KR0170199B1 - Viterbi decoder - Google Patents

Abstract

The present invention relates to a decoding method of a cyclic convolutional code that improves transmission efficiency on a communication path by modifying a survivor path in a Viterbi decoder, thereby eliminating transmission loss present in the convolutional code. After determining whether to decode using the condition that the states should be the same, the first process of decoding the maximum likelihood (ML) of one block of input information, and the initial state and the final state of the survivor path after performing the maximum likelihood decoding. If the two states are different from each other by comparing the same, the second step of modifying the survivor path to the second different path to make the two states the same, and cycle through the received symbol string when ML decodes the input information of one block It consists of a 3rd process of shifting and ML decoding.

Description

Decoding method of cyclic weaving code

1 is a conceptual diagram illustrating a conventional zero tail weaving encoder.

2 is a conceptual diagram illustrating a tail biting weaving encoder according to the prior art.

3 is a performance curve according to the decoding distance of the convolutional code.

4 is Butterfly, which is the basic configuration of Trellis.

5 is a decoding characteristic by DTCC method.

6 shows an example of state transition in the DTCC method.

7 is a circular weaving encoder used in the simulation.

8 shows the performance of the cyclic weaving code with d _free = 10, m = 7, r = 1.2, g ⁽¹⁾ = 237, g ⁽²⁾ = 345, and L = 32.

9 shows statistics in the proposed decoding method.

The present invention relates to a decoding method of a cyclic convolutional code, and more particularly, to improve transmission efficiency on a communication path by eliminating a transmission loss present in the convolutional code by modifying a survivor path in a vitervi decoder. It relates to a decoding method of a circular convolutional code.

In general, a transmitting end of a digital wireless communication system includes a source encoder, a channel encoder, a modulator, and the like, and a receiving end includes a demodulator, a channel decoder, a source decoder, and the like.

At this time, the source encoder and the decoder reduces the data to reduce the occupied band on the transmission channel, and restores the original data. On the other hand, the modulator and the demodulator are called a modem together, and is a device for carrying the modulated data on a carrier frequency to transmit in a spread frequency band, or to receive and demodulate from a spread frequency band.

In addition, the channel encoder and decoder encode or decode a channel to correct an error on the channel, which is called channel coding.

In this case, the channel encoder plays a role of adding redundancy to a signal to be transmitted on a channel, and the channel decoder corrects and decodes an error added in a channel from the data having redundancy. Among the channel coding techniques, a convolutional code is widely used.

In this case, the convolutional coding scheme encodes all signals to be transmitted by the transmitting end (assuming the magnitude of this signal is k) and additionally encodes and transmits '0' bits by the constraint length, thereby receiving the register from the receiving end. Analyze the transition (Trellis Diagram), which shows all possible states where the state starts from the '0' state and ends in the '0' state, and then corresponds to the optimal path of the paths on the transition. Decoding with a codeword.

At this time, the maximum likelihood decoding (ML) method is used as the decoding method.

In this way, a convolutional code that adds '0' bits of constraint length 'm' to the end of input information of 'k' bits and encodes each information bit into 'n' symbols is (n, k, m) ZT ( Zero Tail) Weaving code.

The symbol refers to a result of encoding one input bit. In addition, the added '0' bit is called a tail bit.

Two definitions are commonly used in the definition of the constraint, one of which is based on the viewpoint of the number of input bits used to make the output symbol of the encoder, and the other is the shift register used to construct the encoder. In the latter case, 'm' constituting the coder of the convolutional code is referred to as a constraint length or constraint length.

On the other hand, a relationship of 'k = m + 1' is established between the constraints according to the above two viewpoints.

For example, a (n, k, m) convolutional code is transmitted on a channel by mapping input information of 'k' into 'n' symbols, where transmission loss is 'm', When the length is 'L', the transmission loss rate is m / (m + L).

The large transmission loss here means that the bandwidth occupied by the communication channel is increased.

In other words, even when communication is possible in the frequency band of 30 kHz, communication in a wider frequency band is required, which makes it difficult to effectively use a constant frequency resource. Therefore, in this method, the larger the length of the constraint field or the smaller the size of data to be encoded, the greater the loss on the transmission channel due to additional information transmission.

Referring to FIG. 1 attached to the encoding process of the Zero Tail (ZT) convolutional encoder as described above is as follows.

FIG. 1 is an exemplary diagram for explaining a (2, 1, 6) ZT convolutional encoder using a conventional method as an example, and the (2, 1, 6) convolutional encoder is one bit input signal mapped to two symbols and constrained. The length is 6, and the ratio is 1/2.

When the illustrated adder is called a binary adder (Modulo-2 ADDER), (a) denotes a process of encoding the first input signal and (b) denotes a process of encoding the last signal.

In the case of such a ZT convolutional code, since all the input information bits are encoded, the encoding is performed by adding 6 bits of 0, resulting in a loss of a bit rate.

Therefore, when performing encoding by the ZT convolutional encoder, a method for eliminating the transmission loss as described above should be provided. For this, a direct truncation method and a cyclic convolutional coding method are mainly used. The method is a circular convolutional coding method.

Referring to FIG. 2 of the accompanying drawings for the cyclic convolutional coding method, FIG. 2 is an exemplary diagram for describing a coding process of a (2, 1, 6) TB (Tail Biting) convolutional code, which is a cyclic convolutional coding method. to be.

Here, (a) shifts to the last six input bits (I _k , I _k-1 , I _k-2 , I _k-3 , I _k-4 , I _k-5 ) of _k input bits to be encoded. After initializing the register, the process of encoding the first input bit l ₁ is shown. Once all k bits are encoded in order, it becomes as shown in (b). If the state of (b) is shifted, the register is initialized (I _k , I _k-1 , I _k-2 , I _k-3 , I _k-4 , I _k-5 ). That is, in the cyclic convolutional coding method, when the size of information to be encoded is 'k' bits, the shift register is first initialized with the last 'm' bits, and then the input information is sequentially encoded. In this way, after the input information of the 'k' bits is encoded, the register becomes the same as the initial state. Therefore, the decoder can decode using the ML decoding method by using the fact that the initial state and the final state of the register are the same.

However, the above-described cyclic convolutional coding method has the effect of eliminating the transmission loss due to the tail bit as compared to the ZT convolutional code by not encoding additional information (Tail bit). The disadvantage is that a memory of the 'k' bit size is required to obtain the last 'm' bit of the input information. In addition, there is a problem in that an encoding delay is required to stop encoding until input information having a 'k' bit size occurs.

In the case of voice communication, the speech transmission delay time after the talker speaks until the talker can hear the speech should be about 70 msec or less. If the speech transmission delay time due to the encoding delay is 70 msec or more, Everyone feels awkward about the call. Therefore, the encoding delay affects the entire communication system.

In this case, the voice propagation delay time includes a delay time occurring in all blocks of the communication system such as a source encoder, a channel encoder, a modulator, a demodulator, a channel decoder, a source decoder, and the like to reduce the voice propagation delay time to 70 msec or less. Difficulties in system design, such as minimizing the coding delay in each block as possible, are generated, resulting in a problem of inferior reliability of the system.

On the other hand, in order to solve the above problems briefly look at the contents described in the Republic of Korea Patent Application No. 93-16054 in a recently proposed method, the content is shifted to the last 'm' bit of the 'k' bit input information. Instead of the conventional method of initializing, a method of initializing a register with the first 'm' bits of the 'k' bits of input information to reduce transmission loss and encoding delay, and to reduce the amount of memory required during the encoding process, In the improved cyclic convolutional code, the encoding delay problem may be solved to some extent, but it does not solve the other problem of cyclic convolutional coding, that is, a large amount of computation is required for ML (Maximum Likelihood) decoding.

That is, the cyclic convolutional coder does not know the start state or the end state of the coder, so it needs to decode with a codeword that starts and ends in all possible states during Viterbi decoding. do. Therefore, in the case of the cyclic convolutional encoder, even though the performance of the code is very excellent, it is not practically used due to the amount of computation during decoding.

Accordingly, in recent years, many studies have been conducted to solve the problem of decoding calculation in the cyclic convolutional coder and to maintain a certain degree of performance. The method is a suboptimal decoding method. The most recently proposed decoding method among the sub-optimal decoding methods is a circular Viterbi decoding method that requires the least amount of computation. The circular Viterbi decoding method was proposed by Cox and Sundberg in 1994, which utilizes the characteristic that the trellis diagram of the circular weaving code is cycled. The following three methods are proposed in accordance with the Stopping Rule to stop the tracking of Trellis as a method of continuously tracking the Trellis even after the tracking is completed.

[Stop Condition 1]

Compute and save the metric in each state by calculating the Viterbi Update (VU) for all states, then save the metric of the 'k' state at any time (t). when we say _t (k), the difference between S _t (k) and S _{t + N} (k) will be stopped when the VU exactly the same for all k. This is because subsequent VUs produce the same results. N is the size of the input information string, and VU is the basic operation of performing the Viterbi Algorithm by adding, comparing, and selecting ACS operations in all states performed in one time interval.

There are three problems in the stopping condition as described above. First, a very large amount of information must be stored in memory, which requires 2 ^M (N + 1). Secondly, after starting the N + 1th VU, a comparison must be performed for all possible states to determine whether the differences in all states are the same, which requires a significant amount of computation since every time interval must be compared for all states. Third, in the case of performing such a comparison, the difference in S _t (k) may be the same because the comparison value is also an integer in the case of hard decision, but may not be the case in annual decision. Therefore, it is necessary to set Tolerance Error ε.

In order to solve the above problems, the following stopping conditions have been proposed.

[Stop Condition 2]

Compares the decision words before N symbol times after performing the first N VUs, and when M consecutive decision words become equal, stops the update and decodes the code word with the optimal metric at this time. do. The reason for selecting M consecutive decision words is because M is the memory size, and if this value is correct, the state at that time can be estimated accurately.

[Stop Condition 3]

The VU is stopped when the above stop conditions 1 and 2 are satisfied at the same time.

The decoding calculation of the cyclic convolutional code by the cyclic Viterbi algorithm described above is true in the case of decoding on the nonlinear convolutional code compared to the conventional method. In comparison, it requires about twice as much computation. Therefore, until now, the decoding calculation amount of the cyclic convolutional codes of any of the above-described methods does not overcome the conventional problem, that is, the limitation of about 70 msec, which is the allowable range of speech transmission delay time.

An object of the present invention for solving the above problems is to estimate the estimated time and the state of passing the Collect Path at any arbitrary time on a Trellis diagram of a cyclic convolutional code. By using Viterbi decoding from the state, the decoding calculation amount can be reduced, thereby eliminating the transmission loss present in the convolutional code, thereby providing a decoding method of the cyclic convolutional code to improve the transmission efficiency on the communication path. There is.

A characteristic of the present invention for achieving the above object is a cycle of weaving encoding the input information that determines the initial state of the weaving encoder using a portion of the input information, and convolutionally encodes the remaining input information, and then determines the initial state. 1. A method of decoding a convolutional code, comprising: a first process of determining whether to decode a block using maximum likelihood (ML) after determining whether to decode using a condition that an initial state and a final state of a survivor path must be the same; After performing ML decoding, if the initial state and the final state of the survivor path are the same, and the two states are different from each other, the second process of modifying the survivor path to another path such that the two states are the same and input information of one block In the ML decoding, a third process of performing ML decoding by cyclically shifting the received symbol string is included.

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.

First, the theoretical background to be used in the present invention will be briefly described as follows. In general, since a cyclic convolutional code performs a cyclic encoding by forming an information string that starts and ends an input information, a corresponding trellis must have a form in which a start and an end are connected. Performing the decoding process from the trellis diagram in the circular band form is equivalent to estimating which path on the trellis the collect path passes every time unit. In other words, by performing ML decoding Viterbi decoding in the trellis diagram, the path determined as the survivor path should have a ring shape. Thus, the survivor path on this trellis has a beginning and an end.

The survivor path is the main agenda of the decoding method. In the existing ZT convolutional code, the decoding process is performed as a survivor path in which the state of the encoder starts and ends in the state of '0', whereas the cyclic convolutional code starts in any state. Decode the ML path among all paths that have the same status and end status. Therefore, in the cyclic convolutional code, if it is possible to estimate the state that the collect path passes at any arbitrary time, the decoding process from this is the same as the existing Viterbi decoding process, which reduces the amount of computation time and improves the same performance. You will get

Accordingly, the present invention uses the following two features to estimate the state that the collect path will pass at any time.

1) The performance in the direct truncation method is similar to the conventional zero tail convolutional code when the path memory size τ is τ5m (m: restraint).

2) If a certain number of errors occur within a specific section of the channel, the Survivor Path may be different from the Collector Path.

Due to these two features, convolutional code is inferior in performance to other coding methods in the case of burst error. Conversely, in contrast to the above characteristics, if an error of less than a certain number is caused in a specific section, the Viterbi Algorithm in the section can predict at least the first state in the section. It is to use.

The above two features are already known in ML decoding technology, and will be well understood by those skilled in the art, and thus detailed descriptions thereof will be omitted.

Figure 3 corresponds to the assumption that d _free = 10, m = 7, g ⁽¹⁾ = 237, g ⁽²⁾ = 345, length L of information bits L = 60 to identify the first of the above features. This is an exemplary diagram showing the results of simulating the performance according to the decoding depth for the convolutional code. 3 shows the performance of a decoding method for DTCC, ZTCC, and cyclic convolutional codes (CCC) in a binary symmetric channel (BSC) channel having a channel error rate p = 0.035 according to each decoding length.

Here, the decoding of the CCC performed ML decoding. Looking at the simulation state diagram shown in FIG. 3, it can be seen that the performance of the CCC is similar to that of ZTCC.

However, ZTCC outperforms CCC in lengths of m bits at both ends of the information block. This occurs because the encoder state estimate is accurate because it assumes that ZTCC starts in a known state ('0' state) and ends in a known state ('0' state).

In other words, if the encoder state at a specific time is correct, decoding of m bits back and forth from that time becomes relatively accurate.

Because of this known encoder state, the decoding of ZTCC does not perform exactly equal error protection.

However, in the CCC, since all bits have the same encoding, if the state estimation error probability is the same in any part of the information block, the same decoding performance is shown for all the information bits.

On the other hand, in case of DTCC, there is no error protection for the last received information bit.

Therefore, the decoding of the last bit in DTCC is equal to the error probability on the channel. That is, the last bit is the same as the case of no coding.

However, since the DTCC also starts in the known state (0 state), the initial state estimation in the decoder is accurate, so the decoding performance of the initial part is the same as that of the ZTCC. In the DTCC graph, the performance is similar to that of ZTCC in the portion larger than approximately 5m from the decoding point.

The present invention proposes a decoding method of a cyclic convolutional code using the characteristics of the convolutional code as follows.

Proposed decoding algorithm:

Step 1: At t = 0 set the initial metric value M ₀ (k) of all states to '0'.

Step 2: Perform Viterbi algorithm on all received signals. At this time, the initial state of the survivor path in each state is stored.

Step 3: Finally, if the initial state and the final state of the path having the best metric among the survivor paths for all states are the same, the survivor path is regarded as a collect path and is decoded by a codeword for this path. If the initial state and the final state in the survivor path having the optimal metric are not the same, the received signal is shifted by a certain length tau ₁ greater than the constraint length m and repeated from step 1. (Ie, start from 1 = τ ₁ ). If step 1 is performed a predetermined number of times τ _{2, then} step 4 is performed.

Step 4: Obtain an error pattern between the survivor path and the received signal with the optimal metric, and store the time corresponding to the middle of the longest sequence of no error sequences and the passing state at this time. Performs Viterbi decoding at the state where the encoder starts and ends.

In step 3 of the proposed method, the path modification technique is used to compare the initial state and the final state of the survivor path.

This path correction technique does not exclude the possibility that the survivor path in state i ₂ is incorrectly selected due to an error in the received signal in the butterfly structure, which is the basic configuration of the Trellis diagram as shown in FIG.

That is, suppose that the state of the encoder has transitioned from state i to state i ₂ ,

However, if an error occurs in the received signal at the receiving end and the branch of state i ₂ is selected as the survivor path in state i ₁ , the initial state and the final state in step 3 will be inconsistent.

If the initial state and the final state are inconsistent, the branch selected at both ends of the survivor path is considered to be another possible branch (in this case, i to i ₂ ). Technique.

The above decoding method uses the conventional direct truncation method and the DTCC method repeatedly uses the DTCC method because the estimation of the state becomes inaccurate when the error is concentrated at the beginning or the end of the received signal.

That is, as in FIG. 3, the reason why the decoding performance is good in the length of the first m bits by DTCC is that it is assumed that the encoder always starts in the zero state.

If the encoder in DTCC does not start at zero but starts at any state, the decoding performance of this encoder is considerably degraded.

In CCC decoding, although the initial state of the encoder is not known, the condition that the initial state and the final state must be the same is assumed. Therefore, the decoding performance can be expected to be improved compared to the DTCC.

In this proposed method, Viterbi decoding can be performed again by cyclically shifting by a certain length τ ₁ larger than the constraint length m. This determines that it is difficult to estimate the initial state or the final state of the encoder when the survivor path of the optimal metric whose initial state and the final state are the same by the path modification cannot be selected. The reason is that the received signal of length m can be transitioned to all of the following states, and if an error occurs more than a certain number of times in this section, its initial state cannot be estimated.

In addition, this proposed method puts a certain threshold on the amount of calculation in consideration of the fact that the amount of calculation increases according to the channel state like other methods.

The proposed method is a method of repeatedly using the existing DTCC method.

However, in the existing DTCC method, there is no criterion for determining the survivor path with the optimal metric. However, in the proposed method, the decoding condition that the initial state and the end state of the encoder must be the same is added. can do.

Therefore, in order to predict the expected effect of the proposed method, we examine the decoding characteristics by the existing DTCC method.

5 shows decoding characteristics when the CCC coded code symbol string is decoded by the DTCC decoding method when m = 7, r = 1/2 and the length of the information bit L = 32.

In this gram, the probability of transmission error p = 0.0225, 0.0298, 0.0375, 0.0448 was assumed to be BSC (Binary Symmetric Channel) channel, and 100000 experiments were performed.

The initial state of the optimal path is a, t = 1, the next state b, t = 32, the final state d, and the state immediately before t = 31, c, and P _ad is the initial state. Probability in case of selecting the optimal path transitioned from a to the final state d as the survivor path (see FIG. 6). And P _c represents the probability that the state at the time when survivor path t = 31 passes state c.

In addition, P _{ad '} represents the probability when the state at t = 31 is c and the final state transitions to d' starting from the initial state a.

This probability can be expressed by the following butterfly structure in the BSC channel.

In general, in a BSC having a symbol error probability p on a channel, when the correct state transition probability is represented by P ₁ and the state transition error probability is represented by P ₂ , they can be expressed as follows.

From the results of FIG. 5, it can be seen that the decoding performance by DTCC is considerably inferior in its decoding performance. This performance deterioration is caused by a large number of decoding errors when the survivor path is not the optimal path in the decoding by DTCC.

However, the decoding performance only when the survivor path is selected as the optimal path among the DTCC decoding methods shows a good performance of about 2.35 * 10 ^-4 in the BSC channel having p = 0.225. And the probability that the decoding method by DTCC selects the optimal path is over 95%.

Therefore, the reason why the decoding performance by DTCC is lowered is that the number of decoding error bits is quite large when the invalid path is selected as the survivor path, and the probability in this case is less than about 5%.

The last term in FIG. 5 shows the ratio of the number of decoding error bits only when the optimal path is selected as the survivor path and the number of bits of decoding errors when the remaining non-conforming path is selected as the survivor path.

In other words, the DTCC decoding method selects an optimal path as a survivor path for 95% or more, and the number of decoding bit errors at this time shows a significantly smaller number of decoding errors than the rest of the cases.

At this time, the ratio between the decoding error rate in the optimal path and the decoding error rate when the nonconforming path is selected as the survivor path is about 1: 328 when p = 0.0225.

That is, most of the decoding errors due to DTCC depend on decoding errors when the optimum path does not become a survivor path.

In addition, P _c represents the probability when the survivor path up to t = 31 is the optimal path and an error exists in the final code word, so that the transition to the d 'state is not performed. Therefore, P _c -P _ad represents the probability of selecting a last but different path as a survivor path compared to the optimal path.

This probability value indicates that the performance can be improved by the path correction in the proposed method.

In addition, in the proposed decoding method, by using the condition that the initial state and the final state must be the same, DTCC decoding can be performed again from the beginning when the initial state and the final state are not the same even when the path correction technique is used.

In this case, the error is dense at the beginning and the end of the reception symbol sequence, and the estimation of the state by the Viterbi algorithm is inaccurate, so that the overall decoding performance can be improved by circulating the reception symbol sequence by longer than the constraint length to resume DTCC decoding. Can be.

We have measured the performance of the proposed CCC decoding algorithm through computer simulation and compared the performance of the recently published CCC decoding algorithm with the method of C _OX , which is the least computational method to date. At the time of simulation, the conditions under which C _OX were simulated were used as the basis of performance comparison.

That is, a case where the length of the information string L = 32 is input to a convolutional code of m = 7, r = 1/2, g ⁽¹⁾ = 237, and g ⁽²⁾ = 345, where d _free = 10. Hard decision was made, and the performance of 10000 tests was compared.

This weaving encoder is shown in FIG.

In addition, the error probability was performed for each BSC channel with p = 0.0225, 0.0298, 0.0375, 0.048.

In the proposed method, the thresholds were τ ₁ = 8 and τ ₂ = 4.

The results performed in this test environment are shown in FIG.

In this figure, T is the performance of the ideal case of knowing the initial state or the final state at the transceiver, and the rest shows the performance by the method of C _OX .

As shown in FIG. 8, the method proposed in the present invention has similar performance to the existing method for each channel, and the average VU (Viterbi Update) is reduced by about 50% compared to the existing method.

In Fig. 9, as the decision statistic in the proposed method, the number in Step represents the number of times the Viterbi algorithm is executed, and the error block represents the number of blocks in which a decoding error has occurred.

From this figure, about 98% of the BSC channel with error probability of 0.0225 can be decoded by Viterbi algorithm. Only 93% of BSC channel with error probability of 0.0448 can be decoded by one Viterbi algorithm. It was.

The cyclic convolutional coding method is a method of improving the rate loss in the conventional linear convolutional code, which requires a large amount of decoding calculation.

In the present invention, as a decoding method for reducing such a large amount of decoding calculation, a little decoding calculation amount is required as compared to the decoding of the conventional linear convolutional code, but a cycle requiring the least amount of calculations to date among the decoding methods of the conventional cyclic convolutional code. (Circular) Compared to the Viterbi decoding method, decoding is performed with half the decoding calculation amount.

Decoding performance is also similar to the circular Viterbi decoding method.

The decoding calculation amount of the cyclic convolutional code achieved in the present invention can be decoded while maintaining satisfactory performance by adding a small amount of decoding calculation to the conventional linear convolutional code, and thus, the cyclic convolutional code can be practically used.

The conventional decoding method of cyclic convolutional codes has not been practical because it requires a large amount of decoding calculation.

Claims (1)

In the method of decoding a cyclic convolutional code using a portion of the input information to determine the initial state of the convolutional encoder, convolutionally encoding all the other input information, and then convolutionally encoding the input information that has determined the initial state. A first process of determining whether to decode using the condition that the state and the final state are the same, and then decoding the input information of one block to the maximum likelihood (ML); A second step of modifying the survivor path with a second different path such that if the two states are different from each other by comparing the initial state and the final state of the survivor path after performing the maximum likelihood decoding; And ML decoding is performed by cyclically shifting the received symbol sequence when ML decodes the input information of one block.