RU2755055C1 - Method for transmitting multiblock messages by cascade code [rs (32, 16, 17), bch (31, 16, 7)] - Google Patents

Abstract

FIELD: information processing.

SUBSTANCE: invention relates to the field of processing and transmission of discrete information. To realise the described effect, a method for transmitting multiblock messages by cascade code is proposed, consisting in the fact that the source information on the transmitting side is divided into blocks of a predetermined length, used to form a message. A message is comprised of a title used to determine the sequence number of the blocks, an information or verification block, and a verification stage. Sets of verification blocks are then formed for sets of these blocks. A synchronising sequence is added to each block encoded by a cascade code, and the obtained combination of characters is transmitted to the receiving side. Synchronisation is performed not only by error-free code words, but also by code words containing errors. Decoding is performed simultaneously for hard and soft solutions, and multiple attempts are made in decoding the matrices of the multiblock message. Low-level matrices are used in encoding. After the blocks are decoded, the original messages are collected and transmitted to the recipient.

EFFECT: increasing the reliability of transmission of multiblock messages and reducing the time of transmission thereof.

3 cl

Description

The invention relates to the field of processing and transmission of discrete information and can be used for noise-immune transmission of multi-block messages in communication complexes.

One of the main ways to improve the reliability of message transmission is the use of error-correcting coding. In communication complexes, messages of a certain length are transmitted, for which a corresponding error-correcting code has been developed, which provides the required probability of correct reception. Typically, such messages are divided into blocks, each of which is encoded with an error-correcting code. With an increase in the complexity of the problems being solved, the length of the transmitted formalized messages increases. As the message length increases, the number of blocks into which these messages are split increases. The probability of receiving a message will be P ^m , where P is the probability of receiving one block, m is the number of blocks in this message. With an increase in the message length, the probability of its reception decreases, since if m2> m1 and P <1, then P ^m2 <P ^m1 , and may not satisfy the requirements for transmission reliability for such a message. To improve the reliability of transmission of long messages, it is required to increase the correcting ability of the error-correcting code. Along with this, it is also necessary to preserve the algorithms of the previous error-correcting coding for the possibility of using the equipment of the old park and for compatibility with it.

A known method of transmitting multi-block messages in telecode communication complexes [RF Patent No. 2710911, IPC N041. 1/20 (2006.01), Н03М 13/29 (2006.01), publ. 01/14/2020 Bul. No. 2], where at first on the transmitting side the message is divided into information blocks. Each information block is encoded with the original error-correcting code. Then the sequence of the original error-correcting codes is encoded with a multidimensional concatenated code, a synchronization sequence is added, and the resulting combination of symbols is transmitted to the receiving side. On the receiving side, first, frame synchronization is performed, determining the beginning of the sequence of the original error-correcting codes, then the original error-correcting codes are decoded with control of the correct decoding and erasing the incorrectly decoded original error-correcting codes. Next, decoding of the codes of the first stage of the multidimensional concatenated code is performed with the correction of the erased original error correcting codes and the erasure of the codes of the first stage of the multidimensional concatenated code, in which the correction of the erased original error correcting codes is impossible. Then, the codes of the second stage of the multidimensional concatenated code are decoded with the correction of the codes of the first stage of the multidimensional concatenated code and the erasure of the codes of the second stage of the multidimensional concatenated code, in which the correction of the erased codes of the first stage of the multidimensional concatenated code is impossible. Finally, the decoding of the codes of the last stage of the multidimensional concatenated code, the number of which corresponds to the number of measurements of the multidimensional concatenated code, is performed. Then the recovered information blocks are collected into one message, which is transmitted to the recipient of this message. On the transmitting side, the symbols of the sequence of the original error correcting codes with the same numbers are first encoded with the code of the first stage of the multidimensional concatenated code. Then the code symbols of the first stage of the multidimensional concatenated code with the same numbers are coded with the code of the second stage of the multidimensional concatenated code and, finally, they are coded with the code of the last stage of the multidimensional concatenated code, the number of which corresponds to the number of measurements of the multidimensional concatenated code. On the receiving side, multiple attempts are made to decode the multidimensional concatenated code. After each decoding attempt, the recovery of message information blocks is checked, and decoding is repeated only when the number of erased message information blocks is reduced in comparison with the previous decoding attempt. While maintaining the same number of erased information blocks of the message when compared with the previous decoding attempt, decoding attempts are terminated and the entire message is erased.

In one of the variants of this method, on the transmitting side, the check part of the code of the first stage of the multidimensional concatenated code is formed as a bitwise sum modulo two of the original error correcting codes in accordance with the check relations of the code of the first stage of the multidimensional concatenated code. The check part of the second stage code of the multidimensional concatenated code is formed in the form of a bitwise sum modulo two codes of the first stage of the multidimensional concatenated code in accordance with the check relations of the second stage code and so on.

In a further variant of this method, a multidimensional iterative code with one parity check is used as the multidimensional concatenated code.

When 2m erasures of the original error-correcting codes are detected, located at the vertices of an m-dimensional rectangular parallelepiped, where m is the number of measurements of the multidimensional concatenated code, the message is erased.

The disadvantage of this method is the ineffective use of the existing equipment fleet. In the case of bitwise summation modulo two of an even number of the original error-correcting codes, the synchronization sequences of the equipment of the old fleet are erased, therefore, additional external equipment is required to add these synchronization sequences. In addition, additional external hardware is required to implement multidimensional concatenated coding protocols. A significant amount of RAM will be required to store encoded received blocks, which have high redundancy, in order to be used later for recovering undecoded blocks.

The greater the redundancy of the blocks, the more the time of their transmission increases. The need to work together with crypto protection equipment further complicates the task. It is required to make complex algorithms, the implementation of which should be on microprocessors and programmable logic integrated circuits (FPGAs), to provide feedbacks with the decoder and crypto protection equipment and receive independent messages with a higher priority added to the array data stream, block identification to the message, and others. tasks.

It should also be noted that in this method, data on the structure of multidimensional coding and their protocols are external and not protected for transmission by a powerful noise-immune concatenated code of the equipment of the old fleet and by the multidimensional coding itself.

The formula of this method indicates that decoding is retried only when the number of erased message information blocks is reduced. In the proposed method, a repeated decoding attempt is performed both with a decrease in the number of erased message information blocks and with a decrease in the number of erased message check blocks.

Closest to the proposed method is a method (prototype) for transmitting multi-block messages with a cascade code in communication complexes [RF Patent No. 2671989, IPC H03M 13/29 (2006.01), H041. 1/24 (2006.01), publ. 08.11.2018 Bul. No. 31], which allows you to use the equipment of the old park without the disadvantages of the above-mentioned previous method, which consists in the fact that first a message of a certain length with initial information is selected on the transmitting side, then this message is divided into blocks, for each specific set of blocks with initial information is formed, using bitwise summation modulo two, its check block, for a set of check blocks, then additional check blocks are formed to increase the probability of their correct reception, the received message, taking into account the check blocks, is again divided into new blocks, each of which is added a header containing a sign - information or a verification block, its sequence number in the message, a sign of the verification stage, if a message is subjected to cryptographic protection operations before being encoded with a concatenated code, then after encryption it is once again divided into blocks with their own headers, according to which the message is restored on the receiving side for carrying out i decryption, in each concatenated-coded block intended for transmission to the channel, a synchronization sequence is added and the resulting combination of symbols is transmitted to the receiving side, on the receiving side, frame synchronization is performed to determine the boundaries of blocks encoded with an error-correcting code, and then each block is decoded, when In this case, the received blocks are analyzed and the initial information of the undecoded blocks is restored using the initial information of a set of correctly received blocks with the initial information and their check blocks, after decoding and restoration, the blocks with the initial information are assembled into a message and transmitted to the recipient.

The disadvantage of this method is the insufficiently high noise immunity of the transmission of multi-block messages with a concatenated code in communication complexes, since only one decoding attempt is performed, which leads to a decrease in the transmission reliability. Also, the possibility of increasing the noise immunity of the transmission of multi-block messages by improving the synchronization and decoding of each block of the concatenated code has not been considered.

The aim of the invention is to improve the reliability of the transmission of multi-block messages, to reduce the time of their transmission, to use the old formats and cyclic synchronization of the old fleet equipment as part of the error-correcting coding, the possibility of using the old fleet equipment and compatibility with it.

To achieve the goal, a method is proposed for transmitting multi-block messages with a concatenated code [РС (32,16,17), BCH (31,16,7)], which consists in the fact that on the transmitting side the initial information is divided into blocks of a certain length, from which the message is formed ... Each message contains a header that allows you to determine the sequence number of blocks, information or check block, stage of check and other information about the structure of the message. Then, for the sets of these blocks, using the bitwise sum modulo two, sets of check blocks are formed and the matrix blocks of the first stage are obtained, from which the blocks of the second stage matrix are formed, and by bitwise summation modulo two, sets of check blocks are obtained for this second stage matrix. Then, from the blocks of the second stage matrix, blocks of the third stage matrix are obtained, and by bitwise summation modulo two, sets of check blocks are obtained for this matrix of the third stage, and according to this algorithm, the matrix of the next stage is formed from the blocks of the matrix of the previous stage. The size of each block to be encoded corresponds to a certain number of bits. If a message is subjected to a cryptographic protection operation before being encoded with a concatenated code, then after this operation it is once again divided into blocks with headers. A synchronization sequence is added to each concatenated block, bitwise summing modulo two, and the resulting combination of symbols is transmitted to the receiving side. On the receiving side, frame synchronization is performed and the boundaries of blocks coded with an error-correcting code are determined. Then each block is decoded. The header for crypto messages is protected by an error-correcting concatenated code, and after decoding it, encrypted messages are recovered using this header to decrypt them. The header for messages with information and check blocks is protected by error-correcting concatenated code and complementary coding for multi-block messages. This header is recovered using a set of correctly received information and check blocks. After decoding the blocks, decrypting them, restoring the original information of the undecoded blocks according to the message structure contained in the header, from these blocks, in accordance with their numbering, the original messages are collected and transmitted to the recipient. The novelty is that in order to increase the probability of receiving a multi-block message on the receiving side, multiple attempts are made to decode the matrices of the multi-block message. In each cycle, after decoding the last stage of the matrix, the recovery of information and check blocks of the message is checked, and the next decoding attempt is performed only when the number of erased blocks in this message matrix decreases compared to the previous attempt to decode the matrix. At the end of the next last decoding cycle of the matrix, while maintaining the same number of erased information and check blocks of the previous last decoding cycle for this message matrix, the next decoding attempt is not made and the entire message containing such a matrix is considered not received.

The novelty is that the probability of receiving a multi-block message is increased by increasing the probability of correct reception of each block due to the capabilities of the correcting ability of the error-correcting concatenated code [PC (32,16,17), BCH (31,16,7)]. Synchronization is performed not only on error-free codewords, but also on codewords containing errors caused by channel quality, and decoding is performed simultaneously for hard and soft decisions. To reduce the transmission time of a multi-block message during encoding, matrices of low steps are used, while providing a given probability of receiving messages.

In the proposed method, the probability of receiving a multi-block message is maximized by using matrices containing the minimum number of information blocks during encoding, the matrix of the first stage contains two information and one check block, the matrix of the second stage contains four information and five check blocks, the matrix of the third stage contains eight information and nineteen check blocks, and so on.

Coding is carried out according to the algorithms of the equipment of the previously developed communication complexes with the preservation of the previous frame synchronization. On the receiving side, after frame synchronization and decoding, the received blocks are analyzed. The initial information for non-decoded blocks is restored using correctly received sets of blocks with initial information and check blocks. Blocks with original information and check blocks are protected by concatenated code and complement coding for multi-block messages, therefore, even with significant distortions in the channel, they are usually restored during decoding.

An increase in the probability of correct reception of a multi-block message is achieved when synchronization is performed not only by error-free code words, but also by code words with possible errors due to the quality of the channel [S. A. Trushin, I. A. Romacheva. Calculation of the probability of receiving a two-stage concatenated code in a communication channel with independent errors // Proceedings of the XVI Russian Scientific and Technical Conference "New Information Technologies in Communication and Control Systems" June 3, 2015. Kaluga. Noosphere. S. 219-225.]. In this case, not only hard solutions are used, but also hard and soft solutions are applied simultaneously. With the simultaneous use of soft and hard solutions for decoding the concatenated code [PC (32,16,17), BCH (31,16,7)], you can correct up to six errors in the words of the BCH and up to eight words in the PC code. As a codec of the code [PC (32,16,17), BCHH (31,16,7)], you can use the device described in the patent of the Russian Federation No. 245064, H04L. 7/00 (2006.01), publ. 05/10/2012 Bul. No. 13. Depending on the quality of the communication channel for the self-synchronizing two-stage concatenated code [PC (32,16,17), BCH (31,16,7)] when synchronizing by error-free words, the optimal synchronizing sequence should contain two codewords; when synchronizing on codewords containing at most one error, the optimal synchronizing sequence should contain three codewords; when synchronizing by codewords containing no more than two errors, the optimal synchronization sequence should contain six codewords; when synchronizing by codewords containing no more than three errors, the optimal synchronizing sequence should contain sixteen code words [Trushin S.A. 7)] for tough decisions depending on the quality of the channel // International scientific and technical journal "Science-Intensive Technologies", vol. 2, No. 6, 2019, p. 47-53.].

An example of a method for code frame synchronization for concatenated code PC (32,16,17), BCH (31,16,7)] for hard decisions when synchronizing by codewords containing no more than three errors is given in RF patent No. 2633148, H041. 7/08 (2006.01), publ. 11.10.2017 Bul. No. 29.

The coding algorithm for a block of initial information with a concatenated Reed-Solomon [RS (32,16,17)] code and a Bowse-Chowdhury-Hawkingham code [BCHH (31,16,7)] is given in RF patent No. 2671989, IPC Н03М 13/29 ( 2006.01), N041. 1/24 (2006.01), publ. 08.11.2018 Bul. No. 31]. To carry out such encoding, the initial information is divided into blocks of 256 bits, which can be represented as

where

j = 0, 1, ..., k,

k is the number of the block of initial information in the message,

i = 0, 1, ..., n-1,

n = 256 - the number of bits in the block,

a _ji - numbers of the location of i bits of the sequence in the j block.

In serial products, the maximum message size contains four blocks of information. Therefore, for the use of the equipment of the old park, multi-block messages are transmitted by four-block messages. Each such message contains a header that allows you to determine the sequence number of blocks, information or check block, stage of check and other information about the structure of the message. The four-block message can be represented as

At the first stage of additional coding, a matrix of four blocks is formed, each of which contains a four-block message. The initial information is sequentially located in the columns of these four blocks, and the fifth block contains verification information

Then, taking into account the check block, the probability of receiving the blocks of the first stage matrix will be

where

V is the number of transmitted information blocks A _j in each matrix of the first stage of the message,

R _bl - the probability of bringing each A _j block of information or check block.

For the second stage of additional coding, a matrix of sixteen information and four check _{blocks A 4} , A ₉ , A ₁₄ , A ₁₉ of the first stage and new five check blocks A ₂₀ - A _{24 of the} second stage is formed.

Four bits in information blocks for each row in the matrices of the first stage are bitwise summed modulo two, and their results A ₄ , A ₉ , A ₁₄ , A ₁₉ are check bits for the summed bits of the corresponding rows. In the matrix of the second stage for the formation of check blocks A ₂₀ - A ₂₃ modulo two, four bits are summed in the corresponding information blocks of each column. Block A ₂₄ is both a check for its row and for its column. The probability of receiving check blocks is equal to the probability of receiving information blocks, because the sets of check blocks of the first and second stages have their own check block A ₂₄ .

Let's calculate the probability of receiving matrix blocks of the second stage, taking into account the processing of information in the first stage.

The probability of receiving each row of the second stage matrix corresponds to formula (1), since the rows of the second stage matrix correspond to the matrices of the first stage. Therefore, the probability of receiving any one block A _j in a row of this matrix, taking into account the check in the first stage, will be

Similarly to formula (1), the probability of receiving any column of the second-stage matrix will be

where

V is the number of information blocks in this column.

Substitute the value of P _bl1 from (2) into (3) and get

To accept the information of the entire matrix of the second stage, it is necessary to accept the information of all columns of this matrix and the probability of such an event will be

To calculate the probability of receiving the blocks of the third stage matrix, we construct the corresponding matrix from V matrices of the second stage, and the (V + 1) matrix contains new check blocks.

The second stage matrix contains (V + 1) ² blocks of 256 bits * 4 each. Therefore, the probability of receiving any such block in this matrix will be

The third stage matrix column contains such V information blocks of the second stage and a check block. To accept all the blocks of the third stage matrix, it is necessary to accept all (V + 1) ² columns. The probability of receiving one column of the third stage matrix, similarly to formula (1), will be

Substitute P ₆₃ from (6) into (7) and obtain

The third stage matrix contains (V + 1) ² such columns. To accept all blocks of the third stage matrix, it is necessary to take all (V + 1) ^{2 of} its columns, while the value of the probability of such an event will be

Having analyzed formulas (3), (5), (9), we can write a generalizing formula for the probability of receiving blocks for a matrix of any stage

where

i - step number,

V is the number of rows for the matrix of the first stage (for the next stages it is supposed to use square matrices, in the considered calculation the number V = 4)

If a message is subjected to a cryptographic protection operation before being encoded with a concatenated code, then after this operation it is once again divided into blocks with a header. The header for crypto messages is protected by an error-correcting concatenated code, and after decoding it, encrypted messages are recovered using this header to decrypt them.

Let us set the probability of receiving a one-block message P _bl = 0.98, then the probability of receiving a four-block message will be

P _M0 = 0.98 ⁴ = 0.922368.

The probability of receiving the first stage matrix will be

P _M1 = 0.922368 ⁴ [1 + 4 (1-0.922368)] = 0.948556.

The probability of receiving the second stage matrix will be

P _M2 = 0.948556 ⁴ [1 + 4 (1-0.948556 ^1/5 ] ⁵ = 0.994606.

The probability of receiving the third stage matrix will be

P _M3 = 0.994606 ⁴ [1 + 4 (1-0.994606 ^1/25 )] ²⁵ = 0.999988306.

Р _М0 - the probability of receiving a four-block message, which contains 2 ¹⁰ bits of information. To transfer 1 MB of information, you need to transfer 2 ³ -2 ²⁰ = 2 ²³ bits, that is, 2 ^{23/2 10} = 2 ¹³ four-block messages.

The first stage matrix contains four four-block information messages and one verification message. To transfer 1 Mbyte of information, it is necessary to transfer 2 ^{13/2 2} = 2 ¹¹ matrices of the first stage.

The second stage matrix contains sixteen four-block information messages and nine four-block check messages. To transfer 1 Mbyte of information, it is necessary to transfer 2 ^{13/2 4} = 2 ⁹ matrices of the second stage.

Each third stage matrix contains sixty-four four-block information messages and sixty-one four-block verification messages. To transmit one megabyte must pass 2 ^{13/2 6} = 2 ⁷ matrixes of the third stage, that for P = 0.999988306 _M3 corresponds to the probability of reception P _MB = ¹²⁸ = 0.998504 0.999988306. With the probability of receiving P = 0.98, such matrices of the third stage can transmit 13.49 Mbytes of information.

Let us set the probability of receiving a one-block message P _bl = 0.99, then the probability of receiving a four-block message will be

P _M0 = 0.99 ⁴ = 0.960596.

The probability of receiving the first stage matrix will be

P _M1 = 0.960596 ⁴ [1 + 4 (1-0.960596)] = 0.985661.

The probability of receiving the second stage matrix will be

P _M2 = 0.985661 ⁴ [1 + 4 (1-0.985661 ^1/5 )] ⁵ = 0.999586.

The probability of receiving the third stage matrix will be

P _M3 = 0.999586 ⁴ [1 + 4 (1-0.999586 ^1/25 )] ²⁵ = 0.999999931.

The probability of transferring one megabyte by such matrices of the second stage will be

The probability of transferring one megabyte by matrices of the third stage will be

With the probability of receiving P = 0.98, such matrices of the third stage can transmit 2301.33 Mbytes of information.

Let us set the probability of receiving a one-block message P _bl = 0.999, then the probability of receiving a four-block message will be

P _M0 = 0.999 ⁴ = 0.996005.

The probability of receiving the first stage matrix will be

P _M1 = 0.996005 ⁴ [1 + 4 (1-0.996005)] = 0.999837.

The probability of receiving the second stage matrix will be

P _M2 = 0.999837 ⁴ [1 + 4 (1-0.999837 ^1/5 )] ⁵ = 0.999996.

The probability of receiving the third stage matrix will be

P _M3 = 0.999996 ⁴ [1 + 4 (1-0.999996 ^1/25 )] ²⁵ = 0.999999999993.

The probability of transferring one megabyte by such matrices of the second stage will be

With the probability of receiving P = 0.98, such matrices of the second stage can transfer 9.86 Mbytes of information.

The probability of transferring one megabyte by such third-stage matrices is

With the probability of receiving P = 0.98, such matrices of the third stage can transmit 20202707.30 MB of information.

Thus, for single decoding of multi-block messages with a reception probability of 0.98 by the matrices of the third stage

with P _M0 = 0.98 ⁴ = 0.922368, 13.49 MB of information can be transferred,

with Р _М0 = 0.99 ⁴ = 0.960596 2301.33 MB of information can be transferred

with P _M0 = 0.999 ⁴ = 0.996005, 20202707.30 MB of information can be transferred.

где s - число сообщений в матрице первой ступени. Соответственно в квадратной матрице n - ступени число комбинаций из двух стираний будет

Поэтому вероятность неприема сообщений для квадратной матрицы n - ступени будетThe first stage matrix contains four information messages and one verification message. Uncorrectable combinations for matrices of the first stage will be the erasure of two or more four-block messages. The number of combinations of two erasures in the first stage matrix will be

where s is the number of messages in the first stage matrix. Accordingly, in a square matrix of n - steps, the number of combinations of two erasures will be

Therefore, the probability of non-receipt of messages for a square matrix of n - stage will be

where

Р _М0 - probability of receiving a one-block message.

The probability of receiving messages for a square matrix n - stage will be

The algorithm for multiple decoding of multi-block messages starts working with matrices of the second stage and higher, that is, for n> 1.

For the algorithm for multiple decoding of multi-block messages, let us carry out a calculation for the third stage matrix, taking into account unrecoverable configurations of eight blocks located at the vertices of a rectangular parallelepiped, which are formed for the third stage matrix. For a third stage matrix containing 125 four-block messages, the number of uncorrectable configurations out of eight unaccepted four-block messages is one thousand. The formula for determining the probability of non-acceptance of the third stage matrix will be

where

Р _М0 - probability of receiving a four-block message. Calculations using formula (13) give the following results

The probability of transferring one megabyte by such third-stage matrices is

With the probability of receiving P = 0.98, such matrices of the third stage can transmit a message L, which is in the interval 119.53 Mbytes <L <392.83 Mbytes.

The probability of transferring one megabyte by such third-stage matrices is

With the probability of receiving P = 0.98 such matrices of the third stage, it is possible to transmit a message L, which is in the interval

26305.60 MB <L <664456.26 MB.

The probability of transferring one megabyte by such third-stage matrices is

R _Mb = 0.999999999999999935 ¹²⁸ = 0.99999999999999168.

With the probability of receiving P = 0.98, such matrices of the third stage can transfer 2428210014124.93 Mbytes of information.

Thus, with multiple decoding of multi-block messages with a reception probability of 0.98 by the matrices of the third stage

with P _M0 = 0.98 ⁴ = 0.922368, you can send a message in the interval

119.53 MB <L <392.83 MB,

with P _M0 = 0.99 ⁴ = 0.960596, you can send a message in the interval

26305.60 MB <L <664456.26 MB

with P _M0 = 0.999 ⁴ = 0.996005, 2428210014124.93 MB of information can be transferred.

For the transmission of short messages in order to reduce redundancy and, accordingly, the transmission time of messages, a second stage matrix can be used. The formula for determining the probability of non-acceptance of the second stage matrix will be

where

Р _М0 - probability of receiving a four-block message.

Calculations using formula (14) give the following results

The probability of transferring one megabyte by such matrices of the second stage will be

The probability of transferring one megabyte by such matrices of the second stage will be

R _MB = 0.999758 ⁵¹² = 0.883.

The probability of transferring one megabyte by such matrices of the second stage will be

0.999999974527 ⁵¹² = 0.9999869579 <P _Mb <0.999999974528 ⁵¹² = 0.9999869584.

With the probability of receiving P = 0.98 such matrices of the second stage, it is possible to transmit a message L, which is in the interval

1518 MB <L <1549 MB.

The formula for determining the probability of receiving the first stage matrix will be

where

Р _М0 - probability of receiving a four-block message.

Suppose that Р _М0 = 0.9999 = 0.999600, then Р _М1 will be equal to 0.999998401 and the probability of receiving one megabyte by such matrices of the first stage will be 0.999998401 ²⁰⁴⁸ = 0.996730. With a probability P = 0.98, such matrices of the first stage can transmit a message of 6.169 MB. The matrix of the first stage has the minimum redundancy and the minimum decoding time in comparison with the matrices of the next stages, therefore, when transmitting multi-block messages by the matrices of the first stage, the transmission time is reduced.

On the other hand, it is possible, by increasing the redundancy, to achieve an increase in the reliability of receiving multi-block messages. The maximum redundancy will be when a check block is formed for only two blocks. For this variant, when four-block messages are transmitted, the probability of non-reception of the second stage matrix will be

where

Р _М0 - probability of receiving a four-block message.

The probability of transferring one megabyte by such matrices of the second stage will be

R _Mb = 0.999999997707 ²⁰⁴⁸ = 0.999995303.

With the probability of receiving P = 0.98, such matrices of the second stage can transmit a message of 4301 MB.

With a minimum set of information blocks with a probability of receiving 0.98 by the matrices of the third stage when transmitting by four-block messages with P = 0.98 ⁴ = 0.922368, a message can be transmitted

in the range of 553 MB <L <573 MB,

with P = 0.99 ⁴ = 0.960596 a message can be sent

in the range of 125663 MB <L <126233 MB,

with P = 0.999 ⁴ = 0.996005, you can send a message

in the range 11261897810967 MB <L <11261905892879 MB.

The fourth stage matrix of four-block messages can be represented as

With a minimum set of information blocks with a reception probability of 0.98 by matrices of the fourth stage when transmitting by four-block messages with P = 0.98 ⁴ = 0.922368, a message can be transmitted

in the range of 279901418824 MB <L <279907440048 MB,

with P = 0.99 ⁴ = 0.960596 a message can be sent

in the interval 14421473162010368 Mbytes <L <14421473206211177 Mbytes,

at Р = 0.999 ⁴ = 0.996005 for the calculation we apply the approximate formula

и, следовательно, можно передать сообщение в интервале

and, therefore, it is possible to transmit a message in the interval

1.1571403925964986814928577763562⋅10 ³² MB <L <

1.1571403925964986816430190083947⋅10 ³² MB

Thus, when transmitting multi-block messages, to increase the correcting ability of the error-correcting code, redundancy can be introduced due to new stages in the matrix and using matrices containing a smaller number of information blocks. On the other hand, keeping the same redundancy or even reducing it in the design of the codes to increase the noise immunity of the transmission, it is necessary to achieve the theoretical correcting ability of the codes used in the circuit design. The above calculation shows the advantages of multiple decoding over single decoding. There is also a positive effect in increasing the likelihood of receiving a four-block message by the concatenated code. To ensure high reliability of receiving a four-block message, it is necessary to simultaneously improve the synchronization and decoding algorithms of the concatenated code. For example, in cyclic synchronization, apply words with correctable errors not only by hard decisions, but also by soft decisions at the same time [Trushin SA, Romacheva I.A. Calculation of the probability of receiving a two-stage concatenated code in a communication channel with independent errors // Proceedings of the XVI Russian Scientific and Technical Conference "New information technologies in communication and control systems" June 3, 2015. Kaluga. Noosphere. S. 219-225.]. Depending on the quality of the channel, apply the optimal lengths of the synchronizing sequences of the self-synchronizing concatenated code [RS (32,16,17), BCH (ZG, 16,7)] [Trushin S.A. Calculation of the optimal lengths of the synchronizing sequences of the self-synchronizing two-stage concatenated code [PC (32 , 16,17), BChH (31,16,7)] for tough decisions depending on the quality of the channel // International scientific and technical journal "Science-Intensive Technologies", v. 2, No. 6, 2019, p. 47-53.], In the concatenated code [РС (32,16,17)] to correct the maximum possible theoretical number of errors. An example of a concatenated codec codec [RS (32,16,17), BCH (31,16,7)], in which not only hard decisions, but also soft decisions are applied at the same time, is given in RF patent No. 245064, H04L. 7/00 (2006.01), publ. 05/10/2012 Bul. No. 13. Calculations and circuitry solutions in the above works and patents make it possible to implement the reception of a single-block message with a probability of 0.999 with an average probability of an error per bit up to 10 ^-1 .

In the proposed method, additional check blocks are formed for the initial information. Therefore, the algorithm for the operation of crypto-protection of the equipment of the old park is preserved. The original information, together with additional verification blocks, is encrypted and decrypted according to the algorithms of the equipment of the old fleet. Usually, the initial information is in a computer, and then from it enters the equipment, which encodes and decodes the information. Therefore, in a computer without additional equipment, it is possible to programmatically perform operations to form check blocks for the initial information and restore undecoded blocks of information and thereby ensure interaction with the equipment of the old park, both without using crypto protection operations, and using crypto protection operations.

The achieved technical result of the proposed method for transmitting multi-block messages in telecode communication complexes is to increase the reliability of the transmission of multi-block messages and reduce the time of their transmission, as well as the possibility of using the previously developed equipment park of communication complexes for transmitting and receiving multi-block messages.

Claims (3)

1. The method of transmitting multi-block messages by the concatenated Reed-Solomon code [RS (32,16,17)] and the Bowse-Chowdhury-Hockingham code [BChH (31,16,7)], which consists in the fact that on the transmitting side the initial information is divided into blocks of a certain length, from which a message is formed, each message contains a header that allows you to determine the sequence number of blocks, an information or check block, a check stage, then for sets of these blocks, sets of check blocks are formed using bitwise summation modulo two, and blocks are obtained matrices of the first stage, from which the blocks of the second stage matrix are formed and by bitwise summation modulo two, sets of check blocks for this matrix of the second stage are obtained, then from the blocks of the second stage matrix blocks of the third stage matrix are obtained and by bitwise summation modulo two sets of check blocks are obtained for this matrices of the third stage and, according to this algorithm, the matrix of the next stage is formed from blocks of matrix n at the previous stage, the volume of each block intended for encoding corresponds to a certain number of bits, if a message is subjected to cryptographic protection operations before being encoded with a concatenated code, then after this operation it is again divided into blocks with headers, into each block encoded with a concatenated code, bitwise summing modulo two, add a synchronization sequence and the resulting combination of symbols is transmitted to the receiving side, on the receiving side, frame synchronization is performed and the boundaries of blocks encoded with an error-correcting code are determined, and then each block is decoded, the header for crypto-messages is protected by an error-correcting concatenated code and after its decoding, this header is restored messages with cryptographic protection for their decryption, the header for the message with information and check blocks is protected by an error-correcting concatenated code and additional coding for multi-block messages, this header is restored using collection of the received information and check blocks, after decoding the blocks, decrypting them, restoring the original information of the undecoded blocks according to the message structure contained in the header, from these blocks, in accordance with their numbering, collect the original messages and transmit them to the recipient, characterized in that for increasing the probability of receiving a multi-block message on the receiving side, multiple attempts are made to decode the matrices of a multi-block message, in each cycle after decoding the last stage of the matrix, the recovery of information and check blocks of the message is checked and the next decoding attempt is performed only when the number of erased blocks in this message matrix is reduced compared to the previous one by an attempt to decode the matrix, at the end of the next last cycle of matrix decoding while maintaining the same number of erased information and check blocks of the previous last decoding cycle for this message matrix, the next n decoding experience is not done and the entire message containing such a matrix is considered rejected. 2. The method according to claim 1, characterized in that the probability of receiving a multi-block message is increased by increasing the probability of correct reception of each block due to the capabilities of the correcting ability of the error-correcting concatenated code [PC (32,16,17), BCH (31,16,7) ], where synchronization is performed not only on error-free codewords, but also on codewords containing errors arising from the channel quality, and decoding is carried out simultaneously for hard and soft decisions, to reduce the transmission time of a multi-block message during encoding, low-step matrices are used , while providing a given probability of receiving messages. 3. The method according to claim 1, characterized in that the probability of receiving a multi-block message is maximized by using matrices containing the minimum number of information blocks during encoding.