RU2500074C1 - Soft decision code frame synchronisation method - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: at transmission, a sequence of code words is generated in form of internal words of a cascade code; at reception, a sequence of words of noise-immune cyclic codes is obtained; said sequence is decoded; error combinations of said sequence are obtained; the weight of the obtained error combinations of the sequence is estimated; the weight of error combinations imposed on the synchronising sequence is then estimated; overall accuracy of words of the noise-immune cyclic codes is then determined, which is compared with a threshold value. If overall accuracy of words of the noise-immune cyclic codes is greater than the threshold value, frame synchronisation is established; if overall accuracy of words of the noise-immune cyclic codes is less than or equal to the threshold value, the sliding reception window is shifted by one symbol on the input sequence and calculation of the overall accuracy of words of the noise-immune cyclic codes is repeated.

EFFECT: high accuracy of establishing frame synchronisation.

5 cl

Description

The invention relates to methods for code cyclic synchronization of messages during the transmission of digital information and can be used for cyclic synchronization of cascade codes, turbo codes and cascade signal-code structures.

To increase the likelihood of message delivery in error communication channels, error-correcting coding is used. The most effective in terms of the noise immunity ratio of message reception and the complexity of the technical implementation is the use of cascade noise-immune code. For proper decoding of a cascade code, you need to know the boundaries of this code. On the receiving side, code loop synchronization is used to determine the beginning of the code. In code cycle synchronization, the synchronization sequence is transmitted in the verification part of the cascade code. Code cyclic synchronization can be established in the presence of distortions in the received cascade code that does not exceed a certain threshold value. After establishing the cyclic code synchronization, the synchronization sequence is subtracted from the verification part of the cascade code, without reducing its corrective ability. It is possible to increase the likelihood of establishing synchronization due to soft decisions when establishing synchronization of cascading code. In this case, the threshold value of the number of undistorted characters of the cascade code, at which the code cycle synchronization is established, takes into account the soft weights of the code symbols characterizing the reliability of these symbols. Soft cycle code synchronization can also be used in other codes with cascading of composite codes, for example, in turbo codes and in signal-code constructions (CCMs) based on block or convolutional codes.

There is a method of code cyclic message synchronization, in which an output sequence is formed on the transmitting side, consisting of information and verification symbols of an error-correcting code, which are then transmitted together with the synchronization sequence via a communication channel. On the receiving side, in the reception sliding window, the received synchronization sequence is compared with the transmitted synchronization sequence, and when the received synchronization sequence and the transmitted synchronization sequence coincide, cyclic synchronization is established, which coincides with the location of the beginning of the receiving reception window. If the received synchronization sequence and the transmitted synchronization sequence do not match, the reception sliding window is shifted by one character in the input sequence and the received synchronization sequence and the transmitted synchronization sequence are compared again and so on until the received synchronization sequence matches the transmitted synchronization sequence [Discrete message transmission . Ed. V.P. Shuvalova. - M .: Radio and communication. 1990. Pages 348-349].

However, this method reduces the amount of useful information transmitted over the communication channel, due to the need for a separate transmission of a special service synchronization sequence.

A known method of code cyclic synchronization, which consists in the fact that the received input sequence, consisting of several successive words, each of which is a bitwise sum modulo two error-correcting cyclic code, synchronizing sequence and numbering sequence, is multiplied by a check polynomial of error-correcting cyclic code and on the test polynomial of the numbering sequence and get the sum of the error-correcting cyclic code syndrome and sync niziruyuschey sequence. Then, the numbering sequence of the received error-correcting cyclic code is allocated, it is compared with the numbering sequences of previously received error-correcting cyclic codes, and the number of matches of the numbering sequence with previously received numbering sequences in one of the hit counters is stored. Moreover, if the numbering sequence coincides with the previously adopted numbering sequences, the number in the corresponding coincidence counter is increased by 1, and if the number recorded in the corresponding coincidence counter of the threshold value is exceeded, a decision is made on the code cycle synchronization of the input sequence (RF patent No. 2401512, IPC H04L 7 / 08. Kvashennikov VV, Sosin PA The method of code cyclic synchronization. Prior. March 16, 2009, publ. 10.10.2010, bull. No. 28).

However, with this method, the probability of establishing cyclic synchronization is not high enough because the reliability of the symbols of the synchronization sequence, which depend on the quality of the reception of the symbols and the state of the communication channel, are not taken into account.

Closest to the proposed method is a method of code cyclic synchronization of messages with soft solutions (prototype), which consists in the fact that on the transmitting side a sequence of code words is formed in the form of successive internal words of a cascade code, each of which is a sum modulo two error-correcting cyclic code and synchronizing sequence. On the receiving side, the input sequence received in the sliding reception window is divided into the generating polynomial of the noise-resistant cyclic code. As a result of the division, the sum of the error-correcting cyclic code syndrome and the synchronization sequence are obtained. Next, the synchronizing sequence is subtracted from the sum obtained and the noise-tolerant cyclic code syndrome is isolated. Then, according to the error-correcting cyclic code syndrome, a combination of errors in the error-correcting cyclic code is calculated and its weight is estimated. Then, by the weight of the error combination, the reliability of the successive words of the error-correcting cyclic code is calculated. Then these reliability are summarized together and then compare the total reliability of the words error-correcting cyclic codes with a threshold value. When the total reliability of the words of error-correcting cyclic codes is greater than the threshold value, a cyclic synchronization is established that coincides with the beginning of the sliding reception window, with the total reliability of the words of error-correcting cyclic codes more than or equal to the threshold value, the sliding reception window is shifted by one character in the input sequence and the calculation of the total reliability the words of noise-resistant cyclic codes are repeated (RF patent No. 2295198, IPC7 H04L 7/08. Zimikhin DA, Kvashennikov VV Cyclic code method th synchronization.Prior 08.06.2005, publ. 10.03.2007, bull. No. 7).

The disadvantage of this method is the insufficiently high probability of establishing synchronization, due to the fact that the cyclic synchronization of the cascade code is established by the total reliability of the internal words of the cascade code, which does not take into account soft decisions regarding the number and configuration of errors of the internal code of the cascade code, and hence the synchronization sequence.

The purpose of the invention is to increase the likelihood of establishing synchronization due to the fact that the total reliability of the received synchronization sequence takes into account the number and configuration of errors in the synchronization sequence and in the words of the internal code of the cascade code, and also takes into account the reliability of individual symbols of the synchronization sequence.

To achieve the goal, a code cyclic synchronization method for messages with soft solutions is proposed, which consists in creating a sequence of code words on the transmitting side in the form of successive internal words of a cascading code, each of which is a sum modulo two noise-resistant cyclic code and synchronizing sequence. On the receiving side, the input sequence received in the sliding reception window is divided into the generating polynomial of the noise-resistant cyclic code. As a result of the division, the sum of the error-correcting cyclic code syndrome and the synchronization sequence are obtained. Next, the synchronizing sequence is subtracted from the sum obtained and the noise-tolerant cyclic code syndrome is isolated. Then, according to the error-correcting cyclic code syndrome, a combination of errors in the error-correcting cyclic code is calculated and its weight is estimated. Then, by the weight of the error combination, the reliability of the successive words of the error-correcting cyclic code is calculated. Then these reliability are summarized together and then compare the total reliability of the words error-correcting cyclic codes with a threshold value. When the total reliability of the words of error-correcting cyclic codes is greater than the threshold value, a cyclic synchronization is established that coincides with the beginning of the sliding reception window, with the total reliability of the words of error-correcting cyclic codes less than or equal to the threshold value, the sliding reception window is shifted by one character in the input sequence and the calculation of the total reliability intermittent cyclic code words are repeated. It is new that, on the receiving side, the synchronization sequence is subtracted from the input sequence received in the sliding reception window and a sequence of words of noise-resistant cyclic codes is obtained, then this sequence of words of noise-resistant cyclic codes with soft solutions is decoded and as a result of this decoding, combinations of errors of the sequence of words of noise-resistant codes are obtained cyclic codes. Next, the weight of the obtained combinations of errors of the sequence of words of error-correcting cyclic codes is estimated, then the weight of combinations of errors superimposed on the synchronization sequence is estimated, and only then the total reliability of the words of error-correcting cyclic codes is determined, which is compared with a threshold value. In this case, the total reliability of the words of error-correcting cyclic codes is calculated as a weighted sum of the reliability of the words of error-correcting cyclic codes, the reliability of the synchronizing sequence, depending on the combinations of errors superimposed on it and the reliability of the symbols of the synchronizing sequence. Decoding a sequence of words of noise-resistant cyclic codes with “soft” solutions is carried out according to the Chase decoding algorithm. In this case, on the transmitting side, only the verification symbols of the internal code of the cascade code sum modulo two with the symbols of the synchronization sequence and then the resulting sequence is transmitted via the communication channel, the length of the receiving receiving window being chosen equal to the length of the cascading error-correcting code corresponding to the transmitted message.

We will consider the implementation of the code cyclic synchronization method for messages with soft solutions using the example of synchronization of an error-tolerant cascade code, the internal code of which is the noise-free cyclic Bose-Chowdhury-Hockingham binary code (BCH code), and the external one is the Reed-Solomon code. To this end, on the transmitting side, the original message with a volume of K m-ary (m> 1) characters is first encoded with an m-ary noise-tolerant Reed-Solomon code. The Reed-Solomon code is the code for the first stage of the error-correcting cascade code. As a result of encoding information, a code word of the Reed-Solomon code (N, K) is obtained, the information length of which is K, and the block length is N characters.

Further, the information is encoded by a binary cyclic BCH code with a generating polynomial g (x). The BCH code is an internal code or a second-stage code of a noise-free cascading code. The BCH code has parameters: n is the block length of the code, k is the information length of the code. The coding of the BCH code is performed according to the formula

$$p_{\mathrm{one}}\left(x\right)=ƒ\left(x\right)x^{n-k}+ƒ\left(x\right)x^{n-k}\mathrm{mod}g\left(x\right).\left(\mathrm{one}\right)$$

As a result of encoding the BCH code for all the characters of the Reed-Solomon code, N binary words of the BCH code (n, k) or a binary sequence with a length of nN bits are obtained.

Next, the modulo two symbols of the binary sequence of BCH codes with the symbols of the binary synchronization sequence are added. As a synchronizing sequence, a sequence with good synchronizing properties is selected, for example, a Reed-Muller (PM) code of the 1st order (maximum period sequence). The synchronization sequence is generated in advance in a linear shift register with feedbacks described by a primitive generating polynomial of an appropriate degree. For example, for a generating polynomial of degree 10 we will have a synchronization sequence of length 2 ¹⁰ -1 = 1023 bits. In this case, the synchronization sequence is divided into parts p ₂ (x) of length nk characters each and the symbols of these parts of the synchronization sequence are summed with the corresponding nk characters of the verification part of the corresponding BCH code: p ₃ (x) = p ₂ (x) + p ₂ (x) . To perform this operation, the length of the synchronization sequence must be at least V = (nk) N. A one-to-one correspondence is established between the words of the BCH in the cascade code and the segments of the synchronization sequence (PM code). The verification part of the first BCH word is added to the first segment of the synchronization sequence, the verification part of the second - with the second segment of the synchronization sequence, and so on. This addition is performed with all words of the BCH code of the cascading code.

On the receiving side, an input sequence formed as a modulo sum of two noise-frequency cyclic BCH codes and a synchronization sequence is used for code cycle synchronization. Errors occur in the communication channel due to signal distortions and a combination of errors e (x) is superimposed on the code words of the BCH code p ₃ (x). Therefore, the input sequence on the receiving side can be represented as:

$$p_{\mathrm{four}}\left(x\right)=p_{\mathrm{one}}\left(x\right)+p_2\left(x\right)+e\left(x\right).\left(2\right)$$

Then, on the receiving side, the synchronizing sequence p ₂ (x) is subtracted from the input sequence received in the sliding reception window and a sequence of words of error-correcting cyclic codes with errors is obtained

$$p_5\left(x\right)=p_{\mathrm{four}}\left(x\right)-p_2\left(x\right)=p_{\mathrm{one}}\left(x\right)+e\left(x\right).\left(3\right)$$

Next, decoding of this sequence of words of noise-resistant cyclic codes with “soft” solutions is performed. Decoding can be carried out, for example, according to one of Chase's decoding algorithms. Three Chase decoding algorithms are known that are usually used to decode binary error-correcting codes beyond their minimum code distance D (Clark J., Jr., Kane J. Error-correction coding in digital communication systems. Transl. From English - M .: Radio and communication, 1987. - 392 p.). For low-noise channels using Chase algorithms, the probability of error for a code with code distance D behaves in much the same way as for a code with correction D-1 errors, which allows you to record approximate estimates for the noise immunity of the code. The expansion of the corrective ability of the code in Chase's algorithms is achieved as follows. Suppose that a sequence of code symbols y ₁ , y ₂ , ..., y _n with confidence signs α ₁ , α ₂ , ..., α _n , respectively, characterizing the probability of error in the code symbols is accepted. According to certain rules, we will generate an error pattern T, which is added modulo two with the received word Y. The word Y + T is decoded in a “hard” decoder, at the output of which you can determine the corrected error Z. In a hard decoder, you can use syndromic decoding, in which the code word First, it is divided into the generating polynomial of the code and the error syndrome is calculated. Then, according to the error-correcting cyclic code syndrome, a combination of errors in the error-correcting cyclic code is calculated. The minimum value of the error weight w (Z) over the entire set of error samples T gives the most probable error Z, which allows one to determine the adopted codeword X = Y + Z.

Three Chase algorithms are known that differ in the rules for selecting error samples T.

Algorithm 1

Error pattern T contains errors at s = INT (D / 2) places. The number of such error sets will be

$$M={\left(q-\mathrm{one}\right)}^s\cdot C_N^s,\left(\mathrm{four}\right)$$

where q is the base of the code.

Algorithm 2

Error sample T contains or does not contain errors only at s = INT (D / 2) least reliable places. The number of such error sets will be

$$M=q^s.\left(5\right)$$

Algorithm 3

Sample of errors T contains errors at i places. With D even i = 1,3, ..., D-1, with D odd; i = 2,4, ..., D-1. The number of such error sets will be

$$M=q^{INT\left(D/2+\mathrm{one}\right)}.\left(6\right)$$

By the probability of correct reception of the code word, algorithms 1, 2, 3 are arranged in descending order. The number of error sets in all algorithms increases exponentially for binary codes depending on the number of error positions.

As a result of such decoding, combinations of errors e (x) of the received sequence of words of the error-correcting cyclic code are obtained. Next, the weight is estimated, that is, the number of errors in the resulting combination of errors of the error sequence of the cyclic code word

$$W_{\mathrm{one}}=w\left(e\left(x\right)\right).\left(7\right)$$

After that, the weight of error combinations superimposed on the synchronization sequence is estimated

$$W_2=w\left(e_{\mathrm{one}}\left(x\right)\right).\left(8\right)$$

These are those combinations of errors that are superimposed on the verification part of error-correcting cyclic codes.

The weights of the error combinations determine the accuracy of the error-correcting cyclic code words

$${\gamma }_{\mathrm{one}}=\frac{\mathrm{one}}{{\displaystyle \sum _{W_{\mathrm{one}}}{C}_n^{W_{\mathrm{one}}}}}{\gamma }_2=\frac{\mathrm{one}}{{\displaystyle \sum _{W_2}{C}_n^{W_2}}}{\gamma }_3={\displaystyle \sum _{i=\mathrm{one}}^{nN}{\alpha }_i}.\left(9\right)$$

The total fidelity of the words of error-correcting cyclic codes is calculated as the weighted sum of the reliability of the words of error-correcting cyclic codes, the reliability of the synchronizing sequence, depending on the combinations of errors superimposed on it and the reliability of the symbols of the synchronizing sequence.

Then determine the total reliability of the words error-correcting cyclic codes, which is compared with a threshold value. If the total confidence of the code words exceeds some pre-selected threshold confidence value γ _max

$${\displaystyle \sum {\gamma }_i\left(t\right)>{\gamma }_{\max }},\left(10\right)$$

This sets up loop synchronization. This means that the input goes to further processing. The location of the synchronization sequence uniquely determines the beginning of the first error-correcting cyclic BCH code in a cascading code or the beginning of a message.

In the proposed method, on the receiving side, after removing the synchronization sequence from the input sequence of words of error-correcting cyclic codes, decoding of error-correcting cyclic codes is performed using soft solutions, which increases the number of correctable errors in comparison with the hard algorithm used in the prototype. This allows you to generate a more accurate assessment of the reliability of the sequence of words error-correcting cyclic codes. Then, the total reliability of the words of error-correcting cyclic codes is formed, taking into account the reliability of individual code symbols, which also increases the accuracy and reliability of estimates of the reliability of the sequence of words of error-correcting cyclic codes, and therefore increases the accuracy and reliability of determining the synchronization sequence. This allows you to increase the likelihood of establishing cyclic synchronization of cascading code and other codes, the construction of which is based on the principle of cascading.

Achievable technical result of the proposed method of code cyclic synchronization of messages with soft decisions is to increase the likelihood of establishing cyclic synchronization, and therefore increase the likelihood of receiving the entire message.

Claims (5)

1. A method of code cyclic synchronization of messages with soft solutions, which consists in the fact that on the transmitting side a sequence of code words is formed in the form of successive internal words of a cascading code, each of which is a sum modulo two noise-resistant cyclic code and a synchronizing sequence, on the receiving side, the input sequence received in the sliding reception window is divided into the generating polynomial of the error-correcting cyclic code and as a result of division receive the sum of the error-correcting cyclic code syndrome and the synchronization sequence, then the synchronizing sequence is subtracted from the sum obtained and the error-correcting cyclic code syndrome is extracted, then the combination of errors in the error-correcting cyclic code is calculated from the noise-resistant cyclic code syndrome and its weight is estimated, then the reliability of the following each other is calculated by weight of the combination of errors after another words of the error-correcting cyclic code, then these reliability are summed together and then compared the total reliability of the words of error-correcting cyclic codes with a threshold value is obtained, when the total reliability of the words of error-correcting cyclic codes is greater than the threshold value, a cycle synchronization is established that coincides with the beginning of the sliding reception window, with the total reliability of words of error-correcting cyclic codes less than or equal to the threshold value, the sliding reception window offset by one character in the input sequence and the calculation of the total reliability of the words noise-resistant cyclic the codes are repeated, characterized in that on the receiving side the synchronization sequence is subtracted from the input sequence received in the sliding reception window and a sequence of words of noise-resistant cyclic codes is obtained, then this sequence of words of noise-resistant cyclic codes with soft decisions is decoded, and as a result of such decoding, combinations of sequence errors are obtained words of noise-resistant cyclic codes, then evaluate the weight of the resulting combinations of errors after word sequences of error-correcting cyclic codes, then the weight of error combinations superimposed on the synchronizing sequence is estimated, and only then the total reliability of the words of error-correcting cyclic codes is determined, which is compared with a threshold value. 2. The method according to claim 1, characterized in that the total word reliability of the error-correcting cyclic codes is calculated as a weighted sum of the reliability of the words of the error-correcting cyclic codes, the reliability of the synchronization sequence depending on the combination of errors and the reliability of the symbols of the synchronizing sequence superimposed on it. 3. The method according to claim 1, characterized in that the decoding of the sequence of words of noise-resistant cyclic codes with soft decisions is carried out according to the Chase decoding algorithm. 4. The method according to claim 1, characterized in that on the transmitting side only the verification characters of the internal code of the cascading code are summed modulo two with the symbols of the synchronization sequence and then the resulting sequence is transmitted via the communication channel. 5. The method according to claim 1, characterized in that the length of the sliding reception window is chosen equal to the length of the noise-resistant cascading code corresponding to the transmitted message.