RU2595955C1 - Method for combined compression and noiseless coding - Google Patents

Abstract

FIELD: telecommunications.

SUBSTANCE: invention relates to communication and can be used in data exchange via transmission channels with errors. For this purpose at the transmission next part of an information sequence is obtained, check symbols are calculated from it, which are recorded together with the next part of the information sequence into the next part of the noiseless sequence, which is compressed and transmitted, at the receiving the next part of the received sequence is obtained, which is saved and then the saved next parts of the received sequence are decompressed into next parts of the decoded sequence, from which next parts of the restored information sequence and decoded check symbols are identified, from the next part of the restored information sequence check symbols are calculated, which are compared bitwise with the decoded check symbols and in case of their bitwise coincidence the conclusion is made upon absence of transmission errors, in case of non-coincidence - one or more bits in the saved next parts of the received sequence are alternately inverted, which are decompressed, and subsequently the next actions are performed until reaching the output on the absence of transmission errors.

EFFECT: technical result is higher accuracy of detecting and correcting transmission errors.

1 cl, 14 dwg

Description

The claimed technical solution relates to the field of telecommunications and information technology, namely to the technique of compressing redundant binary information and its noise-resistant coding when exchanging data on transmission channels with errors.

The claimed invention can be used to ensure the reliability of redundant binary information transmitted over channels with errors.

A known method of adaptive error-correcting coding according to the patent of the Russian Federation 2375824 IPC H04L 1/20 (2006.01) dated 12/10/2009, which consists in the fact that on the transmitting side the source information is encoded by an error-correcting code with variable parameters, then the error-correcting code is transmitted to the communication channel, on the receiving side the error-correcting code is decoded with the detection and correction of errors depending on the correcting ability of the selected code, the quality of the communication channel is evaluated according to the results of decoding the error-correcting code, and variables parameters of the error-correcting code, providing a given probability of correct reception of the error-correcting code, and then these parameters of the error-correcting code are reported to the transmitting side, characterized in that on the receiving side, based on the results of decoding the error-correcting code, the initial value of the redundancy of the error-correcting code is calculated, which provides a given probability of correct reception of the error-correcting code, evaluate the probability of correct reception of the error-correcting code with the selected parameters, calculate the deviation of the obtained probability of the correct reception of the error-correcting code from the given probability of the correct reception of the code, and depending on the magnitude of this deviation, the redundancy of the error-correcting code is corrected, which is transmitted to the transmitting side, where the error-correcting code is generated with the received redundancy.

The disadvantage of this analogue is the inefficient use of transmission channel bandwidth, caused by the lack of compression of excess binary information when exchanging data on transmission channels with errors.

There is also a method of joint compression and noise-resistant coding of voice messages described, for example, in the book of S. N. Kirillov, V.T. Dmitriev, D.E. Krysyaev, S.S. Popov "Study of the quality of transmitted voice information with a different combination of source and communication channel coding algorithms under the influence of interference". - Ryazan, Vestnik RGRTU, Issue 23, 2008. This method consists in preliminarily generating a plurality of methods for compressing a speech signal, such as pulse-code modulation, adaptive delta modulation, adaptive differential pulse-code modulation, and many methods of noise-resistant coding , such as Hamming coding, Bowes-Chowdhury-Hawkingham coding, on the transmitting side from the sender receive the next part of the speech signal the length of the speech phrase, which is converted into a compressed binary sequence the accuracy using one of the methods of compressing a speech signal, perform error-correcting encoding of a compressed binary sequence using one of the methods of error-correcting encoding, transmit the next part of the encoded sequence along with information about the used method of compressing the speech signal and the method of error-correcting encoding to the receiving side via direct communication channel, on the receiving side receive the next part of the received sequence, the next part of the received sequence they are decoded using the appropriate error-correcting decoding method and the method of reconstructing a speech signal, the quality estimate of the reconstructed speech signal is calculated, and the resulting assessment is compared with the quality threshold value, if the calculated quality assessment of the reconstructed speech signal is not worse than a preset threshold quality value, then the next part of the reconstructed quality is transmitted to the recipient information sequence and the transmitting side from the sender received they receive the next part of the speech signal and perform the following actions, otherwise they transmit via the feedback channel the requirement to change the method of compression of the speech signal and the method of error-correcting coding, and perform the following actions.

The disadvantage of this analogue is the large delay in the transmission of messages over the communication channel, due to the need to search for a suitable method for compressing a speech signal and a method of error-correcting coding.

The closest in technical essence to the claimed method of joint compression and noise-resistant coding is the method of joint compression and noise-resistant coding according to US patent 6892343 IPC H04M 13/00 (2006.01) dated 05/10/2005. The prototype method of joint compression and error-correcting coding is that on the transmitting side, the next part of the information sequence of k≥1 bit length is received from the sender, verification characters of r≥1 bit length are selected from the pre-formed set and written together with the next part of the information sequence in the next part of the error-correcting sequence, perform compression of the next part of the error-correcting sequence into the next part of the compressed sequence, they convert the next part of the compressed sequence into the next part of the modulated sequence, transmit the next part of the modulated sequence to the receiving side, perform the above actions on the transmitting side until the next parts of the information sequence arrive, receive the next part of the received sequence on the receiving side, and convert it to binary the sequence to be memorized, the memorized successive parts of the received sequence are expanded in rare parts of the decoded sequence, from which the next parts of the reconstructed information sequence and decoded verification symbols are extracted, if the decoded verification symbols belong to a preformed set of verification symbols, they conclude that there are no transmission errors and transmit the next part of the restored information sequence to the recipient, otherwise one or one is inverted several bits in the memorized successive parts of the received sequence Nost that the expandable and perform the following steps before reaching conclusions about the absence of transmission errors, perform these actions on the receiving side as long as the next coming of the received sequence.

The prototype method of joint compression and error-correcting coding provides the ability to detect and correct transmission channel errors.

The general scheme of the prototype joint compression and error-correcting coding is presented in FIG. 1. On the transmitting side, joint compression and error-correcting coding of the next parts of the information sequence (IP) are performed, and on the receiving side, joint decompression is performed with the detection and correction of transmission channel errors. On the transmitting side, upon receipt of the next part of the information sequence from the sender in the block of check symbols 1 from the pre-formed set of check symbols, check symbols (PS) are selected, which together with the next part of the information sequence are compressed in the compression block 2. Then, in the modulator 3, the next part of the compressed sequence in the next part of the modulated sequence, which is transmitted over the transmission channel 4. At the receiving side receive the next part received sequence and a demodulator - sequential decoder 5 demodulate it into a binary sequence, which is stored. The stored successive parts of the received sequence are expanded in the expansion unit 6 into successive parts of the decoded sequence, the next part of the restored information sequence and decoded check symbols are extracted from each. The decoded check characters from the next parts of the decoded sequence in the comparison unit 7 are compared with the corresponding check characters read from the check characters 8, and when a match is found, a conclusion is made that there are no transmission errors and the next part of the restored information sequence is transmitted to the recipient. Otherwise, in the demodulator - serial decoder 5, one or more bits are inverted in turn in the remembered successive parts of the received sequence, which are decompressed and perform the following actions until the conclusion about the absence of transmission errors is reached.

A feature of the prototype method is that, on the transmitting side, first introduce noise-tolerant redundancy into the information sequence, and then its compression, and on the receiving side, when uncompressed, transmission channel errors are detected, if any, and if they are detected by trial and error, they are corrected .

However, in this prototype method of joint compression and error-correcting coding, the check symbols are independent of the information sequence. Therefore, on the receiving side, a formal check of the presence of transmission channel errors in decoded check symbols is performed, and the result of this check concludes that there are no transmission errors in the restored information sequence as well. At the same time, it is known that error-correcting codes have the maximum detecting and correcting ability to detect and correct transmission errors, in which the verification symbols are calculated from the information sequence so that each verification symbol is equally likely to depend on each bit of the information sequence, as described in the article C. Shannon "The mathematical theory of communication. Works on information theory and cybernetics." - M., IL, 1963, p. 587-621.

Thus, the disadvantage of the closest analogue (prototype) is the relatively small detecting and correcting ability to detect and correct transmission errors due to the use of check characters that are not dependent on the information sequence.

The technical result of the proposed solution is a joint compression and noise-resistant coding of an excess binary information sequence with an increase in the detecting and correcting ability to detect and correct transmission errors.

The specified technical result in the inventive method of joint compression and noise-resistant coding is achieved by the fact that in the known method of joint compression and noise-resistant coding, namely, on the transmitting side, the next part of the information sequence of k≥1 bit length is received from the sender, verification characters of length r are written ≥1 bit together with the next part of the information sequence into the next part of the noise-resistant sequence, compress the next part of the interference a stable sequence into the next part of the compressed sequence, transmit the next part of the sequence to the receiving side, perform the above actions on the transmitting side until the next parts of the information sequence arrive, on the receiving side receive the next part of the received sequence, which is stored, the remembered next parts of the received sequence unclench into the next parts of the decoded sequence, from which the next parts are recovered information sequence and decoded check symbols, make a conclusion about the absence of transmission errors and transmit to the recipient the next part of the restored information sequence, otherwise they invert one or more bits in the stored next parts of the received sequence, which are decompressed and perform the following actions until the conclusion about the absence of transmission errors is reached perform the above actions on the receiving side until the next part of the received sequence, additionally after receiving the next part of the information sequence, verification symbols are calculated from it, the next part of the compressed sequence is transmitted to the receiving side, on the receiving side, the verification symbols are calculated from the next part of the restored information sequence and the calculated verification symbols are bitwise compared with the decoded verification symbols and, if bit by bit coincidence they conclude that there are no transmission errors, and the arithm is used for compression matic coding or Huffman coding, as is used for a release, respectively, the arithmetic decoding or Huffman decoding.

In the proposed set of actions, on the transmitting side, verification symbols are calculated from the next part of the information sequence, and on the receiving side, the next part of the restored information sequence and decoded verification symbols are extracted from the next part of the decoded sequence, verification symbols and calculated verification symbols are calculated from the next part of the restored information sequence compared with decoded check characters, etc. and bit by bit, they conclude that there are no transmission errors. Verification symbols are completely dependent on the information sequence; they are calculated in accordance with the rules for generating error-correcting codes that provide the maximum achievable detecting and correcting ability to detect and correct transmission errors.

Therefore, this new set of actions allows, when performing joint compression and error-correcting coding of an excess binary information sequence, to increase the detecting and correcting ability to detect and correct transmission errors.

The claimed method is illustrated by drawings, which show:

- in FIG. 1 is a general diagram of joint compression and noise-resistant coding in the closest analogue (prototype);

- in FIG. 2 is a general diagram of joint compression and noise-resistant coding in the proposed method;

- in FIG. 3 - algorithm for joint compression and noise-resistant coding on the transmitting side;

- in FIG. 4 is a timing diagram of joint compression and noise-resistant coding on the transmitting side;

- in FIG. 5 is a compression diagram of an error-correcting sequence based on arithmetic coding;

- in FIG. 6 is a state table of arithmetic coding of the first four successive parts of the error-correcting sequence;

- in FIG. 7 is a timing diagram of arithmetic coding of the first four successive parts of an error-correcting sequence;

- in FIG. 8 is a timing diagram of joint decompression and error correction on the receiving side;

- in FIG. 9 - algorithm for joint expansion and correction of errors on the receiving side;

- in FIG. 10 is a diagram of the decompression of a received sequence based on arithmetic decoding;

- in FIG. 11 is a state table of arithmetic decoding of a received sequence with a transmission error;

- in FIG. 12 is a state table of arithmetic decoding of a received sequence with a transmission error when inverting its first bit;

- in FIG. 13 is a state table of arithmetic decoding of a received sequence with a transmission error when inverting its second bit;

- in FIG. 14 is a comparison of corrective and detecting abilities for the prototype method and the claimed method.

The implementation of the inventive method is presented on the example of the joint compression and noise-resistant coding system shown in FIG. 2. On the transmitting side, joint compression and error-correcting coding of the next parts of the information sequence are performed, and on the receiving side, joint decompression is performed with detection and correction of transmission channel errors. On the transmitting side, upon receipt of the next part of the information sequence from the sender, verification symbols are generated from it in the checker 1, which together with the next part of the information sequence are compressed in compression unit 2 using arithmetic coding or Huffman coding. From the output of the compression unit 2, the next part of the compressed sequence is transmitted via the binary transmission channel 3. At the receiving side, the next part of the received sequence is received and stored in the serial decoder 4. The stored successive parts of the received sequence are expanded in the compression unit 5 using arithmetic decoding or Huffman decoding into successive parts of the decoded sequence, from which the next parts of the reconstructed information sequence and decoded check symbols are extracted. From each successive part of the reconstructed information sequence, the verification symbols are computed in the verification symbol generator 6, and the calculated verification symbols in the comparison unit 7 are bitwise compared with the decoded verification symbols. If they are bit-wise, they conclude that there are no transmission errors and transfer to the recipient the next part of the restored information sequence, otherwise in the serial decoder 4, one or more bits in the stored next parts of the received sequence are alternately inverted, which are expanded in the decompression unit 5 until bit by bit The calculated check symbols and decoded check symbols will match, which means error correction of the transmission channel.

The algorithm of joint compression and error-correcting coding on the transmitting side is presented in figure 3.

In the method of joint compression and noiseless coding, the following sequence of actions is implemented.

On the transmitting side, the next part of the information sequence of length k≥1 bits is received from the sender. An exemplary view of the first four consecutive parts of a binary PI with a length of k = 4 bits is shown in FIG. 4 (a). For example, the first part of the IP has the form "1111", the second part is "1011", the third part is "1001". Single bit values in the figures are shown in the form of shaded pulses, zero bit values in the form of unshaded pulses.

, тем выше обнаруживающая и исправляющая способность по обнаружению и исправлению ошибок передачи, как описано в статье К. Шеннона "Математическая теория связи. Работы по теории информации и кибернетике". - М., ИЛ, 1963, стр. 587-621. Простейшим случаем вычисления проверочных символов является формирование единственного проверочного символа (r=1 бит) при суммировании по модулю 2 всех выходов ячеек памяти с использованием единственного сумматора. Такой простейший помехоустойчивый код называется код с проверкой на четность и способен обнаружить произвольные ошибки канала передачи кратностью 1, 3, 5 и так далее числа ошибок. Примерный вид проверочных символов длиной r=1 бит, вычисленных из первых четырех очередных частей двоичной ИП, показан на фиг. 4(б). Например, проверочный символ первой части ИП является нулевым двоичным символом, проверочный символ второй части ИП является единичным двоичным символом и т.д.Methods for calculating test characters of length r≥1 bits from the next part of the information sequence are known and described, for example, in the book of V.V. Zolotarev "Theory and algorithms of multi-threshold decoding." - M., Radio and communications, Hot line-Telecom, 2006, 22-27. The next part of the information sequence of length k≥1 bits is recorded in a serial binary register with k memory cells. In accordance with the generating matrix of the error-correcting code, the binary bits of the information sequence are read from the outputs of the corresponding memory cells and summed in r adders modulo 2. The binary output values r of these adders are test characters of length r≥1 bits. The greater the number r of test characters and the smaller the ratio

, the higher the detecting and correcting ability to detect and correct transmission errors, as described in the article by K. Shannon "Mathematical Communication Theory. Works on Information Theory and Cybernetics." - M., IL, 1963, p. 587-621. The simplest case of calculating check characters is the formation of a single check character (r = 1 bit) when summing modulo 2 all the outputs of the memory cells using a single adder. Such a simple error-correcting code is called a parity check code and is capable of detecting arbitrary transmission channel errors of multiplicity 1, 3, 5, and so on, of the number of errors. An exemplary form of check symbols with a length of r = 1 bits calculated from the first four subsequent parts of a binary PI is shown in FIG. 4 (b). For example, the check character of the first part of the PI is a zero binary character, the check character of the second part of the PI is a single binary character, etc.

Methods of recording test characters together with the next part of the information sequence in the next part of the noise-tolerant sequence are known and described, for example, in the book by W. Shilo "Popular digital circuits." - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences. For this, the next part of the binary information sequence from the first to the kth bit is written in parallel to the first memory cell shift register of length k + r bits. Check characters in the form of a binary sequence of length r bits are written in parallel to the subsequent, starting from k + 1-st, memory cells of the same shift register. As a result, the next part of the error-correcting sequence of length k + r bits is recorded in the shift register. For example, the first part of the error-correcting sequence (PP) has the form "11110", the second part is "10111", the third part is "10010".

Methods of compressing the next part of the error-correcting sequence into the next part of the compressed sequence are known and described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. Archiver device, image and video compression." - M., DIALOGUE-MEPhI, 2002, p. 31-49. For example, compression may be performed using arithmetic coding or Huffman coding.

Methods of compressing the next part of the error-correcting sequence into the next part of the compressed sequence using arithmetic coding are described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin, "Data compression methods. Archiver device, image and video compression." - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequentially compressing the binary symbols of the next part of the error-correcting sequence into the next part of the compressed sequence in accordance with the current values of the coding interval of the arithmetic coding and the current values of the probabilities of the encoded zero characters and single characters. An arithmetic coding compression scheme based on arithmetic coding is shown in FIG. 5, in which, as binary symbols arrive at the input, the number of null coding symbols and the number of coding unit symbols is proportional to the coding interval of the arithmetic coding is divided into the sub-interval of null coding symbols and the sub-interval of coding unit symbols, according to which the arithmetic encoder sequentially generates a compressed sequence (Joint venture).

Before compressing the first part of the error-correcting sequence, the initial values of the first and second coding registers are set. The initial lower value of the encoding interval is set to the minimum value, and the initial upper value of the encoding interval is set to the maximum value. For example, when representing the values of an encoding interval with eight binary characters, the initial lower value of the encoding interval of the arithmetic encoding L [0] is set to the minimum value equal to zero in decimal or 00000000 in binary representation, where the most significant binary characters are written to the left and the initial upper value the coding interval of the arithmetic coding H [0] is set to a maximum value of 255 in decimal or 11111111 in binary representation. An example of an initial state (Start state) of arithmetic coding is shown in FIG. 6.

, а начальное значение вероятности кодируемых единичных символов p₁[0] вычисляют по формуле вида

, где N₀[0] - начальное число закодированных нулевых символов, N₁[0] - начальное число закодированных единичных символов, а N[0] - начальное число закодированных нулевых и единичных символов, равное N[0]=N₀[0]+N₁[0]. В известных способах, описанных, например, в книге Д. Ватолин, А. Ратушняк, М. Смирнов, В. Юкин "Методы сжатия данных. Устройство архиваторов, сжатие изображений и видео". - М., ДИАЛОГ-МИФИ, 2002, стр. 124-130, устанавливают начальное число закодированных нулевых символов равным N₀[0]=1, а начальное число закодированных единичных символов - равным N₁[0]=1, то есть начальные значения вероятности кодируемых единичных и нулевых символов устанавливают равными: p₁[0]=p₀[0].The initial state of arithmetic coding also consists in setting the initial probability value of the encoded zero characters p ₀ [0] and the initial probability value of the encoded single characters p ₁ [0]. When setting the initial probability value of encoded null characters p ₀ [0] and the initial probability value of encoded null characters p ₁ [0] to the selected values, a restriction of the form should be satisfied: p ₀ [0] + p ₁ [0] = 1. The initial probability value of the encoded null characters p ₀ [0] is calculated by the formula of the form

, and the initial probability value of encoded single characters p ₁ [0] is calculated by the formula of the form

, where N ₀ [0] is the initial number of encoded zero characters, N ₁ [0] is the initial number of encoded single characters, and N [0] is the initial number of encoded zero and single characters, equal to N [0] = N ₀ [0 ] + N ₁ [0]. In the known methods described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. The device archivers, image and video compression." - M., DIALOGU-MIFI, 2002, pp. 124-130, set the initial number of encoded null characters to N ₀ [0] = 1, and the initial number of encoded single characters to N ₁ [0] = 1, that is, the initial the probability values of the encoded single and zero characters are set equal to: p ₁ [0] = p ₀ [0].

The initial value of the coding interval of arithmetic coding I [0], equal to I [0] = H [0] -L [0], is divided into the initial values of the sub-interval of zero characters D ₀ [0] and the sub-interval of single characters D ₁ [0], length which are directly proportional to the initial values of the probabilities of the encoded null characters p ₀ [0] and unit characters p ₁ [0], respectively. The initial length of the sub-interval of single characters D ₁ [0] is determined by the formula of the form D ₁ [0] = I [0] × p ₁ [0], and the initial length of the sub-interval of single characters of D ₀ [0] is determined by the formula of the form D ₀ [0] ] = I [0] -D ₁ [0]. For example, the initial length subslot single symbol D ₁ [0] has a value of 128 decimal or 10000000 in binary representation, and the initial length subslot zero symbols D ₀ [0] has a value of 127 decimal or 01111111 in binary representation. A sub-interval of single characters is located above the sub-interval of null characters, as shown, for example, in FIG. 7. The upper boundary of the null-character subinterval is designated as the Q value, and this subinterval starts from the bottom of the lower bound of the arithmetic coding coding interval to the Q value exclusively, and the single-character subinterval extends from the Q value inclusive to the upper limit of the arithmetic coding coding interval exclusively. The initial Q value has a decimal value 127, as shown in FIG. 6 in the first row at t = 0.

An exemplary compression of the first four successive parts of the error-correcting sequence of the form “11110 10111 10010 10100” into the first four successive parts of the compressed sequence (SP) is shown in FIG. 4 (g).

When the first compressible character, which is a single binary character, arrives at the input of the arithmetic coding, the lower value of the encoding interval of the first character L [1] is set to the value of Q, for example, 127, and the upper value of the encoding interval of the first character of the arithmetic coding H [1] is set equal to the initial upper value of the arithmetic coding coding interval H [0], for example, equal to 255, as shown in FIG. 6 and in FIG. 7 at t = 1.

The leftmost bit of the binary representation of the value L [1] is compared with the leftmost bit of the binary representation of the value H [1], for example, of the form 01111111 and 11111111, respectively, as shown in FIG. 6 at t = 1. If they do not match, they go on to compress the next character.

и текущее значение вероятности кодируемых единичных

. В соответствии с этим длина подинтервала нулевых символов D₀[1] становится в 2 раза меньше длины подинтервала единичных символов D₁[1], а параметр Q принимает значение 170, как показано на фиг. 6, вторая строка сверху и на фиг. 7.After performing compression of each successive character, the number of encoded null characters and single characters is specified. Since the first compressed symbol is single, the number of encoded single characters is increased by a single value and it is N ₁ [1] = 2, and the number of encoded zero and single characters becomes N [1] = N ₀ [1] + N ₁ [1] = 3. Recalculate the current probability value of encoded null characters

and the current probability value of the encoded units

. Accordingly, the length of the zero-character subinterval D ₀ [1] becomes 2 times less than the length of the single-character subinterval D ₁ [1], and the parameter Q takes on the value 170, as shown in FIG. 6, the second row from above and in FIG. 7.

When the second compressible character, which is a single binary character, arrives at the input of arithmetic coding, the lower value of the encoding interval of the second character L [2] is set equal to the value of Q, for example, 170, and the upper value of the encoding interval of the second character of arithmetic coding H [2] is set equal to the upper value of the coding interval of arithmetic coding H [1], equal to, for example, 255, as shown in FIG. 6 at t = 2.

и текущее значение вероятности кодируемых единичных

. В соответствии с этим длина подинтервала нулевых символов D₀[2] становится в 3 раза меньше длины подинтервала единичных символов D₁[2], как показано на фиг. 6, третья строка сверху и на фиг. 7.After performing compression of each successive character, the number of encoded null characters and single characters is specified. Since the second compressed symbol is single, the number of encoded single characters is increased by a single value and it is N ₁ [2] = 3, and the number of encoded zero and single characters becomes N [2] = N ₀ [2] + N ₁ [2] = 4. Recalculate the current probability value of encoded null characters

and the current probability value of the encoded units

. Accordingly, the length of the zero-character subinterval D ₀ [2] becomes 3 times less than the length of the single-character subinterval D ₁ [2], as shown in FIG. 6, the third row from above and in FIG. 7.

The leftmost bit of the binary representation of the value L [2] is compared with the leftmost bit of the binary representation of the value H [2], for example, of the form 10101001 and 11111111, respectively, as shown in FIG. 6 at t = 2. When they coincide, the value of the leftmost bit of the binary representations of the values L [2] and H [2] is read as the next bit of the compressed sequence (Code symbol in Fig. 6). For example, when compressing the first part of the error-correcting sequence, the first bit of the first part of the compressed sequence is the unit binary symbol that coincides when comparing, as shown in FIG. 6, the fourth line from the top. The read bit is removed from the binary representations of the values L [2] and H [2], which are reduced to a length of 7 bits of the form 0101001 and 1111111, respectively. Binary symbols of binary representations of the values of L [2] and H [2] are shifted from right to left by one digit and are added to the right by a zero binary symbol. For example, binary representations of the values L [2] and H [2] take the form 01010010 and 11111110, respectively. Methods for reading binary characters with the removal of read characters are known and described, for example, in the book: V. Shilo "Popular digital circuits." - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences. The right-to-left shift operations by one bit and the addition of a binary binary symbol to the right increase the values of L [2] and H [2] by 2 times and are called normalization of arithmetic coding parameters. Methods of shifting one bit in the direction of the higher bits of binary sequences and writing to the freed low order of the zero binary symbol are known and described, for example, in the book: V. Shilo "Popular Digital Circuits". - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences, and in essence are multiplication by two decimal values of the lower and upper values of the encoding interval.

After each normalization run, the leftmost bit of the binary representation of the lower value of the encoding interval is compared again with the leftmost bit of the binary representation of the upper value of the encoding interval. If they coincide, the value of the leftmost bit of these binary representations is read as the next compressed bit, otherwise, they go on to compress the next next character and so on, as shown in FIG. 6.

When the next IP symbol, which is a binary binary character, is received at the arithmetic coding input, the lower value of the coding interval is set equal to the previous lower value of the coding interval of the arithmetic encoder, and the upper value of the coding interval is set to the current value of Q. For example, when the fifth arithmetic coding is received at the input count of the symbol IP, which is a zero binary symbol, the lower value of the encoding interval of the fifth character L [5] is set equal to the previous lower value of the coding interval of the arithmetic encoder L [4], for example, 44, and the upper value of the coding interval of the fifth character of the arithmetic coding H [5] is set to the current value of Q, for example, 78, as shown in FIG. 6 at t = 5.

An exemplary compression of the first four successive parts of an error-correcting sequence of the form “11110 10111 10010 10100” into the corresponding successive parts of the compressed sequence of the form “110 01110 1,000,000 010” is shown in FIG. 4 (g).

Methods of transmitting to the receiving side the next part of the compressed sequence are known and described, for example, in the book of A.G. Zyuko, D.D. Klovsky, M.V. Nazarov, L.M. Fink "Theory of signal transmission." - M .: Radio and communications, 1986, p. 11. An exemplary view of the received sequence (Pr. P) is shown in FIG. 8 (a). The received sequence during transmission is distorted in the second bit and has the form "100011101000000010".

An algorithm for joint decompression and error correction on the receiving side is shown in FIG. 9. The decompression scheme based on arithmetic decoding is shown in FIG. 10, in which, as the decoding is performed, the number of null decoding symbols and the number of single decoding symbols are calculated proportionally to which the decoding interval of the arithmetic decoding is divided into the sub-interval of null decoding symbols and the sub-interval of single decoding symbols, according to which the arithmetic decoder decodes the received sequence in sequence.

Methods of storing the next parts of the received sequence are known and described, for example, in the book: V. Shilo "Popular Digital Circuits". - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences.

Methods of decompressing the stored next part of the received sequence into the next part of the decoded sequence using arithmetic decoding are described, for example, in the book D. Compression Methods, Data Compression, Image and Video Compression Methods by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin . - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequential decoding using arithmetic decoding of the next part of the received sequence in accordance with the current values of the decoding interval of the arithmetic decoding and the current probability values of the decoded zero characters and single characters.

Before expanding the first part of the received sequence, the initial values of the first and second decoding registers are set. The initial lower value of the decoding interval is set to the minimum value, and the initial upper value of the decoding interval is set to the maximum value. For example, when representing coding interval values with eight binary characters, the initial lower value of the arithmetic decoding decoding interval LL [0] is set to the minimum value equal to zero in decimal or 00000000 in binary representation, where the most significant binary characters are written to the left and the initial upper value arithmetic decoding decoding interval HH [0] is set to a maximum value of 255 in decimal or 11111111 in binary representation lenii. An example of an initial state (initial state) of arithmetic decoding is shown in FIG. 11. The initial states of arithmetic coding and arithmetic decoding are set identically.

, а начальное значение вероятности декодируемых единичных символов pp₀[0] вычисляют по формуле вида

, где NN₀[0] - начальное число декодированных нулевых символов, NN₁[0] - начальное число декодированных единичных символов, а NN[0] - начальное число декодированных нулевых и единичных символов, равное NN[0]=NN₀[0]+NN₁[0]. В известных способах, описанных, например, в книге Д. Ватолин, А. Ратушняк, М. Смирнов, В. Юкин "Методы сжатия данных. Устройство архиваторов, сжатие изображений и видео". - М., ДИАЛОГ-МИФИ, 2002, стр. 124-130, устанавливают начальное число декодированных нулевых символов равным NN₀[0]=1, а начальное число декодированных единичных символов - равным NN₁[0]=1, то есть начальные значения вероятности декодируемых единичных и нулевых символов устанавливают равными: pp₁[0]=pp₀[0].The initial state of arithmetic decoding also consists in setting the initial probability value of the decoded null symbols pp ₀ [0] and the initial probability value of the decoded unit symbols pp ₁ [0]. When setting the initial probability value of decoded null characters pp ₀ [0] and the initial probability value of decoded null characters pp ₁ [0] to the selected values, a restriction of the form: pp ₀ [0] + pp ₁ [0] = 1, must be fulfilled. The initial probability value of decoded null characters pp ₀ [0] is calculated by the formula of the form

, and the initial probability value of decoded unit characters pp ₀ [0] is calculated by the formula of the form

where NN ₀ [0] is the initial number of decoded zero characters, NN ₁ [0] is the initial number of decoded unit characters, and NN [0] is the initial number of decoded zero and unit characters equal to NN [0] = NN ₀ [0 ] + NN ₁ [0]. In the known methods described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. The device archivers, image and video compression." - M., DIALOGU-MIFI, 2002, pp. 124-130, set the initial number of decoded zero characters to NN ₀ [0] = 1, and the initial number of decoded single characters to NN ₁ [0] = 1, that is, the initial the probability values of the decoded unit and zero characters are set equal to: pp ₁ [0] = pp ₀ [0].

The initial value of the decoding interval of the arithmetic decoding II [0], equal to II [0] = HH [0] -LL [0], is divided into the initial values of the decoding sub-interval of zero characters DD ₀ [0] and the decoding sub-interval of single characters DD ₁ [0] whose lengths are directly proportional to the initial probabilities of decoded null characters pp ₀ [0] and unit characters pp ₁ [0], respectively. The initial length of the decoding sub-interval of single characters DD ₁ [0] is determined by the formula of the form DD ₁ [0] = II [0] × pp ₁ [0], and the initial length of the decoding sub-interval of decoding of zero characters DD ₀ [0] is determined by the formula of the form DD ₀ [0] = II [0] -DD ₁ [0]. For example, the initial length of the decoding sub-interval of single characters DD ₁ [0] has a decimal value of 128 or 10,000,000 in binary representation, and the initial length of the decoding sub-interval of single characters DD ₀ [0] has a decimal value of 127 or 01111111 in binary representation. The unit character decoding sub-interval is located on top of the null character decoding sub-interval. The upper limit of the null-symbol decoding interval is designated as the QQ value, and this sub-interval starts from the bottom of the lower boundary of the arithmetic coding decoding interval to the QQ value exclusively, and the unit decoding interval of the single symbols extends from the QQ value inclusive to the upper limit of the arithmetic decoding decoding interval exclusively. The initial QQ value has a decimal value of 127, as shown in FIG. 11 in the first line at t = 0.

An exemplary view of decompressing a received sequence of the form “100011101000000010” into a decoded sequence shown in FIG. eleven.

The input of the arithmetic decoding receives a part of the received sequence of length R bits equal to the bit depth of the operations performed, as with the previously described arithmetic coding. Initially, the first 8 bits of the form “10001110” are read in turn at the input of the arithmetic decoding, which corresponds to the decimal number 142. The current value of the read sequence is compared with the boundaries of the initial value of the decoding sub-interval of zero characters DD ₀ [0], for example, ranging from 0 to 127 and with the borders of the initial value subslot decoding unit DD symbols ₁ [0] located, e.g., in the range from 127 to 255. depending on whether within a subslot decoding symbols had s current value of the read sequence, make a decision on the decoding of the next symbol decoded sequence.

и по формуле вида

, соответственно. Устанавливают текущие длины подинтервалов декодирования единичных символов и нулевых символов и устанавливают текущее значение QQ=170 с двоичным представлением вида "10101001", как показано на фиг. 11 при t=1.For example, since the current value of the read sequence turned out to be greater than the QQ value, the first decoded symbol is single and the following boundaries of the decoding interval are set to the corresponding boundaries of the value of the decoding sub-interval of single characters DD ₀ [0]. As a result of decoding the first symbol, the lower value of the arithmetic coding decoding interval LL [1] is set to QQ, for example, LL [1] = 127, and the upper value of the arithmetic coding decoding interval HH [1] is set to the previous value HH [0], for example , HH [1] = 255, as shown in FIG. 11 in the second row at t = 1. After decoding each symbol, the current probability value of the decoded zero characters and the current probability value of the decoded zero characters are recalculated, for example, after decoding the first character that is single, according to the formula

and according to the formula of the form

, respectively. Set the current lengths of the decoding intervals of single characters and zero characters and set the current value QQ = 170 with a binary representation of the form "10101001", as shown in FIG. 11 at t = 1.

The decoded unit symbol is read from the arithmetic decoding output as the first symbol of the decoded sequence.

и по формуле вида

, соответственно. Устанавливают текущие длины подинтервалов декодирования единичных символов и нулевых символов и таким образом уточняют значения первого и второго регистров декодирования.After each change in the arithmetic decoding state, the leftmost bit of the binary representation of the LL value is compared with the leftmost bit of the binary representation of the HH value, for example, at t = 1 of the form “01111111” and “11111111”, respectively. When they coincide, normalization of arithmetic decoding is performed, otherwise decoding is continued, for example, the second character of the received sequence is decoded. The input of the form “10001110” is still read to the arithmetic decoding input, which corresponds to the decimal number 142. The current value of the read sequence is compared with the boundaries of the values of the decoding sub-interval of zero characters DD ₀ [1], for example, ranging from 127 to 170 and with boundaries of the value of the decoding subinterval of single characters DD ₁ [1], for example, ranging from 170 to 255. Depending on the limits of the subinterval of character decoding, the current value of the last read sequence, decide to decode the next character of the received binary information sequence. For example, since the current value of the read sequence turned out to be less than the QQ value, the second decoded symbol is zero and the following decoding interval boundaries are set to the corresponding boundaries of the decoding subinterval value of the zero symbols DD ₀ [1]. As a result of decoding the second symbol, the lower value of the decoding interval of the arithmetic coding LL [2] is set to the previous value LL [1], for example, LL [2] = 127, and the upper value of the decoding interval of the arithmetic coding HH [2] is set to QQ, for example , HH [2] = 170, as shown in FIG. 11 in the third row at t = 2. After decoding each symbol, the current probability value of the decoded null symbol and the decoded null symbol is recalculated, for example, after decoding the second symbol, which is null, according to the formula

and according to the formula of the form

, respectively. Set the current lengths of the decoding sub-intervals of single characters and zero characters and thus specify the values of the first and second decoding registers.

After decoding each symbol, the leftmost bit of the binary representation of the LL value is compared with the leftmost bit of the binary representation of the HH value. For example, after decoding the fourth character, the leftmost bit of the binary representation of the LL [4] value of the form “10001100” is compared with the leftmost bit of the binary representation of the HH [4] value of the form “10010101” and, if they coincide, the arithmetic decoding is normalized: the value of the leftmost bit of the binary representations of the values of LL and HH are deleted and the binary characters of binary representations of the values of LL and HH are shifted from right to left by one digit and are added to the least significant bit from right to left by a binary binary character. At the same time, the value of the leftmost bit of the input data is deleted and the binary characters of the input data are shifted from right to left by one digit, and the next binary character of the received sequence is added to them, for example, the ninth character of the received sequence, which is a single character, as shown in FIG. . 11 in the sixth line of "normalization." Given the added binary character, the input data acquires the binary representation "00011101" and decimal value 29. The LL variable takes the decimal value 24 and the binary representation "00011000", and HH the decimal value 42 and the binary representation "00101010". Since the leftmost bits of the binary representations LL and HH coincide again, they perform normalization again in the same way, etc.

As a result of arithmetic decoding of the first-by-one characters of the received sequence, the first and second part of the decoded sequence (DP) are decoded, having, for example, the form “10010” and “01110”, as shown, for example, in FIG. 8 (b) and in FIG. eleven.

Methods for extracting from the next part of the decoded sequence the next part of the reconstructed information sequence and decoded check symbols are known and described, for example, in the book by V. Shilo "Popular Digital Circuits". - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences. The next part of the decoded sequence is sequentially recorded in the memory cells of the shift register of length k + r bits. From the first memory cells of this shift register, the next part of the reconstructed information sequence of length k bits is read in parallel. From the subsequent, starting from k + 1, memory cells of the same shift register, decoded check symbols of r bit length are read in parallel. For example, from the first part of the DP of the form "10010", the first part of the reconstructed information sequence (VIP) of the form "1001" and the decoded verification symbol of the form "0" are extracted.

Verification symbols are calculated from the next part of the reconstructed information sequence in the same way as on the transmitting side, verification symbols are calculated from the next part of the information sequence. For example, from the first part of the restored information sequence of the form "1001", a verification character of the form "0" is calculated.

The calculated check symbols are bitwise compared with the decoded check symbols and, when bit-wise coincided, they conclude that there are no transmission errors. For example, in the first part, the calculated verification symbol coincided with the decoded verification symbol and no transmission channel error was detected. But in the second part of the decoded sequence of the form "01110" from the restored information sequence of the form "0111", a verification symbol of the form "1" is calculated, which does not coincide with the decoded verification symbol of the type "0". Therefore, a transmission error in the received sequence is detected.

To correct transmission errors, one or more bits are inverted in turn in the remembered next part of the received sequence. Methods of inverting bits in the stored next part of the received sequence are known and described, for example, in the book by V. Shilo "Popular digital circuits." - M., Radio and Communications, 1987, 104-123, using shift registers with parallel writing / reading of binary sequences and binary inverters. The invertible bit from the shift register is read in parallel to the inverter input and from the inverter output is written in parallel to the same shift register memory cell.

For example, in the stored received sequence, the first bit is inverted (Jn 1. Ex. P) and it takes the form "000011101000000010" shown in FIG. 8 (c). The compression order of the stored received sequence with the inverted first bits is shown in FIG. 12. As a result of arithmetic decoding, John 1. Ex. P decodes the first four parts of the decoded sequence with the inverted first bit (DP1) having, for example, the form “00000”, “00000”, “00000” and “01000”, as shown, for example, in FIG. 8 (d) and in FIG. 12. An uncorrected transmission error in the received sequence is detected only in the fourth part of the decoded sequence.

Since the inversion of the first (or only the first) bit of the received sequence did not correct the transmission error, the second bit is inverted in the stored received sequence (Jn 2. Ex. P) and it takes the form "110011101000000010" shown in FIG. 8 (d). The compression order of the stored received sequence with the inverted second bits is shown in FIG. 13. As a result of arithmetic decoding, John 2. Ex. P decodes the first two parts of the decoded sequence with the inverted second bit (DP2) having, for example, the form “11110” and “10111”, as shown, for example, in FIG. 8 (e) and in FIG. 13. Based on the results of a bit-wise comparison of the calculated check symbols with the corresponding decoded check symbols, a conclusion is made that there are no transmission errors. Indeed, the first two parts of the decoded sequences are identical to the first two parts of the error-correcting sequence shown in FIG. 4 (c).

If there is no transmission error, the next parts of the restored information sequence are transmitted to the recipient, for example, the first two parts of the restored information sequence of the form “1111” and “1011” shown in FIG. 8 (g).

Huffman coding can be used to compress the next parts of the error-correcting sequence, and Huffman decoding can be used to decompress the received sequence, similarly to the described arithmetic coding and arithmetic decoding.

Verification of the theoretical background of the claimed method of joint compression and noise-correcting coding was verified by its analytical studies.

Joint compression and noise-resistant coding of several successive parts of the information sequence was performed using the prototype method and the proposed method, the results are shown in FIG. 14. Joint compression and error-correcting coding of N = 10 consecutive parts of the information sequence of length k = 4 bits and k = 20 bits was performed using test characters of length r = 1 bit. The next parts of the binary information sequence with the probability of single symbols of 0.5, 0.2, 0.1, 0.01 and 0.001, respectively, were subjected to compression and noise-resistant coding. The compressed sequence transmitted over the transmission channel was randomly distorted by one error. On the receiving side, the probability of detecting an error P _obn and the probability of correcting an error P _{correct were calculated} . It was revealed that as the redundancy of the information sequence increases, the probability of error detection and the probability of error correction increase. Also, the probability of error detection and the probability of error correction increases with increasing length of the next part of the information sequence from k = 4 bits to k = 20 bits. For all investigated cases, the proposed method provides an increase in the detecting and correcting ability to detect and correct transmission errors in comparison with the prototype method.

Thus, in the inventive method for joint compression and error-correcting coding of an excess binary information sequence, an increase in the detecting and correcting ability to detect and correct transmission errors is provided.

Claims (2)

1. The method of joint compression and error-correcting coding, which consists in the fact that on the transmitting side from the sender receive the next part of the information sequence of length k≥1 bits, write test characters of length r≥1 bits together with the next part of the information sequence in the next part of the error-correcting sequence, perform compression of the next part of the error-correcting sequence into the next part of the compressed sequence, transmit the next part of the sequence to the receiving station they perform the listed actions on the transmitting side until the next parts of the information sequence arrive, on the receiving side receive the next part of the received sequence, which is stored, the stored next parts of the received sequence are expanded into the next parts of the decoded sequence, from which the next parts of the restored information sequences and decoded check symbols conclude that there are no transmission errors and transmit to the teacher the next part of the restored information sequence, otherwise one or more bits in the remembered next parts of the received sequence are alternately inverted, which are decompressed and perform the following actions until the conclusion about the absence of transmission errors is reached, perform the listed actions on the receiving side until the next parts of the received sequence, characterized in that after receiving the next part of the information sequence from it, check e symbols transmit the next part of the compressed sequence to the receiving side, on the receiving side, the verification symbols are calculated from the next part of the reconstructed information sequence and the calculated verification symbols are bitwise compared with the decoded verification symbols and, if bit-wise, they conclude that there are no transmission errors. 2. The method according to claim 1, characterized in that arithmetic coding or Huffman coding is used for compression, and arithmetic decoding or Huffman decoding, respectively, is used for compression.

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