KR20020058757A - Decoding algorithm using map algorithm - Google Patents

Abstract

PURPOSE: A decoding algorithm using a MAP(Maximum A Posteriori) algorithm is provided to improve a processing speed of data by using a decoding algorithm with a fast decoding speed. CONSTITUTION: A decoder receives an encoded signal and decodes the encoded signal by using a decoding algorithm. The decoder performs a decoding process by using the decoding algorithm including a MAP algorithm. The decoder includes a MAX function and a Viterbi algorithm. The decoder uses the Max function and the Viterbi algorithm in the decoding process when generating an output value to decode the encoded signal. The decoder generates the output value by using a natural log value when generating the output value to decode the encoded signal. The decoder uses an ACS(Add-Compare-Select) module in a forward metric recursion process a backward metric recursion process to generate the output value of the decoder.

Description

Decoding Algorithm using MAP Algorithm

The present invention relates to a decoding algorithm used in a SISO decoder (Soft-Input Soft-Output Decoder) for error correction caused by the channel, and more particularly to a MAP (Maximum A) that reduces the complexity of the system implementation and increases the decoding speed. Posteriori: hereinafter referred to as MAP) relates to a decoding algorithm using.

As the development of communication systems and their proliferation have increased, various decoders and decoding algorithms have been developed to prevent channel errors in communication systems.

1 is a block diagram of a conventional turbo coder, in which two Recursive Systematic Convolutional (RSC) coders, which make a parity symbol using an input consisting of a frame of N information bits, are connected in parallel. It can be configured in a desired size in consideration of the error correcting ability.

1 is a Recursive Systematic Convolutional (RSC) coder that makes a parity symbol (Y _1k , Y _2k ) 114, 120 using an input consisting of a frame of information bits (X _k ) 110. (First RSC encoder, second RSC encoder) 112, 118; And

An interleaver 116 is provided which reverses the order of data entered into the second RSC encoder, and treats burst errors that occur continuously as random errors that occur discontinuously.

FIG transmission of the input data from the turbo code encoder shown in Figure 1 process, accepts noise plus input information data _{X k (110), X k} (110) output process of outputting the X _k (110) into one output and;

A Y _1k (114) output process of inputting the information data X _k (110) to the first RSC encoder (112) and outputting parity information Y _1k (114) with noise added by the first RSC encoder (112); And

The interleaver 116 having the same size as a frame of N information bits receives the information data X _k 110, and the second RSC encoder 118 receives the output value of the interleaver 116 and receives Y _2k (120). Y _2k (120) outputting process is provided.

Therefore, the output of the turbo encoder has dual parity information due to the output (Y _2k ) modified through the interleaver 116 as well as the output (Y _1k ) of the first RSC encoder, and is output by the output process The transmitted X _k 110 and Y _1k 114 and Y _2k 120.

FIG. 2 is a block diagram of a conventional turbo code decoder. The received signals X _k 110, Y1 _k 114, and Y _2k 120 encoded by turbo codes through the encoding process of FIG. 1 are decoded using a decoding algorithm. Decode

FIG. 2 receives X _k 110 and Y _1k 114 encoded through the encoding process of FIG. 1 and uses a decoding algorithm to obtain a Log-Likelihood Ratio (LLR) value. A first decoder (212) outputting (214);

From the first decoder 212 Input 214, By interleaving the value (214) An interleaver 216 for outputting 220;

From the interleaver 216 A second decoder 218 receiving 220 and Y2k 120 and outputting LLR_2 as an LLR value using a decoding algorithm;

A first deinterleaver 222 that receives LLR_2 from the second decoder 218 and outputs Zk 210; And

And a second deinterleaver 224 that receives LLR_2 from the second decoder 218 and restores the interleaved data to its original state and outputs a decoded signal.

In the decoding by the turbo code decoder of FIG. 2, the output values Z _k 210 and the X _k 110 and Y _1k 114 of the first deinterleaver are converted to the first decoder 212 for repeated decoding. Send and decode again.

The second deinterleaver 224 generates a hard output by deinterleaving the LLR_2 and determining that the values are 1 if the values are greater than 0 and 0 otherwise.

The MAP algorithm was proposed in 1993 by Berrou (C. Berrou, A. Glavieux and P. Thitimajshima, 'Near shannon limit error-correcting coding and decoding: turbo codes' Proceedings of ICC '93, Geneva, Switzerland, May 1993). An algorithm that calculates probability values for all paths and outputs soft decision data values for information bits. The decoding algorithm changes according to the size of an information frame.

3 is a diagram illustrating calculation of a forward metric probability value for a conventional MAP algorithm, and a forward metric probability calculation equation of the MAP algorithm is shown in Equation 1) described below.

Equation 1)

In the process of calculating the forward metric probability value of the MAP algorithm of FIG. 3, the forward metric probability value is calculated by summing all the pass metrics of the branch coming into the m state.

FIG. 4 is a diagram illustrating calculation of a backward metric probability value for a conventional MAP algorithm, and the backward metric probability calculation equation is the same as Equation 5 described below.

Equation 2)

The back metric probability calculation process of the MAP algorithm shown in FIG. 4 uses a SUM operation as in the forward metric probability calculation process of FIG. 3.

On the other hand, SOVA (Soft-Output Viterbi Algorithm) calculates the soft decision data value through the relationship with the competitive path, and the time delay required for decoding under the assumption that the delay in the channel and the decoding process is not considered is 7 It is about 9 times and is inferior to decoding performance compared with MAP algorithm.

In theory, the MAP algorithm can accurately estimate the A Posteriori Probability (APP) probability value for each information bit. In practice, however, the MAP algorithm is limited in estimating the exact probability value because the dynamic range of very complex computational and probability values is very large.

To overcome this problem, to reduce the complexity of the MAP algorithm, there are Max-Log-MAP algorithm and Log-MAP algorithm operating in the log area.

The Max-Log-MAP algorithm is a combination of two Viterbi Algorithm algorithms that perform maximum likelihood decoding (MLD) through variables called Branch Metric (BM) and Path Metric (PM). Similarly, the output value LLR (Log-Likelihood Ratio) can be obtained by using the result value of the two processes properly, and the Log-MAP algorithm extends the Max-Log-MAP algorithm and operates in the log domain.

In general, the SOVA, the Log-MAP algorithm, and the Max-Log-MAP algorithm are similar in complexity to their implementation and have a complexity of about 2 to 4 times that of the conventional Viterbi algorithm, which requires a lot of memory. Performance of SOVA <Max-Log-MAP <Log-MAP Appears in MAP order.

As such, the Log-MAP algorithm and the Max-Log-MAP algorithm are superior to the SOVA algorithm in terms of performance, and have similar advantages to the MAP algorithm.

However, in terms of complexity, the complexity is reduced compared to the MAP algorithm, but has a higher complexity than the Viterbi algorithm.

Accordingly, the present invention provides a decoding algorithm that is similar in performance to the existing MAP algorithm by applying the MAX function and the Viterbi algorithm to the MAP algorithm having the best performance in view of the above-described problems, but has a low complexity and a fast decoding speed when implemented. Accordingly, an object of the present invention is to provide a decoding algorithm using a MAP algorithm, which improves performance of a communication system requiring channel error correction, improves data processing speed, and reduces complexity of an entire circuit.

In addition, the performance is similar to that of the existing Log-MAP algorithm, and replaced with an ACS (Add Compare and Select) module that implements the addition operation in half compared to the module for calculating each memory state value of the existing Log-MAP algorithm. The purpose of the present invention is to provide a decoding algorithm using a MAP algorithm which reduces complexity in system implementation and has a fast decoding speed.

1 is a block diagram of a conventional turbo coder.

2 is a block diagram of a conventional turbo code decoder.

3 illustrates the calculation of a forward metric probability value for a conventional MAP algorithm.

4 illustrates calculation of backward metric probability values for a conventional MAP algorithm.

5 is a diagram illustrating calculation of a forward metric probability value of an SMAP algorithm applied to the present invention.

6 is a block diagram showing the backward metric probability calculation of the SMAP algorithm applied to the present invention.

7A shows a graph comparing the performance of the conventional MAP algorithm and SMAP. When the data rate R is 1/3 and the frame size is fixed at 1204 bytes, the number of repeated decoding times is changed once or three times. A graph showing the results of a simulation comparing the performance of the MAP and SMAP algorithms.

FIG. 7B is a graph illustrating performance comparison between a conventional MAP algorithm and a SMAP. FIG. 7B is a graph showing the results of a simulation comparing the performance of a system using the MAP algorithm and a system using the SMAP algorithm when the frame size is small. Figure.

FIG. 7C is a graph illustrating performance comparison between a conventional MAP algorithm and a SMAP. FIG. 7C is a graph illustrating performance comparison simulation results of a MAP algorithm and a SMAP algorithm when a transmission rate is increased from 1/3 to 1/2.

<Description of Symbols for Major Parts of Drawings>

100: turbo coder 110: information bits

112, 118: RSC encoder 114, 120: parity bit

116, 216: interleaver 200: turbo code decoder

210: additional information bits 212, 218: decoder

214, 220 LLR values 222, 224 deinterleaver

In the decoding algorithm of the decoder to receive and decode the coded code signal for achieving the above object,

When the decoder calculates an output value of a decoder for decoding a code signal, the decoder includes a MAX function and a Viterbi algorithm in a decoding process by the MAP algorithm.

According to another embodiment of the present invention, the decoding algorithm of the present invention is further characterized by calculating the output value by using a natural logarithmic function when the decoder calculates an output value of a decoder that decodes a code signal. .

The above objects, features and advantages will become more apparent from the following detailed description taken in conjunction with the accompanying drawings. Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings. The SMAP algorithm and the SLMAP algorithm, which are the decoding algorithm according to the present invention, are applied to the turbo code decoder shown in FIG. The process will be described with reference to FIGS. 5 to 6.

The decoding algorithm according to the present invention is applied to the decoders 212 and 218 to decode the codeword, and the output value LLR of the decoder outputted by the decoding algorithm is a forward metric probability and a pass. Calculated by Path Metric Recursion and Backward Metric Recursion.

The main purpose of the MAP algorithm is to supply the LLR of the posterior probability that the information bit becomes 0 with respect to the posterior probability that the information bit becomes 1, and the process of obtaining the LLR of the MAP algorithm is as shown in Equation 3 below.

Equation 3

In Equation 3), when the memory state is m at time k, and the memory state of k-1 is m ', m and m' have a value between 0 and 2 ^M-1 , and M is the value of the encoder. The number of memories.

here Means received data.

The LLR value of the SMAP (Simplified MAP) algorithm, which is a decoding algorithm using the MAP algorithm according to the preferred embodiment of the present invention, is represented by Equation 4) described below by Equation 3).

Equation 4

The LLR value of the SMAP algorithm shown in Equation 4) takes the max function in Equation 3) to calculate the LLR.

FIG. 5 is a diagram illustrating calculation of a forward metric probability value of an SMAP algorithm applied to the present invention, and a forward metric calculation equation is the same as Equation 5 described below.

Equation 5)

Equations 1) and 5) are when Is, when Is initialized to

Referring to the process of calculating the forward metric probability value of the SMAP algorithm of FIG. 5, the MAP algorithm uses a SUM operation, while the SMAP algorithm uses an Add Compare and Select (ACS) module to pass path matrices into branches. By comparing and then selecting one pass metric value.

FIG. 6 is a block diagram illustrating the calculation of a backword metric probability value of an SMAP algorithm applied to the present invention, and the backward matrix probability calculation equation is the same as Equation 6) described below.

Equation 6

As for the process of calculating the back metric probability of the SMAP algorithm shown in FIG. 6, the ACS module is used as in the forward metric calculation process of FIG. 4. when Is, when Is initialized to

Equations 5) and 6) show that the SMAP algorithm reduces the addition operation from 2 ^{M + 1} to 2 ^M when calculating the metric for each time, and the branch transition probability is expressed by Equation 7 below. Same as

Equation 7

The first term on the right side of Equation 7) indicates the channel transition probability, the second term indicates the probability determined by the encoder, and the third term indicates the state transition probability obtained by using the probability density function of the channel.

7A to 7C are graphs comparing performances of conventional MAP algorithms and SMAPs, and applying the MAP algorithm and SMAP algorithm represented by the above equation to the turbo code encoder of FIG. 1 and the turbo code decoder of FIG. 2. The simulations show the performance comparison of the two algorithms.

7A to 7C illustrate an iter indicating the number of iteration decodings of an decoder, an R indicating a transmission rate, an FS indicating a frame size, a frame size (FS), a signal-to-noise ratio (SNR), and a bit error rate. : BER).

7A to 7C are simulations by increasing the signal-to-noise ratio by 1dB when iter is 1, and simulating by increasing the signal-to-noise ratio by 0.5dB when the iter is 3 times. As the polynomial required for encoding, we used (17, 3) code which requires 3 memories. Also, as in Berrou's paper (C. Berrou, A. Glavieux and P. Thitimajshima, 'Near shannon limit error-correcting coding and decoding: turbo codes' Proceedings of ICC '93, Geneva, Switzerland, May 1993) Since it is impossible to apply it to a real system when it is large enough, in the said simulation, the frame size was fixed to 1024 bytes or 254 bytes.

The reason why the number of repeated decoding is fixed to one or three times in the simulations of FIGS. 7A to 7C is that data decoding is impossible in real time when the number of repeated decoding is four or more. Although large, increasing the number of iteration decodes shows that the performance is improved by the theoretical bit error rate (BNR) calculation formula, but it is impossible to investigate the optimal number of iterations, the generated polynomials, and the frame size. The simulation was performed by selecting a feasible size.

FIG. 7A is a graph showing the results of a simulation comparing the performance of the MAP algorithm and the SMAP algorithm when the data rate R is fixed at 1/3 and the frame size is fixed at 1204 bytes, and the number of repeated decoding is changed once or three times. FIG. .

Referring to the simulation results of FIG. 7A, when the number of iterations is one or three times, the MAP algorithm and the SMAP satisfy a bit error rate of approximately 10 ^ -5 at a signal-to-noise ratio of 2 dB and 4 dB, respectively. The performance of the SMAP algorithm, which is simpler than the algorithm, is nearly identical.

FIG. 7B is a graph showing the results of simulations comparing the performances of the system using the MAP algorithm and the system using the SMAP algorithm when the frame size is small. The frame size is fixed to 254 bytes and other experimental conditions. Was carried out under the same conditions as in FIG. 7A.

Referring to the simulation results of FIG. 7B, when the number of iterations is one or three times, the MAP algorithm and the SMAP algorithm satisfy a bit error rate of approximately 10 ^ -6 at a signal-to-noise ratio of 3 dB and 5 dB, respectively. In the third time, the turbo code decoding method using the SMAP algorithm has a gain of 0.5dB over the turbo code decoding method using the MAP algorithm.

7c is a diagram showing the simulation results of the performance comparison between the MAP algorithm and the SMAP algorithm when the data rate is increased from 1/3 to 1/2. The frame size is fixed to 1024 bytes, and the number of repeated decoding times is changed once or three times. The simulations are performed and the results show that the performance of the MAP algorithm and the SMAP algorithm is almost the same.

The SLMAP (Simplified Log-MAP) algorithm, which is a decoding algorithm using the MAP algorithm according to another embodiment of the present invention, is a natural algorithm derived from the SMAP algorithm, and Equation 8) described below is a branch of the SMAP algorithm. The natural logarithm to the probability of transition.

Equation 8

The last term exponent of Equation 8) is the state transition probability, which is calculated by Equations 9) and 10) described below using additional information L_a (d_k) and is the most important part for improving performance.

Equation 9

(10)

Taking natural logarithm to Equation 4) showing the forward metric probability calculation method of SMAP, Equation 11) is described below.

Equation 11

Equation 11) When is initialized to m = 0, when Is initialized to

If the natural log is taken into Equation 6) showing the method for calculating the back metric of the SMAP algorithm, Equation 12) is described below.

Equation 12

Equation 12) When is initialized to m = 0, when Is initialized to

The LLR calculation method of the SMAP algorithm of Equation 2) can be rewritten as Equation 13) described below.

Equation 13

In Formulas 11) to 13),

In this case, the LLR of the SMAP algorithm is represented by the following equation (14).

Equation 14

The forward metric probability calculation method of the SLMAP algorithm is as shown in Equation 15).

Equation 15

A backword metric probability calculation method of the SLMAP algorithm is as shown in Equation 16 below.

Equation 16

When calculating formulas to derive the SLMAP algorithm The value of is calculated recursively by Equation 17) described below.

(17)

In Equation 17) To, Means.

As described above, according to the present invention, by applying the MAX function and the log function to the conventional MAP algorithm, by providing a SMAP algorithm and a SLMAP algorithm with similar complexity and performance than the MAP algorithm, data processing of a communication system such as IMT-2000 This has the advantage of improving speed and reducing the complexity of the overall circuit implementation.

In addition, by applying to a detector of a high-density recording system, there is an advantage of shortening the reproduction time and improving the quality of the reproduction data.

In addition, preferred embodiments of the present invention are disclosed for the purpose of illustration, those skilled in the art will be able to various modifications, changes, additions, etc. within the spirit and scope of the present invention, such modifications and modifications belong to the following claims You will have to look.

Claims (3)

In the decoding algorithm of the decoder for receiving and decoding the coded code signal, And a maximum function and a Viterbi algorithm during decoding by the MAP algorithm when the decoder calculates an output value of the decoder for decoding a code signal. The method of claim 1, And calculating the output value by using a natural logarithmic function when the decoder calculates an output value of the decoder that decodes a code signal. The method according to claim 1 or 2, Decoding algorithm using a maximum post-decoding (MAP) algorithm, characterized in that it comprises an Add Compare and Select module for calculating the forward metric probability and the back metric probability for calculating the output value of the decoder. .