RU2620731C1 - Method of joint arithmetic and immune construction of coding and decoding - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: in accordance to the invention for the next portion of the transmitted information sequence, the parity is selected, together arithmetically encoded, transmitted, formed of not more than the limiting number Z≥2 alternative received sequences and calculating the degree of similarity to the received sequence in a metric arithmetically decoded alternative received sequence is isolated more parts alternative reconstructed information sequence and alternative decoded parity and if the latter is valid, continuing the alternative received sequence of which is selected sequence with the lowest metric from which, with a predetermined decoding delay, the next part of the recovered information sequence is extracted, which is transmitted to the receiver.

EFFECT: joint arithmetic and noise-immune encoding and decoding of redundant binary information sequence, providing the possibility of practical implementation of correction of multiple transmission errors.

4 cl, 18 dwg

Description

The claimed technical solution relates to the field of telecommunications and information technology, namely to the technique of compression and recovery of redundant binary information and its noise-resistant coding and decoding when transmitting information on channels with errors.

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

The known method of adaptive noise-resistant coding and decoding according to the patent of the Russian Federation 2375824 IPC Н04L 1/20 (2006.01) dated 12/10/2009, which consists in the fact that on the transmitting side the source information is encoded with a noise-resistant code with variable parameters, then the noise-resistant code is transmitted to the communication channel, the receiving side, the error-correcting code is decoded with error detection and correction depending on the correcting ability of the selected code, the quality of the communication channel is estimated from the results of decoding the error-correcting code and select variable parameters of the error-correcting code are provided, which provide a predetermined 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 code, evaluate the probability of correct reception of the error-correcting code with the selected pairs TRAM, calculating the deviation of the received probability of correct reception error-correcting code by a predetermined probability of correct reception of the code and, depending on the magnitude of this deviation is corrected magnitude error-correcting redundancy code which is transmitted to the transmitting side, which is formed with antijamming code 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 and decoding 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 estimate is compared with the threshold quality value, if the calculated quality assessment of the reconstructed speech signal is not worse than a preset threshold quality value, then the receiver receives the next part of the reconstructed 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 select the appropriate method for compressing a speech signal and a method of error-correcting coding.

The closest in technical essence to the claimed method of joint arithmetic and noise-resistant coding and decoding is the method of joint arithmetic and noise-resistant coding and decoding according to US patent 6892343 IPC Н04M 13/00 (2006.01) dated 05/10/2005. The method is a prototype of joint arithmetic and error-correcting coding and decoding: first, the initial interval of arithmetic coding is set on the transmitting side and the initial arithmetic decoding interval corresponding to it is set on the receiving side, and the next part of the information sequence of length k≥1 is received on the transmitting side from the information source bit, divide the current arithmetic encoding interval into the current null sim encoding subinterval the ox and for the current coding sub-interval of a single symbol, from the pre-formed set, test characters of r≥1 bit length are selected and the next part of the error-correcting sequence is formed from the next part of the information sequence and the selected test symbols, arithmetic coding of the next part of the noise-resistant sequence into the next part of the coded sequence is convert the next part of the encoded sequence into the next part of the modules of the given sequence, the next part of the modulated sequence is transmitted to the receiving side, the listed actions are performed on the transmitting side until the next parts of the information sequence arrive, the next part of the received sequence is received on the receiving side, it is converted into a binary sequence that is stored, the current interval is shared arithmetic decoding to the current sub-interval of decoding a null character and to the current sub-interval of decoding a unit of a personal symbol, the stored next parts of the received sequence are arithmetically decoded into the next 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, then a conclusion is made that there are no transmission errors and transmitted to the recipient the next part of the restored information sequence, in than they invert one or several bits in the stored successive parts of the received sequence and perform their arithmetic decoding until reaching the conclusion that there are no transmission errors, perform the above actions on the receiving side until the next parts of the received sequence arrive.

A feature of the prototype method is that on the transmitting side, the selection of test characters is performed, and then the next parts of the information sequence and test characters are compressed by arithmetic coding, and on the receiving side, transmission errors are detected, if any, and when they are detected by trial and error, their correction. The prototype method of the joint arithmetic and noise-resistant coding and decoding provides the ability to detect and correct transmission errors.

However, in this prototype method of joint arithmetic and noise-correcting coding and decoding, transmission errors are corrected by brute force, inverting one or more bits in the stored next parts of the received sequence and performing their arithmetic decoding until reaching the conclusion on the correction of these errors. With a length of N bits of stored successive parts of the received sequence and the number W of correctable errors, this requires parallel or serial operation of an average of the order of N ^W / 2 arithmetic decoders with the corresponding number of error detection devices. When arithmetic decoding of compressed redundant binary sequences, a transmission error is detected with the length of the stored next parts of the received sequence up to tens of bits. Therefore, in this prototype method of joint arithmetic and noise-resistant coding and decoding, the complexity of implementing the correction of multiple transmission errors is very great.

Thus, the disadvantage of the closest analogue (prototype) of joint arithmetic and noise-correcting encoding and decoding of excess binary information is the practically unrealizable complexity of correcting transmission errors when the error rate is more than one.

The technical result of the proposed solution is the development of a method for joint arithmetic and noise-correcting coding and decoding of an excess binary information sequence, which provides the possibility of practical implementation of the correction of multiple transmission errors.

The specified technical result in the claimed method of joint arithmetic and noise-resistant coding and decoding is achieved by the fact that in the known method of joint arithmetic and noise-resistant coding and decoding, namely, that the initial interval of the arithmetic coding is set on the transmitting side and the corresponding initial interval on the receiving side arithmetic decoding, on the transmitting side from the source of the information sequence receive the next part of the information sequence with a length of k≥1 bits, divide the current interval of arithmetic coding into the current sub-interval of encoding a zero character and the current sub-interval of encoding a single character, select test characters of length r≥1 bits, form the next part of the error-correcting sequence from the next part of the information sequence and selected check characters, perform arithmetic coding of the next part of the error-correcting sequence into one part of the encoded sequence, the next part of the sequence is transmitted to the receiving side, the listed actions are performed on the transmitting side until the next parts of the information sequence arrive, the next part of the received sequence is received on the receiving side, the current arithmetic decoding interval of the received sequence is divided into the current decoding sub-interval zero character and the current sub-interval of decoding a single character, arithmetically encode the received sequence into successive parts of the decoded sequence, from which the next parts of the restored information sequence and decoded check symbols are extracted, transmit the next part of the restored information sequence to the recipient, perform the above actions on the receiving side until the next parts of the received sequence arrive, additionally preset limit number of alternative received sequences s and the value of delay Z≥2 T≥2 decoding and alternative metric values received sequences to zero.

On the transmitting side, the test characters are selected as zero characters if the current probability of zero characters of the information sequence determined by arithmetic coding is greater than or equal to the current probability of single characters in the information sequence, otherwise the test characters are selected as single characters. On the transmitting side, the next part of the coded sequence is transmitted to the receiving side, and on the receiving side, the next part of the received sequence is received and the next bit is read from it, the current arithmetic decoding interval of each alternative received sequence is divided into the current decoding subinterval of the null symbol and the current decoding subinterval of a single symbol this sequence. For each alternative received sequence, a continuation in the form of a null character and a continuation in the form of a single character are formed, the value of the continuation metric in the form of a null character and the value of the continuation metric in the form of a single character relative to the next bit of the next part of the received sequence are calculated, and the value of the continuation metric in the form of a null character relative to the next bit of the next part of the received sequence is calculated as a zero value if the next bit of the next part and the received sequence is a zero bit, otherwise it is calculated as a single value, and the continuation metric value as a single symbol relative to the next bit of the next part of the received sequence is calculated as zero if the next bit of the next part of the received sequence is a single bit, otherwise it is calculated as a single value.

For each alternative received sequence with its continuation, calculate the value of its metric by summing the metric of the sequence itself and its continuation, arithmetically decode each alternative received sequence with its continuation into the next parts of the corresponding alternative decoded sequence, from which the next parts of the alternative restored information sequence and alternative decoded test characters.

If the alternative decoded check characters are null characters, provided that the arithmetic decoding current probability of the null characters of the alternative reconstructed information sequence is greater than or equal to the current probability of unit characters of this sequence, or if the alternative decoded check characters are unit characters, provided that the current arithmetic decoding probability of single characters alternative th reconstructed information sequence greater than the current probability of null characters of the sequence, the alternative decoded parity are permissible.

If alternative decoded check symbols are valid, then the next parts of the alternative restored information sequence of the corresponding alternative received sequence are stored with its continuation, otherwise the metric value of this alternative received sequence with its continuation is set to the maximum value.

Compare with each other the metric values of the alternative received sequences with their extensions and select from them no more than Z alternative received sequences with their extensions having the smallest metric values into which the corresponding extensions are added, for these alternative received sequences the next parts of the corresponding alternative restored information are stored sequences and metric values.

The next bit of the next part of the received sequence is read and if its number is less than the number T, then the above actions are performed on the receiving side, otherwise the metrics of the alternative received sequences are compared and the alternative received sequence is selected from them with the lowest metric value.

Transfer to the recipient, as the next part of the restored information sequence, the next part of the alternative restored information sequence corresponding to the selected alternative received sequence. Perform the above actions on the receiving side until the next part of the received sequence arrives.

In the proposed set of actions on the receiving side, when decoding each next bit of the next part of the received sequence, a limited number Z of alternative received sequences are stored and continued with their continuations having the smallest metric values, that is, maximizing the probability of correction of transmission errors, and all other sequences are erased. The complexity of decoding a limited number Z of alternative received sequences with their extensions is substantially less than the complexity of decoding N ^W / 2 received sequences, as proposed in the prototype method.

Therefore, this new set of actions allows, when performing joint arithmetic and noise-correcting coding and decoding of an excess binary information sequence, to provide the possibility of practical implementation of the correction of multiple transmission errors.

The claimed method is illustrated by drawings, which show:

- in FIG. 1 - a general scheme of joint arithmetic and noise-resistant coding and decoding;

- in FIG. 2 is a diagram of a decoding unit 7;

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

- in FIG. 4 is a state table of arithmetic coding of the first six successive parts of the error-correcting sequence;

- in FIG. 5 is a timing diagram of arithmetic coding of the first two successive parts of an error-correcting sequence;

- in FIG. 6 is a timing chart of the joint arithmetic and noise-resistant coding of the first six successive parts of the noise-resistant sequence;

- in FIG. 7 - time diagrams of joint arithmetic and noise-free decoding of the first six successive parts of the received sequence on the receiving side;

- in FIG. 8 - algorithm for joint arithmetic and noise-free decoding at the receiving side;

- in FIG. 9 is a view of alternative accepted sequences in the form of a tree structure;

- in FIG. 10 is an exemplary view of selectable no more than L = 8 alternative received sequences;

- in FIG. 11 is a table of decoding states of an alternative received sequence of the form "00101110 0";

- in FIG. 12 is a table of decoding conditions of an alternative received sequence of the form "00101110 1";

- in FIG. 13 is a table of decoding conditions of an alternative received sequence of the form "00101110 00";

- in FIG. 14 is a table of decoding conditions of an alternative received sequence of the form "00101110 10";

- in FIG. 15 is a decoding state table of an alternative received sequence “00101110 11”;

- in FIG. 16 is a table of decoding conditions of an alternative received sequence of the form "00101110 010110";

- in FIG. 17 is a table of decoding states of an alternative received sequence with its sequential extensions of the form "00101110 000110";

- in FIG. 18 is a comparison of the complexity of the practical implementation of the correction of multiple transmission errors for the prototype method and the proposed method.

The implementation of the claimed method is presented on the example of the joint arithmetic and noise-resistant coding and decoding system shown in FIG. 1. On the transmitting side, joint arithmetic and noise-resistant coding of the next parts of the information sequence is performed, and on the receiving side, joint arithmetic and noise-resistant decoding of the received sequence is performed with the detection and correction of transmission channel errors. On the transmitting side, when the next part of the information sequence is received from the sender of the binary character, when the zero character is received, the counter of the number of zero characters 1 increases the number of zero coding characters by a unit value, and when a single character is received, the counter of the number of single characters 2 increases the number of coding unit characters by a unit value. Proportionally calculated numbers of null and single coding symbols in the subinterval boundary generator 3, the current arithmetic coding interval is divided in the arithmetic encoder 5 into the current null symbol encoding subinterval and the current single character encoding subinterval. In the block for selecting the verification symbols 4, verification symbols are selected, which together with the symbols of the next part of the information sequence are encoded in the arithmetic encoder 5 into the next part of the encoded sequence and transmitted via the transmission channel to the receiving side.

At the receiving side, in Z decoding units 7, the next parts of the received sequence are received. A diagram of the decoding unit 7 is shown in FIG. 2. In decoding unit 7, an alternative received sequence generator (APT) with a zero extension of 7.1 and an APT generator with a unit extension of 7.8 form alternative received sequences with corresponding continuations, which in arithmetic decoder 7.2 and arithmetic decoder 7.9, respectively, arithmetically decode into successive parts of the corresponding them alternative decoded sequences. When decoding a zero symbol from an APT with zero continuation, the counter of the number of zero symbols 7.3 increases the number of zero decoding symbols of this sequence by a unit value, and when decoding a single symbol, the counter of the number of unit symbols 7.4 increases the number of unit decoding symbols by a unit value. Proportional to the calculated numbers of zero and single decoding symbols in the boundary interval generator 7.6, the current interval of arithmetic decoding of an AMS with zero continuation is divided into the current sub-interval of decoding a zero symbol and the current sub-interval of decoding a single symbol for a given sequence.

Accordingly, when decoding a zero symbol from an APT with a unit extension, the counter of the number of zero characters 7.10 increases the number of zero decoding characters of this sequence by a unit value, and when decoding a single character, the counter of the number of unit characters 7.11 increases the number of unit decoding characters by a unit value. Proportional to the calculated numbers of null and single decoding symbols in the boundary interval generator 7.13, the current arithmetic decoding interval of the APT with a single continuation is divided into the current null symbol decoding sub-interval and the current single-symbol decoding sub-interval for this sequence.

In the APT 7.7 metric calculation block, for each alternative received sequence with its continuation, the value of its metric is calculated by summing the metric of the sequence itself and its continuation, where the continuation metric is calculated as the degree of similarity of the corresponding continuation to the next bit of the next part of the received sequence. In arithmetic decoders 7.2 and 7.9, from the next parts of the corresponding alternative decoded sequences, the next parts of the alternative reconstructed information sequence and alternative decoded check symbols (APSS) are extracted. If during the verification in the verification unit of the verification characters 7.5 AVPS corresponding to the alternative received sequence with zero continuation are valid, then in the block of the selection of the AMS 8 remember the next parts of the alternative restored information sequence corresponding to the alternative received sequence with the zero continuation, otherwise in the calculation block of the metric AMS 7.7 set the metric value of this alternative received sequence with zero continuation to the maximum value e.

Accordingly, if when checking in the verification unit of the verification characters 7.12 the APSS corresponding to the alternative received sequence with unit continuation are valid, then in the selection block APP 8 the next parts of the alternative restored information sequence corresponding to the alternative received sequence with unit continuation are stored, otherwise in the metric calculation unit AMS 7.7 sets the metric value of this alternate accepted sequence with a unit continued in maximum value.

In the selection block APP 8, the metric values of the alternative received sequences with their continuations are compared with each other and no more than Z alternative received sequences with their continuations having the smallest metric values are added to which the corresponding extensions are added, for these alternative received sequences the next parts are stored the corresponding alternative reconstructed information sequence and metric value.

Starting from the T-th bit of the received sequence in the block of the selection of the APT 8, the metrics of the alternative received sequences are compared with each other and the alternative received sequence with the lowest metric value is selected from them and the next part of the alternative restored information sequence.

The method implements the following sequence of actions.

The algorithm for joint arithmetic and noise-resistant coding on the transmitting side is presented in figure 3.

The methods of presetting on the transmitting side of the initial interval of arithmetic coding and on the receiving side of the corresponding initial interval of arithmetic decoding are known and described, for example, in the book “Data compression methods. Archiver device , image and video compression. " - M., DIALOGUE-MEPhI, 2002, pp. 35-43. The initial interval of arithmetic coding starts from its initial lower value and ends with its initial upper value. The initial lower value of the encoding interval is set to the minimum value of the encoding interval, 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] at time t = 0 is set to a minimum value equal to zero in decimal or 00000000 in binary representation, where the most significant binary characters are written left, and the initial upper value of 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 arithmetic coding interval is shown in FIG. 4 at t = 0 (first row) and in FIG. 5 at t = 0.

Also, the limit number of alternative received sequences Z≥2 and the decoding delay value T≥2 are pre-set, and the metric values of the alternative received sequences are set to zero. Methods for pre-setting the limit of the number of alternative received sequences Z and the decoding delay T, are known and described, for example, in B. Sklar's book "Digital Communication. Theoretical Foundations and Practical Applications". - M, Publishing House "William", 2003, pp. 430-439. For example, it is recommended to choose the maximum number of alternative received sequences Z from a number of values of the form 2, 4, 8, 16, taking into account the fact that with an increase in the selected number Z, it is possible to correct a larger number of transmission errors, but the complexity of implementing error correction increases linearly.

The value of the decoding delay T is numerically equal to the number of bits of the next parts of the received sequence, after decoding of which they decide on the next part of the restored information sequence. For example, it is recommended to choose a decoding delay value numerically equal to (2 ... 4) × Z, which allows you to correct the most common combinations of transmission errors without significantly increasing the complexity of implementing error correction. Methods for pre-setting the metric value of alternative accepted sequences to zero are known and described, for example, in B. Sklar's book "Digital Communication. Theoretical Foundations and Practical Applications". - M., Williams Publishing House, 2003, pp. 432-434.

On the transmitting side from the information source, the next part of the information sequence of length k≥1 bits is received. An exemplary view of the first six consecutive parts of a binary PI with a length of k = 2 bits is shown in FIG. 6 (a). For example, the first part of the IP has the form "00", the second part is "01", the third part is "01", etc. Single bit values in the figures are shown in the form of shaded pulses, zero bit values in the form of unshaded pulses.

Methods for dividing the current arithmetic coding interval into the current null-character encoding sub-interval and the current single-character coding sub-interval are known and described, for example, in the book “Data compression methods. Archiver devices, D. Arthur, A. Ratushnyak, M. Smirnov, V. Yukin.” image and video compression. " - M., DIALOGUE-MEPhI, 2002, pp. 35-43. For arithmetic coding of the next tth character, where t = 1, 2, ..., the length of the current interval of arithmetic coding I [t-1], equal to I [t-1] = H [t-1] -L [ t-1] is divided into a value of the current subinterval zero symbol D ₀ [t-1] and the current subinterval single symbol D ₁ [t-1]. For this purpose, the current count number of zero-sequence information symbols and parity N _Σ0 [t-1], by summing the current number of zero symbols ₀ Ninf information sequence [7-1], and the current number of zero parity Nproν ₀ [t-1] in the form of : N _∑0 [t-1] = Ninf ₀ [t + 1] + Nproν ₀ [t-1]. Similarly, the current number of unit characters of the information sequence and check characters N _∑1 [t-1] is calculated by summing the current number of unit characters of the information sequence and the current number of unit check characters: N _∑1 [t-1] = Ninf ₁ [t-1 ] + Nproν ₁ [t-1]. For example, at the initial moment at t = 0, the current number of zero characters of the information sequence and the test characters N _∑0 [0] is set to 1, where Ninf ₀ [0] = 1 and Nproν ₀ [0] = 0, and the current number of unit information sequence symbols and check symbols N _∑1 [0] is set to 1, where Ninf ₁ [0] = 1 and Nproν ₁ [0] = 0. Ways to set the number of zero and single characters of an information sequence to a single value at the initial moment of arithmetic coding are known and described, for example, in the book “Data compression methods. Archiver device, image compression” by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin and video. " - M., DIALOGUE-MEPhI, 2002, pp. 124-130. For example, as shown in FIG. 4 in the first line at t = 0, the top line indicates the unit number of zero characters of the information sequence (column N0) and the unit number of unit characters of the information sequence (column N1). Accordingly, in the bottom line at t = 0, the unit number of zero characters of the information sequence and check characters (column N0) and the unit number of single characters of the information sequence and check characters (column N1) are indicated. Column N indicates the total number of zero and single characters, in the upper line only for information sequence symbols, and in the lower line for information sequence symbols and check symbols. When encoding the first character of the account information, which is, e.g., a null symbol, the current number of zero symbols of the information sequence is increased by a unit value: Ninf ₀ [1] = 2, respectively, the current number of zero character sequence information and parity is equal to N _Σ0 [1] = 2, as shown in FIG. 4 in the second row at t = 1.

Starting from the moment of encoding the first and subsequent check symbols at t = 3, t = 6, t = 9, and so on, the current number of zero or single characters of the information sequence begins to differ from the current number of zero or single, respectively, characters of the information sequence and check characters as shown, for example, in FIG. 4 in the fifth row at t = 3.

Then calculate the current probability information sequence zero symbols and parity P _Σ0 [t] according to the _{rule: p Σ0 [t] = N} Σ0 [t] / (N Σ0 [t] + N Σ1 [t]) and the current probability of single characters in the information sequence and test characters p _∑1 [t] according to the rule: p _∑1 [t] = N _∑1 [t] / (N _∑0 [t] + N _∑1 [t). For example, as shown in FIG. 4 in the first line at t = 0, the bottom line shows the value of the current probability of zero characters of the information sequence and test characters (column p0) and the value of the current probability of single zero characters of the information sequence and test characters (column p1), where the initial values are 0, 5.

The length of the current subinterval of a single symbol D ₁ [t] is determined by a formula of the form D ₁ [t] = I [t] × p ₁ [t], and the length of the current subinterval of a single character D ₀ [t] is determined by a formula of the form D ₀ [t] ] = I [f] -D ₁ [t]. For example, the length of the initial subinterval of single characters D ₁ [0] has a decimal value of 128 or 10,000,000 in binary representation, and the length of the initial subinterval of single characters D ₀ [0] has a decimal value of 127 or 01111111 in binary representation. The sub-interval of single characters is located on top of the sub-interval of null characters, as shown, for example, in FIG. 5. The upper boundary of the null character subinterval is designated as the Q value, and this subinterval starts from the bottom of the lower boundary of the coding interval of the arithmetic coding inclusively to the Q value exclusively, and the subinterval of a single symbol extends from the Q value inclusive to the upper boundary of the coding interval of the arithmetic coding exclusively. The initial Q value has a decimal value 127, as shown in FIG. 4 in the first line at t = 0.

Check characters with a length of r≥1 bit are selected as zero characters if the current probability of zero characters in the information sequence determined by arithmetic coding is greater than or equal to the current probability of single characters in the information sequence; otherwise, check characters are selected as single characters. This method of selecting test characters allows the selection of test characters with a predominance of zero or single characters in accordance with the predominance of zero or single characters in the information sequence, which increases the compression ratio of the arithmetic coding of a noise-resistant sequence consisting of redundant information sequence and selected test characters.

The selection of the next check characters is as follows. To select the next verification character, which is the t-th among the information sequence symbols and verification symbols, the current probability of encoded zero symbols of the information sequence pinf ₀ [t-1] according to the rule pinf ₀ [t-1] = Ninf ₀ [t- 1] / (Ninf ₀ [t-1] + Ninf ₁ [t-1]) and the current probability of encoded single characters of the information sequence pinf ₁ [t-1] according to the rule pinf ₁ [t-1] = Ninf ₁ [t- 1] / (Ninf ₀ [t-1] + Ninf ₁ [t-1]), where Ninf ₀ [t-1] and Ninf ₁ [t-1] are the number of encoded zero characters of the information sequence and the number of encoded ones characters of the information sequence, respectively, at the time [t -1].

If a relation of the form pinf ₀ [t-1] ≥pinf ₁ [t-1] holds, then the zero characters of the information sequence prevail and the next check character is selected as having a zero value, otherwise the single characters of the information sequence prevail and the next check character is selected as having a single value. For example, as shown in FIG. 4, at time t = 3, after encoding the first two information symbols, a verification symbol is selected, which is the only verification symbol (r = 1) for two information symbols (k = 2). With the number of successive test characters more than one, the rule for choosing these characters does not change.

At the time of selecting the verification symbol indicated in the example, the probability of the encoded zero characters of the information sequence is pinf ₀ [2] = 3/4 and the probability of the encoded single characters of the information sequence is pinf ₁ [2] = 1/4. Due to the predominance of zero characters of the information sequence, the next check character at t = 3 is chosen as having a zero value. Since further on, the number of zero characters of the information sequence exceeds the number of single characters at the moments of selection of test characters at t = 6, t = 9, t = 12, t = 15, and t = 18, as shown in FIG. 4, then the subsequent check symbols are selected as having a null value for the shown example. An exemplary view of the selected check symbols for the first six successive parts of the information sequence is shown in FIG. 6 (b).

The formation of the next part of the error-correcting sequence from the next part of the information sequence and the selected test symbols can be constructed, for example, as reading into the next part of the error-correcting sequence first the next part of the information sequence, and after it reading the selected test symbols. Methods for reading test characters together with the next part of the information sequence into 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 “000”, the second part is “010”, the third part is “010”, as shown in FIG. 6 (c). It is also possible to change the order of information and test symbols in an error-correcting sequence.

The methods of arithmetic coding of the next part of the error-correcting sequence into the next part of the encoded 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, 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 encoded sequence in accordance with the current values of the coding interval of the arithmetic coding and the current values of the probabilities of zero characters and single characters of the information sequence and check characters. As binary characters arrive at the input, the current number of null characters of the information sequence and check characters and the current number of single characters of the information sequence and check characters are calculated, proportionally to which the current coding interval of the arithmetic coding is divided into the current sub-range of the coding of the zero character and the current coding sub-interval of a single character, in according to which the arithmetic encoder sequentially generates an encoded sequence activity (KP).

When the next binary symbol arrives at the input of the arithmetic encoding of the next part of the error-correcting sequence, which is a single binary symbol, the current encoding interval of this symbol is set equal to the previous encoding sub-interval of a single symbol, and when the binary symbol is arithmetically encoded, the current encoding interval of this symbol is set equal to the previous null character encoding subinterval. For example, when the first binary symbol of the first part of the error-correcting sequence, which is a zero binary symbol, arrives at the input of the arithmetic encoding, the lower value of the encoding interval of the first character L [1] is set equal to the initial lower value of the encoding interval of arithmetic encoding L [0], for example, decimal the value 0, and the upper value of the coding interval of the first character of the arithmetic coding H [1] is set equal to the value of Q, equal to, for example, 127, as shown in FIG. 4 and in FIG. 5 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 00000000 and 01111111, respectively, as shown in FIG. 3 at t = 1. When they coincide, the value of the leftmost bit of the binary representations of the values L [1] and H [1] is read as the next bit of the next part of the encoded sequence (Code symbol in Fig. 4). For example, when encoding the first part of the error-correcting sequence, the first bit of the first part of the CP is the zero binary symbol that coincides when comparing, as shown in FIG. 4, the third line from the top. The read bit is removed from the binary representations of the values L [1] and H [1], which are reduced to a length of 7 bits of the form 0000000 and 1111111, respectively. The binary symbols of the binary representations of the values L [1] and H [1] 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 [1] and H [1] take the form 00000000 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 [t] and H [t] 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 bit of the next part of the CP, otherwise they proceed to the encoding of the next character and so on, as shown in FIG. four.

After arithmetic coding of each successive character, the number of encoded null characters of the information sequence and check characters and the number of encoded single characters of the information sequence and check characters are specified. Since the first encoded character in the indicated example is zero, the number of encoded zero characters of the information sequence and check characters is increased by a unit value and it is N _∑0 [1] = 2, the number of encoded single characters of the information sequence and check characters remains equal to N _{∑ 1} [1] = 1, respectively, the total number of coded zero and unit information and parity symbols become equal to 3. recalculates the current probability value zero symbols information sequence and parity p _Σ0 [1] = 2/3 and the current value of the probability of individual information symbols and the parity sequence p _Σ1 [1] = 1/3. Accordingly, the length of the subinterval of the null symbol D ₀ [1] becomes 2 times the length of the subinterval of a single symbol D ₁ [1], as shown in FIG. 4, the third row from above and in FIG. 5 at t = 1 after normalization.

Arithmetic coding of the next binary symbol is performed, as shown in FIG. 4 and in FIG. 5. The arithmetic coding of test characters does not differ from the coding order of characters of the information sequence.

Upon receipt of an arithmetic coding symbol, which is a single character, the lower value of the encoding interval is set equal to the previous value Q, and the upper value of the encoding interval is set equal to the previous upper value of the encoding interval. For example, when arithmetic coding of the fifth character in a row (t = 5), which is a single character, the lower value of the encoding interval L [5] is set equal to the value Q [4], for example, 169, and the upper value of the encoding interval H [5] set equal to the upper value of the encoding interval H [4], for example, equal to 203, as shown in FIG. 4 at t = 5.

An approximate form of arithmetic coding of the first six successive parts of an error-correcting sequence of the form "000", "010", "010", "000", "100" and "010" into the corresponding subsequent parts of the encoded sequence of the form "00", "1", " 011 "," _ "," 100001 "and" 10 "are shown in FIG. 6 (g). For example, the fourth part of the error-correcting sequence is empty (does not contain binary characters).

Methods of transmitting to the receiving side the next part of the encoded 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 first six parts of the received sequence (Pr. P) is shown in FIG. 7 (a). The received sequence during transmission is distorted in the third and fourth bits of the fifth part of the received sequence and has the form "00", "1", "011", "_", "101101" and "10".

The algorithm for joint arithmetic and error-correcting decoding at the receiving side is shown in FIG. 8.

To initiate arithmetic decoding, it is necessary to take the first N _R binary symbols of the next parts of the received sequence, where N _R is the number of binary symbols representing the values of the encoding interval and, accordingly, the decoding interval. For example, when presenting the values of the encoding interval and the decoding interval with eight binary characters, the first eight bits of the received sequence of the form “00101110” are received, which are the first to fourth and first bits of the fifth part of the received sequence, and the next part of the received sequence is received on the receiving side without allocation the boundaries of these next parts.

Arithmetic and error-correcting decoding of the received sequence at the receiving side is performed by decoding several alternative received sequences. At the time of reading the first bit after the initial N _R bit of the next part of the received sequence, indicated by time t = 1, for the initial received sequence consisting of the first N _R binary symbols of the next parts of the received sequence, a continuation in the form of a null character and a continuation are formed in the form of a single character. For example, for the initial received sequence of the form "00101110", 2 extensions are formed: an alternative received sequence (APT) with a continuation in the form of a null character "00101110 0", and an alternative received sequence with a continuation in the form of a single character "00101110 1". When reading the next bit of the next part of the received sequence (time moment t = 2) for each of the two available alternative sequences, they form continuations in the form of a null character and a continuation in the form of a single symbol, as a result, at time t = 2, the number of alternative received sequences becomes 4 , at time t = 3, the number of alternative received sequences can reach 8, etc.

На фиг. 10 также показано, что среди текущих альтернативных принятых последовательностей с их продолжениями выбирают не более Z последовательностей, имеющих наименьшие значения метрики, остальные последовательности не получают продолжения, что показано символом "X".A view of alternative received sequences in the form of the described tree structure is shown in FIG. 9. Such a structure of alternative received sequences potentially makes it possible to correct multiple transmission errors in the received sequence. For each alternative received sequence, the following arithmetic and noise-correcting decoding steps are performed. Since the number of alternative received sequences in such a tree structure doubles at each subsequent time moment t, which exponentially increases the complexity of the implementation of the correction of transmission errors, to reduce this complexity at each moment t, among alternative received sequences with their extensions, choose and continue no more than L alternative received sequences closest to the accepted sequence in the Hamming metric, and the remaining alternative accepted sequences Vegetations are erased. For example, with a predetermined limit number of alternative received sequences Z = 8, an exemplary view of selectable no more than Z alternative received sequences is shown in FIG. 10. It can be seen that in this structure, called a truncated tree of alternative received sequences, the number of continued alternative received sequences at each moment t does not exceed a given value Z = 8. For example, the number of continued received sequences when decoding the ninth character of the received sequence is 2, when decoding the tenth character - 4, when decoding the next four characters - by 8. Alternative received sequences do not get continued from which, when decoding, alternative decoded check characters are extracted, not valid, which means that they did not fix transmission errors. In FIG. 10 it is shown that when identifying invalid decoded check characters, the metric value of the corresponding alternative received sequence with its continuation is set to the maximum value (M = Max), and such a sequence will not be continued. Identification of invalid decoded check symbols in FIG. 10 and subsequent non-selection of such a path is indicated by the symbol

In FIG. 10 also shows that among the current alternative received sequences with their extensions, no more than Z sequences having the smallest metric values are selected, the rest of the sequences do not continue, as shown by the symbol "X".

In this case, the decision to choose among the continued alternative received sequences the desired received sequence with corrected transmission errors is made with a pre-set decoding delay T. For example, in FIG. 10 shows an example of a decision to choose an alternative received sequence with corrected transmission errors with decoding delay T = 16. When decoding the sixteenth character of the received sequence with the minimum metric M = 2 among the alternative received sequences, the only sequence remains and a sequence is selected, the continuation of which is indicated by an ellipsis, for which the two transmission errors described above have been fixed. The next part of the alternative restored information sequence corresponding to the selected alternative received sequence is transmitted to the recipient as the next part of the restored information sequence. Next, the next bit of the next part of the received sequence is received, for the selected alternative received sequence, the continuations are formed and the above actions are performed until the next parts of the received sequence arrive.

We describe in detail the actions of arithmetic and noise-resistant decoding on the receiving side.

The methods for dividing the current arithmetic decoding interval of each alternative received sequence into the current null-symbol decoding sub-interval and the current decoding sub-interval of a single symbol of this sequence are identical to the methods of dividing the current arithmetic coding interval into the current null-character encoding sub-interval and the current single-character encoding sub-interval. The upper boundary of the current null symbol decoding sub-interval is designated as the QQ value, and this sub-interval starts from the bottom of the current boundary of the LL decoding interval to the QQ value exclusively, and the current single-symbol decoding interval extends from the QQ value inclusive to the upper boundary of the current LV decoding interval exclusively. For example, for the initial received sequence of the form “00101110”, the lower bound of the current decoding interval is LL [Q] = 0, and the upper bound of the current decoding interval is LV [0] = 255, as shown in FIG. 11 in the first line at t = 0.

The length of the current interval of arithmetic decoding of each alternative received sequence II [7-1], equal to II [t-1] = HH [t-1] -LL [t-1], is divided by the value of the current subinterval of the null character DD ₀ [t- 1] and the current subinterval single character DD ₁ [t-1]. To do this, calculate the current number of zero characters of the alternative restored information sequence and alternative decoded check characters of the alternative received sequence NN _∑0 [t-1], summing the current number of zero characters of the alternative restored information sequence NNinf ₀ [t-1] and the current number of zero alternative decoded verification characters NNproν ₀ [t-1] in the form: NN _∑0 [t-1] = NNinf ₀ [t-1] + NNproν ₀ [t-1]. Similarly, the current count number of unit characters alternative reconstructed information sequence and alternative decoded parity of each received an alternative sequence NN _Σ1 [t-1], by summing the current number of unit characters alternative reconstructed information sequence and the number of unit current alternative decoded parity: NN _Σ1 [t-1] = NNinf ₁ [t-1] + NNproν ₁ [t-1]. For example, at the initial moment at t = 0, the current number of zero characters of the alternative reconstructed information sequence and alternative decoded check characters of each alternative received sequence NN _∑0 [0] is set to 1, where NNinf ₀ [0] = 1 and NNproν ₀ [0 ] = 0, and the current number of unit characters of the alternative reconstructed information sequence and alternative decoded check characters NN _∑1 [0] is set to 1, where NNinf ₁ [0] = 1 and NNproν ₁ [0] = 0.

For example, as shown in FIG. 11 in the first line at t = 0 for the initial received sequence of the form "00101110", the top line indicates the unit number of zero characters of the alternative restored information sequence (column NN0) and the unit number of unit characters of the same restored information sequence (column NN1). Accordingly, in the bottom line at t = 0, the unit number of zero characters of the alternative reconstructed information sequence and alternative decoded check characters (column NN0), as well as the unit number of unit characters of the alternative reconstructed information sequence and alternative decoded check characters (column NN1). The column NN indicates the total number of null and single characters, in the top line only for the characters of the alternative restored information sequence, and in the bottom line for the characters of the alternative restored information sequence and alternative decoded check characters.

Then, the current probability of zero characters of the alternative reconstructed information sequence and alternative decoded check symbols pp _∑0 [t] is calculated according to the rule: pp _∑0 [t] = NN _∑0 [t] / (NN _∑0 [t] + NN _∑1 [ t]) and the current probability of unit symbols of the alternative reconstructed information sequence and alternative decoded check symbols pp _∑1 [t] according to the rule: pp _∑1 [t] = NN _∑1 [t] / (NN _∑0 [t] + NN _{∑ 1} [t]). For example, as shown in FIG. 11 in the first line at t = 0, the bottom line shows the value of the initial probability of zero characters of the alternative reconstructed information sequence and alternative decoded check characters (column pp0) and the value of the initial probability of the single characters of the alternative reconstructed information sequence and alternative decoded check characters (column pp1) where the initial values are 0.5.

The length of the current subinterval of the unit characters of the alternative reconstructed information sequence and the alternative decoded check characters DD ₁ [t] is determined by the formula of the form DD ₁ [t] = II [t] × pp _∑1 [t], and the length of the current subinterval of the zero subinterval of the zero characters of the alternative restored information sequences and alternative decoded check symbols DD ₀ [t] is determined by a formula of the form DD ₀ [t] = II [t] -DD ₁ [t]. For example, the length of the initial subinterval of single characters DD ₁ [0] has a decimal value of 128 or 10,000,000 in binary representation, and the length of the initial subinterval of single characters DD ₀ [0] has a decimal value of 127 or 01111111 in binary representation. The sub-interval of single characters is located on top of the sub-interval of null characters, as shown, for example, in FIG. 11. The upper boundary of the null character subinterval of the alternative reconstructed information sequence and the alternative decoded check characters is designated as the QQ value, and this subinterval starts from the bottom of the lower boundary of the arithmetic decoding decoding interval inclusively to the QQ value exclusively, and the single character subinterval extends from the QQ value inclusive to the upper arithmetic decoding decoding interval boundaries exclusively. The initial QQ value has a decimal value of 127, as shown in FIG. 11 in the first line at t = 0.

At the initial moment, the alternative received sequences consist of the initial received sequence having a pre-set zero metric value (M = 0).

After reading the next bit of the next part of the received sequence, a continuation in the form of a zero symbol and a continuation in the form of a single symbol are formed for each alternative received sequence. For example, an alternative received sequence with a continuation in the form of a null character becomes “00101110 0”, as shown in FIG. 11, and an alternative received sequence with the continuation in the form of a single symbol becomes “00101110 1”, as shown in FIG. 12.

After the continuation is formed, the continuation metric value is calculated as a null character and the continuation metric value is a single character relative to the next bit of the next part of the received sequence, while the continuation metric value as a zero character relative to the next bit of the next part of the received sequence is calculated as zero if the next the bit of the next part of the received sequence is a zero bit, otherwise it is calculated as a single value, and also e metric as a single continuing relatively symbol next bit of the next part of the received sequence is calculated as zero, if the next bit is the next part of the received sequence is a single bit, otherwise calculated as a single value. For example, as shown in FIG. 11, the next bit of the next part of Ave. P, the next after reading eight bits of the initial decoding path, has a single value. Therefore, with respect to this bit, the continuation metric in the form of a zero symbol has a unit value, and the continuation metric in the form of a single symbol has a zero value.

Then, for each alternative received sequence with continuation, the value of its metric is calculated by summing the metric of the path itself and the metric of its continuation. For example, the metric of the alternative received sequence "00101110 0" with a continuation in the form of a null character receives a unit value (M = 1), and the metric of the alternative received sequence "00101110 1" with a continuation in the form of a single character receives a null value (M = 0).

The methods of arithmetic decoding of an alternative received sequence with its continuation into the next parts of the corresponding alternative decoded sequence are known and described, for example, in the book “Data compression methods. Archiver device, image compression” by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin and video. " - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequential decoding of the alternative received sequence with its continuation in accordance with the current values of the decoding interval of the arithmetic decoding of this sequence and the current values of the probability of decoded zero characters and single characters of this sequence.

An exemplary arithmetic decoding of an alternative received sequence with its continuation “00101110 0” into characters of the first part of its corresponding alternative decoded sequence is shown in FIG. 11. Initially, the first 8 bits of the form “00101110” are read in turn at the input of arithmetic decoding, which corresponds to the decimal number 46. The current read bits (count) are shown in the second column, the current value is shown in the third column of the same table (Input data) read data. The current value of the read data is compared with the boundaries of the initial value of the decoding sub-interval of the zero characters of the alternative reconstructed information sequence and the alternative decoded check symbols DD ₀ [0], which are, for example, in the range from 0 to 127, and with the boundaries of the initial value of the sub-interval of decoding the individual characters of the alternative restored and alternative information sequence decoded DD ₁ [0] parity located, e.g., within t 127 to 255. Depending on whether any subinterval within decode symbols turned current value of the read data, decide on the value of the current symbol alternative decoded sequences (December. sim.).

For example, since the current value of the read data was less than the value QQ (46 <127), the first decoded symbol is zero and the next decoding interval boundaries set values corresponding boundaries subinterval decoding null symbols ₀ DD [0]. As a result of decoding

the first character sets the lower value of the arithmetic decoding decoding interval LL [1] to the previous value LL [0], for example, LL [1] = 0, and the upper value of the arithmetic decoding decoding interval HH [1] to the QQ value, for example, HH [ 1] = 127, as shown in FIG. 11 in the second row at t = 1.

After decoding each symbol, the current probability value of the decoded null symbols of the alternative reconstructed information sequence and alternative decoded check symbols and the current probability value of the decoded single symbols of the same sequence are recalculated, for example, after decoding the first symbol that is null according to the formula of the form pp _∑0 [1] = NN _∑0 [1] / (NN _∑0 [1] + NN _∑1 [1]) = 2/3 and according to a formula of the form pp _∑1 [1] = NN _∑1 [1] / (NN _∑0 [ 1] + NN _∑1 [1]) = 1/3, respectively.

After each change in the arithmetic decoding state (Dec. Dec.), 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, for t = 1 of the form "0000 0000" and "0111 1111", respectively. If they coincide, the arithmetic decoding is normalized: the value of the leftmost bit of the binary representations of the LL and HH values is deleted and the binary characters of the binary representations of the LL and HH values are shifted from right to left by one digit and are added to the least significant bit to the right with the zero binary symbol. 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 bit and the next read binary character of this alternative received sequence is added to them with its continuation. As described above, the next binary character read is the ninth character of this alternative received sequence with its continuation, having a zero value. With the reading of this bit, the metric of this alternative received sequence c, its continuation, “00101110 0” has taken a single value (M = 1), as shown in FIG. 11 in the fourth column. Given the binary character read, the input received the binary representation "01011100" and the decimal value 92. The variable LL saved the decimal value 0, and HH received the decimal value 254 and the binary representation "11111110". Again, 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, and if they coincide again, they perform normalization again in the same way, etc.

As a result of arithmetic decoding of the alternative received sequence with the continuation in the form of a null character of the form “00101110 0” shown in FIG. 7 (b), decode, for example, three characters of the first part of its corresponding alternative decoded sequence (ADP), having the form "000", as shown in FIG. 7 (c) and in FIG. eleven.

Methods of extracting from the next part of the ADP the next part of the alternative restored information sequence (AVIP) and alternative decoded check symbols (ADPS) 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 alternative decoded sequence is sequentially written to the shift register memory cells of length k + r bits. From the first memory cells of this shift register, the next part of the alternative restored information sequence of length k bits is read in parallel. From the subsequent, starting from k + 1, memory cells of the same shift register, alternatively decoded check symbols of length r bits are read in parallel. For example, from the first part of an ADP of the type "000", the first part of the AVIP of the type "00" is extracted, as shown in FIG. 7 (d), and ADPS of the form “0”, as shown in FIG. 7 (d).

If the alternative decoded check characters are null characters, provided that the arithmetic decoding current probability of the null characters of the alternative reconstructed information sequence is greater than or equal to the current probability of the unit characters of this sequence, or if the alternative decoded check characters are unit characters, provided that the arithmetic decoding current probability of single characters alternative th reconstructed information sequence greater than the current probability of null characters of the sequence, the alternative decoded parity are permissible. Therefore, to establish the admissibility of ADPS, the current probability of zero characters of an alternative reconstructed information sequence and, accordingly, the current probability of single characters of this sequence are calculated. The current probability zero symbols alternative reconstructed information sequence pinf ₀ [t] is counted by the rule pinf ₀ [t] = Ninf ₀ [t] / (Ninf ₀ [t] + Ninf ₁ [t]) and the current probability of single characters alternative reconstructed information sequence pinf ₁ [t] - according to the rule pinf ₁ [f] = Ninf ₁ [t] / (Ninf ₀ [t] + Ninf ₁ [t]), where Ninf ₀ [t] and Ninf ₁ [t] - the number of zero characters alternative restored information sequence and the number of unit characters of the alternative restored information sequence, respectively, on my ent t-th decoding symbol alternative decoded sequences.

For example, after decoding an alternative decoded check symbol from the first part of the ADP corresponding to the alternative received sequence with the continuation of the form "00101110 0", the current probability of zero characters of the alternative reconstructed information sequence is pinf ₀ [3] = 3/4, and the current probability of unit characters is alternative reconstructed information sequence - pinf ₁ [3] = 1/4, as shown, for example, in FIG. 11 in the fifth line with t = 3 in the top line. Therefore, for this alternative decoded check symbol, which is a null character, the relation pinf ₀ [3] ≥pinf ₁ [3] holds and this alternative decoded check symbol is valid. Thus, at the moment, in the alternative received sequence with its continuation of the form “00101110 0”, invalid alternative decoded check characters have not been identified and the next parts of the alternative restored information sequence and the metric value equal to M = 1 are stored in it.

Similarly, arithmetic decoding of an alternative received sequence with its unit continuation of the form “00101110 1” shown in FIG. 7 (e), in three characters of the first part of its corresponding ADF, an exemplary view of which is shown in FIG. 7 (g) and FIG. 12. It can be seen that this sequence also led to the decoding of a valid ADPS, and the next parts of the alternative reconstructed information sequence and the value of its metric are remembered corresponding to it. The metric of this alternative received sequence with its continuation retained a zero value (M = 0), that is, at the time of reading and decoding a given bit of the received sequence, its chances of choosing as an alternative received sequence with the lowest metric value are preferred compared to the previously considered alternative accepted sequence with its continuation of the form "00101110 0".

Then, the metric values of the alternative received sequences are compared with each other and their continuations are selected and no more than Z alternative received sequences having the smallest metric values are selected from them. These methods are known and described, for example, in the book by M. Shibuya, T. Yamamoto "Data Processing Algorithms". - M., Mir, 1986, pp. 122-134, and consist in alternately comparing the values of the AMP metric with their extensions, sorting the sequences as the values of the metric increase, and choosing among the sorted sequences of the first Z sequences with the lowest metric values. For example, after reading and decoding the current, ninth, bit of the received sequence, there are two alternative received sequences with their extensions, therefore, when the value Z = 8 is set, both alternative accepted sequences considered above with their extensions are selected.

In the selected received sequences with their extensions, the corresponding extensions are added; for these APPs, the next parts of the corresponding alternative restored information sequences and metric values are stored. For example, as a result, an APP of the type "00101110 0" with the corresponding alternative restored information sequence of the form "000" and the metric M = 1 is saved, as well as an APP of the type "00101110 1" with the corresponding alternative restored information sequence of the form "000" and the metric M = 0.

Then the next bit of the received sequence, the tenth in a row, is read, and if its number is less than the number T, then the above actions are performed on the receiving side. For example, the tenth number of the next bit of the received sequence is less than the set decoding delay value T = 16. For an APT of the form "00101110 0", a continuation in the form of a null character and a continuation in the form of a single character are formed. For the obtained APT with a continuation in the form of a null character of the form "00101110 00", its metric equal to M = 2 is calculated, and for the obtained APT with the continuation in the form of a single character of the form "00101110 01", its metric equal to M = 1 is calculated.

Arithmetic decoding of the APT with the continuation in the form of a null character of the form "00101110 00" is presented, for example, in FIG. 13. The decoding of this sequence is a continuation of the decoding of the previous AMS with the continuation in the form of a single symbol of the form "00101110 1", previously shown in FIG. 11. After the third decoded symbol at time t = 3, normalization is performed according to the previously described rule: the zero symbol is read from the current continuation, taking into account which the input data is set to 184, during normalization, the current lower value of the decoding interval of arithmetic coding LL is set [3] = 0, the current upper value of the decoding interval of the arithmetic coding HH [3] = 254 and the value QQ [3] = 169. Then, at time t = 4, the fourth symbol of the alternative decoded sequence, which is a null symbol, is decoded, and at time t = 5, the fifth symbol of the alternative decoded sequence, which is a single symbol, is decoded. Note that when reading the next bits of the AMS, a different number of ADF symbols can be decoded. It can be seen that at time t = 5 for this APT with the continuation in the form of a null character of the form "00101110 00" the second part of the corresponding alternative decoded sequence is not fully decoded.

Similarly, the arithmetic decoding of the APP is performed with the continuation in the form of a single character of the form "00101110 01".

Also, when reading the tenth next bit of the received sequence for the AMS of the form "00101110 1", a continuation in the form of a null character and a continuation in the form of a single character are formed. For the obtained APT with a continuation in the form of a null character of the form "00101110 10", its metric equal to M = 1 is calculated, and for the obtained APT with the continuation in the form of a single character of the form "00101110 11", its metric equal to M = 0 is calculated.

Arithmetic decoding of the APT with the continuation in the form of a null character of the form "00101110 10" is presented, for example, in FIG. 14, and an alternative received sequence with the continuation in the form of a single symbol of the form “00101110 11” is presented, for example, in FIG. 15. The decoding of these sequences is a continuation of the decoding of the previous AMS with the continuation in the form of a null character of the form “00101110 0”, previously shown in FIG. 12. The results of decoding these sequences are similar to the results of decoding APP with the continuation in the form of a null character of the form "00101110 00", with the exception of differences in the values of the input data and metrics. As shown, for example, in FIG. 10, at this stage, the APT with their continuations select 4 from their current number 4, then when reading the eleventh character of the received sequence, 8 from their current number 8.

When reading the twelfth character of the received sequence, 16 APTs with their continuations are decoded arithmetically. At the same time, in the APT with continuations of the form “00101110 1101”, “00101110 1110” and “00101110 1111”, invalid alternative decoded check symbols are detected and these sequences are not selected among the Z alternative received sequences with their continuations having the smallest metric values. In particular, the APP with the continuation of the form “00101110 1101” turned out to be rejected, which had the lowest metric value (M = 0).

Among the remaining APPs with their extensions, three APPs with their extensions with a metric value M = 1 of the type "00101110 0101", "00101110 1001" and "00101110 1100" and five APPs with their extensions with a metric value of M = 2 are selected. At this stage, all APPs with continuations having metric values M = 3 and M = 4 turned out to be rejected.

When reading the thirteenth character of the received sequence of three APTs with corresponding extensions with the value of the metric M = 1, only one sequence remains with the value of the metric M = 1 of the form "00101110 01011". When reading the fourteenth character of the received sequence from this APT with its continuation as “00101110 010110” shown in FIG. 7 (h), at time t = 12, four parts of the alternative decoded sequence of the form “000 010 010 001” shown in FIG. 7 (s), from the fourth part of which an alternative decoded check symbol is selected, which is a single symbol. As a result of its verification, its inadmissibility was revealed, since the current probability of zero characters of the alternative restored information sequence pinf ₀ [12] = 6/10 exceeds the current probability of single characters of the alternative restored information sequence pinf ₁ [12] = 4/10, which is a condition for recognition only a null alternative decoded check character is valid.

If an invalid alternative decoded check symbol is detected, the metric value of the corresponding alternative received sequence is established with its continuation to the maximum value. For example, set the value of the APP metric with its continuation of the form "00101110 010110" equal to M = 1000, which will inevitably lead to the fact that this APP with its continuation will not be selected in L APP having the smallest metric values.

As a result, among the remaining APPs with their extensions there is no sequence with the metric value M = 1 and there are 3 sequences with the metric value M = 2, as shown, for example, in FIG. 10. When reading the subsequent characters of the received sequence in two of the three sequences with the corresponding continuations having a metric value of M = 2, invalid alternative decoded check characters will be detected. With the metric value M = 2, the remaining sequence with the corresponding continuation of the form “00101110 000110” will be the sequence with the smallest metric value satisfying the requirement of admissibility of alternative decoded check symbols, as shown, for example, in FIG. 17.

If the number of the next bit of the next part of the received sequence is not less than the number T, then the metric values of the alternative received sequences are compared and the alternative received sequence is selected from them with the lowest metric value, the next part corresponding to the selected alternative received sequence is transferred to the recipient as the next part of the restored information sequence alternative reconstructed information sequence. For example, at T = 16, the alternative accepted sequence with its successive extensions of the form "00101110 000110" has the smallest metric value M = 2. As shown in FIG. 17, as a result of its arithmetic decoding, an ADF of the form “000 010 010 000 1” is formed, shown, for example, in FIG. 7 (l) containing the first 4 parts of an alternative reconstructed information sequence of the form “00 01 01 00”, shown, for example, in FIG. 7 (m). Of these, the first part of this alternative reconstructed information sequence of the form “00”, shown, for example, in FIG. 7 (n). Then, as the next bits of the next parts of the received sequence are read and decoded, the next parts of the restored information sequence are transmitted to the recipient.

Verification of the theoretical premises of the claimed method of joint arithmetic and noise-correcting coding and decoding was verified by its analytical studies.

Joint arithmetic and noise-resistant coding and decoding of several successive parts of the information sequence was performed using the prototype method and the proposed method, the results are shown in FIG. 18. In accordance with the prototype method and the proposed method, joint arithmetic and noise-resistant coding and decoding of the next parts of the information sequence of length k = 4 bits with a total length of 1024 bits was carried out using test characters of length r = 1 bit.

On the length N bits of the stored next parts of the received sequence for the prototype method and the length and magnitude of the decoding delay T for the proposed method, provided N = T, transmission errors were superimposed on the encoded sequence in the following variants: only one error (W = 1), two errors (W = 2), three errors (W = 3). For each W value, error configurations were randomly generated 1000 times. At the receiving side, the average number of inverted bits of the received sequence for error correction for the prototype method was calculated, and for the proposed method, the required number of alternative received sequences for error correction. It was found that to correct errors of multiplicity from W = 1 to W = 3 according to the prototype method, it is necessary to perform an average of 6 to 869 attempts to decode the received sequence with inverted bits, and to correct the same errors according to the proposed method, the required number of alternative received sequences lies in the range of values from 4 to 11. The complexity of the practical implementation of the correction of transmission errors is directly proportional to the number of attempts to decode the received sequence with inverted bits and tr Among alternative buoy received sequences, respectively.

The studies confirm that when using the proposed method of joint arithmetic and noise-correcting encoding and decoding of an excess binary information sequence, it is possible to practically correct multiple transmission errors.

Claims (4)

1. The method of joint arithmetic error-correcting encoding and decoding, which consists in the fact that the initial arithmetic encoding interval is set on the transmitting side and the initial arithmetic decoding interval corresponding to it is received on the receiving side, the next part of the information sequence of length k≥ is received from the source of the information sequence 1 bit, divide the current arithmetic coding interval into the current coding subinterval null character and the current sub-encoding interval of a single character, select the test characters of length r≥1 bits, form the next part of the noise-resistant sequence from the next part of the information sequence and the selected test characters, perform arithmetic coding of the next part of the noise-resistant sequence in the next part of the encoded sequence, transmit the next part of the sequence on the receiving side, the listed actions are performed on the transmitting side I, until the next parts of the information sequence arrive, the next part of the received sequence is received on the receiving side, the current interval of arithmetic decoding of the received sequence is divided into the current decoding sub-interval of the null character and the current decoding sub-interval of a single character, the arithmetic decode of the received sequence into the next parts of the decoded sequences from which the next parts of the restored informational sequence sequences and decoded check symbols, transmit to the receiver the next part of the restored information sequence, perform the listed actions on the receiving side until the next parts of the received sequence arrive, characterized in that the limit number of alternative received sequences Z≥2 and the decoding delay T ≥2, as well as the metric values of the alternative received sequences to zero, on the transmitting side n the next part of the encoded sequence is transmitted to the receiving side, and the next part of the received sequence is received on the receiving side and the next bit is read from it, the current arithmetic decoding interval of each alternative received sequence is divided into the current null symbol decoding sub-interval and the current decoding sub-interval of a single symbol of this sequence, for each alternative received sequence form a continuation in the form of a null character continuation in the form of a single symbol, calculate the value of the continuation metric in the form of a zero symbol and the value of the continuation metric in the form of a single symbol relative to the next bit of the next part of the received sequence, for each alternative received sequence with its continuation calculate the value of its metric by summing the metric of the sequence itself and its continuation, arithmetically decode each alternative received sequence with its continuation in subsequent parts of the corresponding a alternative decoded sequence, from which the next parts of the alternative reconstructed information sequence and alternative decoded verification symbols are extracted, if the alternative decoded verification symbols are valid, then the next parts of the alternative restored information sequence of the corresponding alternative received sequence are stored with its continuation, otherwise the metric value of this alternative accepted afterbirth Sequences with its continuation to the maximum value, compare the metric values of the alternative received sequences with their extensions and choose from them no more than Z alternative received sequences with their extensions, which have the smallest metric values into which the corresponding extensions are added, for these alternative accepted sequences remember the next parts of the corresponding alternative restored information sequence and metric values, reading the next bit of the next part of the received sequence is read and, if its number is less than the number T, the above actions are performed on the receiving side, otherwise the metrics of the alternative received sequences are compared and the alternative received sequence is selected from them with the lowest metric value, transmitted to the recipient as the next part reconstructed information sequence corresponding to the selected alternative received sequence the next part of the alternative To restore the information sequence, perform these actions on the reception side as long as the part comes next received sequence. 2. The method according to p. 1, characterized in that on the transmitting side, the test characters are selected as zero characters if the current probability of zero characters of the information sequence determined by arithmetic coding is greater than or equal to the current probability of single characters of the information sequence, otherwise the test characters are selected as single characters, and on the receiving side, if the alternative decoded check symbols are null symbols, provided that the arithmetic decoding The current probability of the zero characters of the alternative reconstructed information sequence is greater than or equal to the current probability of the unit characters of this sequence, or if the alternative decoded check characters are unit characters, provided that the arithmetic decoding of the current probability of the unit characters of the alternative reconstructed information sequence is greater than the current probability of the zero characters of this sequence then altern ivnye decoded parity are permissible. 3. The method according to claim 1, characterized in that the value of the continuation metric in the form of a zero symbol relative to the next bit of the next part of the received sequence is calculated as a zero value if the next bit of the next part of the received sequence is a zero bit, otherwise it is calculated as a single value. 4. The method according to p. 1, characterized in that the value of the continuation metric in the form of a single symbol relative to the next bit of the next part of the received sequence is calculated as zero if the next bit of the next part of the received sequence is a single bit, otherwise it is calculated as a single value.

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