decoding, thereby reducing the decoding complexity.

Description

DECODING METHOD AND DEVICE USING NONBINARY BELIEF PROPAGATION ALGORITHM INCLUDING NEW STOPPING CRITERIA}

The present invention relates to a decoding method and apparatus, and more particularly, to a decoding method and apparatus using a non-binary confidence spreading algorithm to which a new stopping criterion is applied.

Noise channel coding theorem proves that there is an error correction code where the error rate converges to zero as the length of the code diverges to infinity if the code rate is less than the channel capacity. do. Since then, various channel codes representing performance close to the channel capacity have been studied.

Among the concatenated codes, concatenated codes represent codes that concatenate relatively simple codes of short length and perform close to a single long code. The decoding complexity can be greatly reduced in that the component codes can be individually decoded. A representative of these concatenated codes is the turbo code. The turbo code performs parallel decoding by placing two identical recursive systematic convolutional codes between the interleaver and performing parallel concatenation, and then performs decoding using the principle of iterative decoding. As the turbo code shows a performance close to the channel capacity, codes using iterative decoding have been studied. Among them, the most representative codes having excellent performance are a low density parity check (LDPC) code and a repeat-accumulate (RA) code.

The RA code is a serial concatenation of a repeater and an accumulator having a code rate of '1' through an interleaver. The RA code shows excellent performance close to the turbo code despite the simple encoder structure. Irregular RA codes are codes that can improve the performance of the RA code by introducing non-uniformity in the repetition rate of repeaters belonging to the RA coder.

Among these, weighted nonbinary repeat- on the finite field GF (q) (Galois Field (q), q = 1,2,4,8,…), which can be regarded as a non-binary form of binary RA code. accumulate (WNRA) code. The encoder of the WNRA code consists of a non-binary repeater, a weighter, an interleaver, and an accumulator on the finite field GF (q). When binary phase shift keying (BPSK) modulation is used in an additive white Gaussian noise (AWGN) channel, the WNRA codes on GF (4) and GF (8) perform better than binary RA codes. In addition, the WNRA code using q-ary orthogonal modulation coherent detection in the AWGN channel shows closer channel capacity as q increases and the code rate converges to zero.

But the problem with these codes is the computational complexity. In the WNRA code, the complexity of the decoding increases exponentially as q increases compared to the binary RA code. Therefore, the complexity of the WNRA code is significantly higher than that of the binary code.

Many methods have been proposed to solve this problem, which is inevitable due to the nature of iterative decoding. Among them, the method using the stop criterion refers to a message in the iterative decoder and stops iteration for a code frame that no longer needs to be repeatedly repeated, thereby reducing the computational complexity in proportion to the number of iterative decoding. .

As such, the decoding abort criterion has the advantage of greatly reducing the decoding complexity by performing only iterations than fixed iterations when performing decoding, but various decoding interruptions are performed for binary trust spreading decoders. Although criteria have been proposed, little research has been done on non-binary confidence spreading decoders. Accordingly, there is a need for a non-binary reliable spreading decoding apparatus or method to which a decoding stop criterion is applied.

An object of the present invention is to provide a decoding method and apparatus to which a new stop criterion is applied using a non-binary confidence spreading algorithm.

According to an aspect of the present invention, there is provided a decoding method for decoding a received signal received from a receiver using a non-binary confidence spreading algorithm. A message vector including a probability for each symbol included in the message of the received signal as an element is transmitted from a variable node to a check node, and the probability for the respective symbol is checked at the check node. Determining reliability on the basis of: transmitting another message vector from the check node to another variable node, wherein the other message vector is updated every iteration according to an element value of the message vector transmitted to the check node And repeatedly transmitting the message vector and the other message vector, and performing repeated decoding to decode a value of a message of the received signal based on the reliability, wherein m (1 ≤ m ≤) of the repeated decoding. N _I) separation value is determined in advance of the message vector element in the second iteration than the threshold _{(θ S) (0 ≤ θ} S ≤ 1) Determine the number T (m) of message vectors having a value, and determine D (m) such that 'D (m) = T (m)-T (m-1)' using the T (m). When the value of D (m) is 0, the repeated decoding is stopped. Where N _I is the maximum number of iterations.

According to the present invention, it is better than average iteration in a confidence spread decoder with a weighted Non Accurate Binary Accurate (RA) code or a Low Binary Low Density Parity Check (LDPC) code on the finite field GF (q). Efficient decoding can be performed with low computational complexity.

1 shows a Tanner graph of a confidence spreading decoder.
2 shows a Tanner graph of the WNRA code on the GF 4.
3 is a decoding flowchart of a non-binary reliable spreading decoder in accordance with an example of the present invention.
4 is a flowchart showing a criterion for stopping repetitive decoding according to an example of the present invention.
5 shows the transition of D (m) according to iteration upon successful decoding.
6 shows the transition of D (m) according to iteration when decoding fails.
7 is a graph showing the FER when the stopping criterion according to the present invention is applied, when the stopping criterion using variance is applied, and when the stopping criterion is not applied.
8 is another graph illustrating the FER when the stopping criterion according to the present invention is applied, when the stopping criterion using variance is applied, and when the stopping criterion is not applied.
9 is a graph showing the computational complexity of the check node operation in FER 10 ^-1 as q increases.
10 shows a decoding apparatus for performing decoding including an abort criterion according to the present invention.

Hereinafter, some embodiments will be described in detail with reference to exemplary drawings. In adding reference numerals to the components of each drawing, it should be noted that the same reference numerals are assigned to the same components as much as possible even though they are shown in different drawings. In the following description of the embodiments of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present disclosure rather unclear.

In addition, in describing the component of this specification, terms, such as 1st, 2nd, A, B, (a), (b), can be used. These terms are only for distinguishing the components from other components, and the nature, order or order of the components are not limited by the terms.

The trust propagation decoder uses a message-passing algorithm to model a given sign into a Tanner graph consisting of nodes and edges, and then to the nodes of the Tanner graph. Iterative decoding is performed repeatedly transmitting and receiving a message, which is information received by a receiver, between nodes. The value of the message is a decoder that becomes increasingly reliable as it performs iterative decoding. For example, when 0 or 1 information is sent from the transmitter, the receiver's decoder first models like a graph according to the structure of the code, and then repeatedly transmits information between nodes with the probability of getting 0 and the probability of getting 1 as a message. Based on this message, it is determined whether it is 0 or 1 after repeated decoding.

The non-binary confidence spread decoder not only considers the probabilities for 0, 1, but also q symbols on the finite field GF (q), i.e., 0, 1, 2,... For example, the probabilities of the symbols represented by q-1 are regarded as a message, and information is exchanged between nodes on the graph in vector units. This vector is called a message vector. There are two types of messages: incoming and outgoing nodes. These messages are updated on every iteration by a function dependent on the messages sent from the edges connected to one node, depending on the nature of the node. Here, updating means updating a message leaving the specific node by a function of messages coming into the specific node.

1 shows a Tanner graph of a confidence spreading decoder.

Referring to FIG. 1, those represented by arrows mean that the edges are connected to each other, and when a message indicating the outgoing message from the node marked '+' is updated to the node X ₀ , the node is entered from the nodes X ₁ to X _{K to the} node '+'. Update by function expression of messages.

In the LDPC code, the nodes represented in the graph are divided into two types according to the characteristics of the code, which is a check node and a variable node. In particular, in the WNRA code, variable nodes are divided into code nodes and information nodes according to their position on the graph.

2 shows a Tanner graph of the WNRA code on the GF 4.

Referring to FIG. 2, the information node substantially corresponds to the symbols of the received signal. If the message of the received signal includes 100 symbols, 100 information nodes are drawn on the graph. A code node is a node corresponding to code symbols generated by encoding received symbols with a WNRA code. For reference, an evidence node provides information or probability about a channel, and always transmits a fixed channel value without being updated.

The relationship between the information symbol transmitted from the transmitter and the code symbol as a result of the encoding or the relationship between the information node and the code node has a close relationship based on the structure of the WNRA code or LDPC code to be used. A node that checks whether this close association, or the condition that the code structure must satisfy, is a check node.

The check node represents the relationship between the information symbol transmitted from this code and the coded code symbol, and performs a function of enabling a more reliable message to be taken while repeatedly performing decoding.

3 is a decoding flowchart of a non-binary reliable spreading decoder in accordance with an example of the present invention.

According to FIG. 3, a message vector having a probability of each symbol included in a message received from a received signal as an element is transmitted from a variable node to a check node (S310). Subsequently, the check node checks the reliability based on the probability of each symbol (S320), and transmits another message vector from the check node to another variable node (S330). The message vector and the other message vector are updated every iteration, in particular the other message vector is represented as a function of the value of the element of the message vector sent to the check node. When the interruption criterion is satisfied while performing the iterative decoding, the iteration is terminated and the iterative decoding is stopped (S340). If the stop criterion is not satisfied, the message vector and the other message vector are repeatedly transmitted to perform repeated decoding for decoding the value of the message of the received signal based on the reliability (S350).

Hereinafter, the interruption criterion for repetitive decoding will be described.

The stopping criterion refers to an algorithm that finds a point for which iterative decoding does not need to be repeated for messages with high reliability while performing iterative decoding. According to the stopping criterion according to the present invention, it is determined whether the message vector is successfully decoded by comparing the value of the message vector in a non-binary reliable spreading decoder with a given threshold. Although the present invention considers the WNRA code on GF (q), it can also be applied to the LDPC code.

4 is a flowchart showing a criterion for stopping repetitive decoding according to the present invention.

Referring to FIG. 4, first, variables and thresholds are initialized (S410), and a message vector is updated (S420). As such, when message vectors in a non-binary confidence spreading decoder are updated every iteration, the updated message vectors tend to increase in value over one element of the vector each time the iteration proceeds. There is this. In the WNRA code on GF (q), the number of repetitions is r, and the number of information nodes is N, and at least one of the elements of the rN message vectors in the m (1 ≤ m ≤ N _I ) th iterations is separated. A number T (m) (0 ≦ T (l) ≦ rN) of message vectors having elements larger than θ _S (0 ≦ θ _S ≦ 1), which is defined as a threshold, is calculated (S430). Since T (m) is the number of message vectors that can be determined to have converged sufficiently among the rN message vectors, it is a criterion for determining that all message vectors have sufficiently converged.

Subsequently, when m ≥ 2, D (m) is calculated, and the definition of D (m) is as shown in Equation 1 below (S440).

D (m) means the number of sufficiently converging message vectors increased in the current iteration from the previous iteration each time iteration ends. At this time, it is possible to divide the transition according to the iteration of D (m) into the case of success or failure of decoding.

Value of D (m) for WNRA code on GF (4) with r = 3, N = 1260, NI = 50 when 4-ary frequency shift keying (FSK), noncoherent detection is used in AWGN channel. The results of the calculation through the experiments are shown in Figures 5 and 6.

5 shows the transition of D (m) according to iteration upon successful decoding. According to FIG. 5, if decoding succeeds, the value of D (m) maintains a positive value during iteration and then converges to zero.

As described above, when D (m) = 0, it means that the value of T (m) does not change even if iteration proceeds (S450).

On the other hand, decoding may fail, and in this case, it should be possible to stop the repeated decoding. 6 shows the transition of D (m) according to iteration when decoding fails.

If decoding fails, the value of D (m) fluctuates within a certain range, so if this phenomenon is observed continuously, iteration can be stopped. In order to understand this trend, θ _D (0 ≦ θ _D ≦ 1) is defined as a difference threshold and θ _O (0 ≦ θ _O ≤ 1) as an oscillation counting threshold.

When the absolute value of D (m) is smaller than the value of N multiplied by the predetermined difference threshold value θ _D (S460), the temporary counter value c is increased by one (S470), and the temporary counter value is previously If it is greater than the determined vibration number threshold θ _O , the iteration being performed is stopped (S480).

Such a non-binary confidence spreading algorithm may be a non-binary confidence spreading algorithm of a weighted non-binary repeat accumulate (RA) code on the finite field GF (q), but a nonbinary low density parity check code on the finite field GF (q). It may be a non-binary confidence spreading algorithm of Density Parity Check code.

In particular, in a weighted non-binary RA code, that is, a WNRA code, a variable node can be divided into an information node and a code node. When a variable node is an information node, another variable node transmitted through a check node is a code node. Can be.

The results of computational experiments to confirm the effectiveness of the stopping criteria according to the present invention are described below. Frame error rates are compared in decoding using the distributions of message vectors, which are the stopping criteria method in the existing non-binary confidence spreading decoder, and decoding without using the stopping criteria.

The method using the variances of the message vector uses the variance of the elements of all the message vectors passed from the check node to the variable node in the non-binary confidence spreading decoder. This means that if the sum of the variances of all the message vectors oscillates as the iterative decoding proceeds, the number of oscillations is determined and the iteration is stopped if the number of oscillations exceeds the given threshold. The parameters used in this computational experiment are as follows.

Modulation Method: q-ary FSK (q = 4, 8, 16, 32)

Information frame length: 2520 bits

Code: WNRA code on GF (q) (r = 3, q = 4, 8, 16, 32)

Decoding Method: Non-Binary Confidence Spreading Decoding

Interleaver: Uniform Interleaver

Channel: Additive white Gaussian noise (AWGN).

The stopping criterion proposed in the present invention requires three threshold values. To select this particular threshold, θ _S is 0.125 steps from 0.250 to 0.875, θ _D is spaced from 0.005 to 0.050 at intervals of 0.005, and θ _O is 5 intervals from 20 to 40 for each combination of three thresholds. Computational experiments were performed. The result is a combination of thresholds with a signal-to-noise loss of less than 0.05 dB and the smallest average iteration count compared to no frame break rate (FR) 10 ^-1 . Θ _S = 0.750, θ _D = 0.020, and θ _O = 25.

In order to compare with the existing halting reference method using variance, when applying the halting reference method using variance, the performance is adjusted so that the SNR loss is within 0.05 dB compared to the non-interruption criterion based on FER 10 ^-1 . By comparison.

7, 8, and 9 are results of computational experiments showing FER performance in a channel environment according to the parameters by comparing before and after using a decoding method using a break criterion according to an example of the present invention.

FIG. 7 shows the present invention when N _I = 50 in a system of AWGN channel, information bit length = 2520, r = 3, 4-ary and 8-ary WNRA codes, q-ary FSK, noncoherent detection. This is a graph showing the FER when the stopping criterion according to the method is applied, when the stopping criterion using variance is applied, and when the stopping criterion is not applied.

8 shows the present invention when N _I = 50 in a system of AWGN channel, information bit length = 2520, r = 3, 16-ary and 32-ary WNRA codes, q-ary FSK, noncoherent detection. This is a graph showing the FER when the stopping criterion according to the method is applied, when the stopping criterion using variance is applied, and when the stopping criterion is not applied.

Figure 9 shows that q increases when N _I = 50 in a system of AWGN channel, information bit length = 2520, r = 3, 16-ary and 32-ary WNRA codes, q-ary FSK, noncoherent detection. Therefore, it is a graph showing the computational complexity of the check node operation in FER 10 ^-1 when applying the stopping criteria according to the present invention, applying the stopping criteria using variance, and not applying the stopping criteria.

In order to grasp the degree of complexity improvement as q increases according to the interruption criteria of the present invention, when the average number of iterations is represented by N _av , the computational complexity of all check node operations is represented by O (q ² N _av N) and the decoding complexity Set the standard.

According to FIG. 7 and FIG. 8, SNR is compared with the case in which the stopping criterion according to the present invention is not applied based on FER 10 ^-1 when the stopping criterion using variance is applied to compare with the existing stopping criterion method using variance. Performance was adjusted so that the signal to noise loss was within 0.05 dB.

According to FIG. 9, as the q increases in FER 10 ^-1 , the proposed stopping criterion improves the complexity as q increases compared to the case where no stopping criterion is applied and the stopping criterion using variance is applied to the q-ary WNRA code. Indicates that the degree is higher.

The interruption criterion using variance is the sum of the variance of message vectors from the check node to the information node, which is the sum of the squares of the elements. The number of multiplications per iteration is qrN and the number of additions is (q-1) rN. When the threshold value of θ _S is set in the stopping criterion according to the present invention, a value that can be expressed as a sum of powers of 2 can be calculated by a bit-wise comparison operation. Therefore, since the number of bit-wise comparison operations per iteration is qrN, the additional computation complexity is drastically reduced compared to the conventional interruption reference method.

10 shows a decoding apparatus for performing decoding including an abort criterion according to the present invention.

According to FIG. 10, the decoding apparatus may include an equalizer 1001, a deinterleaver 1003, a decoder 1005, an interleaver 1007, and. In this case, the decoder 1005 which performs repeated decoding includes an interruption reference algorithm according to the present invention.

Received messages with channel information are first passed through equalizer 1001, which equalizes the distortion that occurs during amplification or transmission of the signal. The interleaver 1007 converts a cluster error that may occur when transmitting traffic through a wireless section into a random error to facilitate error correction, and the deinterleaver 1003 rearranges the interleaver into an interleaver and outputs the output signal in the original order. Change. The value output from the deinterleaver 1003 is input to the decoder 1007, and the decoder 1007 performs repetitive decoding. The pre-information is calculated using post information, and the estimated data bits are encoded. Outputs the reliability of the bit. The reliability of the encoded bit, which is additional information, is input to the interleaver 1007 and interleaved. The reliability of the interleaved encoded bits is combined with the original received signal and inputted to the equalizer 1001 to repeat the decoding process. The decoding process is generally repeated a predetermined number of times, but stops when the interruption criterion according to the present invention is satisfied. The decoder can also be applied to all iterative decoding apparatuses that perform symbol decoding using symbol interleaver and symbol decode.

As described above, the stopping criterion according to the present invention is a separation threshold in which a value of an element of a message vector is predetermined in an iteration of m (1 ≦ m ≦ N _I , where N _I is the maximum number of iterations) of repeated decoding. Determine the number of message vectors T (m) with values greater than (θ _S ) (0 ≤ θ _S ≤ 1), where D (m) = T (m)-T (m-1) Is determined, and if the value of D (m) is 0, the iterative decoding is stopped, and if the value of D (m) is smaller than the predetermined difference threshold value θ _D , the temporary counter value is one by one. If the temporary counter value is larger than the predetermined vibration number threshold θ _O , the repetition of decoding being performed is stopped.

The foregoing description is merely illustrative of the technical idea of the present invention, and various changes and modifications may be made by those skilled in the art without departing from the essential characteristics of the present invention. Therefore, the embodiments disclosed in the present invention are not intended to limit the technical idea of the present invention but to describe the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments. The protection scope of the present invention should be interpreted by the following claims, and all technical ideas within the equivalent scope should be interpreted as being included in the scope of the present invention.

Claims (8)

A decoding method for decoding a received signal received from a receiver using a non-binary confidence spreading algorithm,
Transmitting a message vector including a probability of each symbol included in the message of the received signal as an element from a variable node to a check node;
Checking reliability at the check node based on a probability for each symbol;
Transmitting another message vector from the check node to another variable node, wherein the other message vector is updated every iteration according to the value of an element of the message vector transmitted to the check node; And
Updating the message vector for each iteration and performing repeated decoding of the value of the message of the received signal based on the reliability;
In the m (1 ≤ m ≤ N _I ) th iteration of the iterative decoding, a message vector having a value greater than a predetermined separation threshold θ _S (0 ≤ θ _S ≤ 1) of the element of the message vector Determine the number T (m) of
Using T (m), when m ≥ 2, D (m) is determined such that 'D (m) = T (m)-T (m-1)',
If the value of the D (m) is 0, the decoding method, characterized in that the iterative decoding is stopped.
Where N _I is the maximum number of iterations. The method of claim 1,
When the value of D (m) is smaller than the product of the predetermined difference threshold value θ _D and the number N of information nodes, the temporary counter value is increased by one, and the temporary counter value is a predetermined vibration number threshold value ( If it is greater than θ _O ), the decoding method is stopped. The method of claim 1,
And the non-binary confidence spreading algorithm is a non-binary confidence spreading algorithm of weighted non-binary repeat accumulate (RA) code on a finite field. The method of claim 1,
The non-binary confidence spreading algorithm is a non-binary confidence spreading algorithm of a nonbinary low density parity check code on a finite field.
The variable node is an information node, and the other variable node is a code node. A decoding apparatus for iteratively decoding using a non-binary confidence spreading algorithm,
A decoder for detecting a code by performing the iterative decoding;
The decoder has a message whose value of an element of the message vector is greater than a predetermined separation threshold θ _S (0 ≦ θ _S ≦ 1) in the m (1 ≦ m ≦ N _I ) iterations of the iterative decoding. Determine the number of vectors T (m),
Using T (m), when m ≥ 2, D (m) is determined such that 'D (m) = T (m)-T (m-1)',
And if the value of D (m) is 0, the decoding decoding is stopped.
Where N _I is the maximum number of iterations. The method of claim 5, wherein
When the value of D (m) is smaller than the product of the predetermined difference threshold value θ _D and the number of information nodes N, the temporary counter value is increased by one, and the temporary counter value is a predetermined vibration number threshold value ( If it is greater than θ _O ), it is characterized in that the decoding decoding is stopped. The method of claim 5, wherein
And the non-binary confidence spreading algorithm is a non-binary confidence spreading algorithm of weighted non-binary repeat accumulate (RA) code on a finite field. The method of claim 5, wherein
And the non-binary confidence spreading algorithm is a non-binary confidence spreading algorithm of a nonbinary low density parity check code on a finite field.

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