RU2712096C1 - Method of combined arithmetic and noise-immune encoding and decoding - Google Patents

Abstract

FIELD: information technology.SUBSTANCE: invention relates to the field of telecommunication and information technologies. Such result is achieved by the fact that at the transmitting side performing the arithmetic coding of the next part of the information sequence (IS) with length k≥1 bit, from the current arithmetic coding interval with length D>2, the current permitted encoding interval with length D>2 by rule D=β⋅D, where noise immunity coefficient β selected within 0<β<1, the current allowed encoding interval is divided into a current sub-interval of encoding a null symbol and a current sub-interval of encoding a single symbol, performing arithmetic coding of next part of IS in next part of coded sequence, at the receiving side, storing and continuing no more than Z≥2 alternative received sequences (ARS), closest to Hamming metrics to the received sequence, ARS is arithmetically decoded with control of compliance of current ARS value to current permitted decoding sub-interval, alternative received sequence with minimum metric value is selected, and decoded regular parts of reconstructed information sequence are transmitted to recipient.EFFECT: technical result consists in improvement of noise immunity of transmission of next parts of coded sequence under action of multiple transmission errors.4 cl, 14 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.

A known method of adaptive noise-resistant coding and decoding 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 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 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 select variable parameters of the error-correcting code are provided, which provide 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 code, evaluate the probability of correct reception of the error-correcting code with the selected parameter trams, 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 value of this deviation, the amount of 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 due to 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 of RGRTU, Issue 23, 2008. This method consists in preliminarily generating a variety of speech compression methods, such as pulse-code modulation, adaptive delta modulation, adaptive differential pulse-code modulation, and many noise-resistant coding methods , such as Hamming coding, Bowes-Chowdhury-Hockingham 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 by 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 a 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 noise-resistant 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 noise-resistant coding method.

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 Н04М 13/00 (2006.01) dated 05/10/2005. The prototype method of joint arithmetic and error-correcting encoding and decoding consists in setting the initial arithmetic encoding interval on the transmitting side and the initial arithmetic decoding interval corresponding to it 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 coding interval of length D> 2 by the current coding subinterval of zero character and the current sub-encoding interval of a single character, from the pre-formed set, test characters of length r≥1 bits 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 convert the next part of the encoded sequence into the next part of of the dummy 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 sequence is received on the receiving side, it is converted into a binary sequence that is stored, the current arithmetic interval is shared decoding of length DD> 2 to the current sub-interval of decoding a null character and to the current sub-interval of a decoder of a single symbol, the stored subsequent 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 transmit the next part of the restored information sequence, alternately inverting one or more bits stored in successive portions of the received sequence and perform their arithmetic decoding until the output of the absence of transmission errors, perform these actions on the reception side as long as the next part of the received sequence received at the receiving side.

A feature of the prototype method is that on the transmitting side, the selection of test characters is performed, and then the subsequent parts of the information sequence and test characters are compressed by arithmetic coding, and on the receiving side after arithmetic decoding, transmission errors are detected if any, and when they are detected by the sample method and errors carry out 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 error-correcting coding and decoding of an information sequence, transmission errors are corrected by enumeration, inverting one or more bits in the remembered successive parts of the received sequence and performing arithmetic decoding until reaching the conclusion on the correction of these errors using check symbols . With a length of N bits of stored successive parts of the received sequence and the number W of correctable errors, this requires parallel operation 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, transmission errors are detected with the length of the stored next parts of the received sequence up to tens of bits or more. Therefore, in this prototype method of joint arithmetic and noise-correcting coding and decoding, correction of transmission errors with an error rate of more than one requires the use of many thousands of arithmetic decoders with the corresponding number of error detection devices, which is practically impossible.

Thus, the disadvantage of the closest analogue (prototype) of joint arithmetic and noise-resistant coding and decoding of the information sequence is the low noise immunity of transmission of the next parts of the encoded sequence, due to the practical impossibility of correcting transmission errors with an error rate of more than one.

The technical result of the proposed solution is the development of a method of joint arithmetic and noise-resistant coding and decoding, which provides increased noise immunity of the transmission of the next parts of the encoded sequence when exposed to multiple transmission errors.

The specified technical result in the inventive 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, which consists in the fact 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 of length k≥1 bits, divide the current arithmetic coding interval of length D> 2 into the current null character encoding subinterval and the single character encoding subinterval, perform arithmetic encoding of the next part of the sequence into the next part of the encoded sequence, transmit the next part of the sequence on the receiving side, perform the listed actions on the transmitting side until the next h According to the information sequence, on the receiving side, a sequence is received, the current arithmetic decoding interval is divided into the current decoding interval of a null character and the current decoding interval of a single symbol, the next parts of the received sequence are arithmetically decoded into the next parts of the sequence, the above actions are performed on the receiving side until while the sequence arrives at the receiving side, the restored informational post is transmitted edovatelnost further pre-set limit on the number of received sequences Z≥2 alternatives and alternative metric value received sequences to zero.

On the transmitting side, after receiving the next part of the information sequence from the current arithmetic coding interval of length D> 2, the currently allowed encoding subinterval of length D _β > 2 is distinguished, which is divided into the current encoding subinterval of a null character and the current encoding subinterval of a single character. Moreover, the length D _{β of the} current allowed coding interval is selected as D _β = β⋅D, where the value of the noise immunity coefficient β is set within 0 <β <1. Arithmetic coding of the next part of the information sequence into the next part of the encoded sequence is performed.

The next part of the coded sequence is transmitted to the receiving side, and the next bit of the sequence is received on the receiving side. From the current arithmetic decoding interval of length DD> 2 of each alternative received sequence, the current allowed decoding interval of length DD _β > 2 is extracted, which is divided into the current decoding interval of the zero symbol and the current decoding interval of a single symbol of this sequence. Moreover, the length DD _{β of the} current allowed decoding interval is set from the condition DD _β = β⋅DD.

For each alternative received sequence, a continuation of the sequence in the form of a null character and a continuation of the sequence 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 received sequence are set. The value of the continuation metric in the form of a zero symbol relative to the next bit of the received sequence is set to zero if the next bit of the received sequence is a zero bit, otherwise set to a single value. The value of the continuation sequence metric in the form of a single symbol relative to the next bit of the received sequence is set to zero if the next bit of the received sequence is a single bit, otherwise set to a single value.

For each alternative received sequence with its continuation of the sequence, the value of its metric is calculated, for which the values of the metrics of this sequence and the metrics of its continuation are summed. Arithmetically decode each alternative received sequence with its continuation in the subsequent parts of the corresponding alternative restored sequence, if the current value of the received sequence is within the current allowed decoding interval of the alternative received sequence, then the next parts of the alternative restored information sequence corresponding to this sequence are stored, otherwise they are erased given alter ativnost received sequence and its extension sequence.

Compare with each other the metric values of the alternative received sequences with their sequence extensions and choose from them no more than the maximum number Z of alternative received sequences having the smallest metric values that complement the corresponding sequence extensions. For these alternative received sequences, the next parts of the corresponding alternative reconstructed information sequences and metric values are stored, the listed actions are performed on the receiving side until the next bits of the received sequence arrive. Next, the metric values of the alternative received sequences are compared with each other and the sequence with the lowest metric value is selected from them, after which the alternative restored received information sequence corresponding to the selected alternative received sequence is transmitted as the restored information sequence.

где k≥1 есть длина очередной части информационной последовательности, а n=k+r есть длина очередной части помехоустойчивой последовательности, состоящей из k информационных символов и из r≥1 проверочных символов.In the proposed set of actions on the transmitting side during arithmetic coding of the next part of the information sequence into the next part of the coded sequence, the latter is formed in accordance with the current allowed coding interval, and on the receiving side when decoding the next parts of the received sequence, those alternative received sequences that cannot be formed on the transmitting side in accordance with the current allowed interval, among the remaining a limited number Z of alternative received sequences are stored and continued with their sequence extensions having the smallest metric values, and after receiving the entire sequence, among the best continued alternative accepted sequences by the metric criterion, the sequence with the smallest metric value that is most likely to coincide with the one generated on the transmitting side coded sequence. Thereby, error correction of the transmission channel is performed, and the multiplicity of the corrected errors in the received sequence is ensured by at least the metric value of the selected alternative received sequence. This decoding method belongs to the class of message decoding methods in general, which are theoretically capable of achieving extremely high noise immunity of message transmission. Due to the fact that when decoding the next bits of the received sequence, the alternative received sequences that do not provide error correction are erased and a limited number Z of non-erased alternative received sequences with their sequence extensions that maximize the probability of correcting transmission errors are corrected, it is possible to correct multiple transmission errors by decoding a limited number of alternative received sequences tei. The ability to correct multiple transmission channel errors increases with decreasing noise immunity coefficient β and increasing the limit number Z of alternative received sequences. In the inventive method of joint arithmetic and noise-correcting coding and decoding, the noise-immunity coefficient β, chosen within the range 0 <β <1, is equivalent to the speed of the error-correcting code

where k≥1 is the length of the next part of the information sequence, and n = k + r is the length of the next part of the error-correcting sequence, consisting of k information symbols and r≥1 check symbols.

Therefore, the specified new set of actions when performing joint arithmetic and noise-resistant coding and decoding of the information sequence allows to increase the noise immunity of transmission of the next parts of the encoded sequence when exposed to multiple transmission errors.

The claimed method is illustrated by drawings, which show:

- in FIG. 1 is a general diagram 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 joint arithmetic and noise-resistant coding of the first twelve successive parts of the information sequence;

- in FIG. 5 - time diagrams of joint arithmetic and noise-resistant coding of the first two successive parts of the information sequence;

- in FIG. 6 - time diagrams of joint arithmetic and noise-resistant coding of the first 12 successive parts of the information sequence;

- in FIG. 7 is a timing chart of joint arithmetic and noise-free decoding of the first 19 bits of the received sequence at the receiving side;

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

- in FIG. 9 is a representation of alternative received sequences in the form of a tree structure;

- in FIG. 10 is an exemplary view of selectable no more than Z = 12 alternative received sequences;

- in FIG. 11 is a table of decoding conditions of an alternative received sequence of the form "0000 1100 0";

- in FIG. 12 is a table of decoding states of an alternative received sequence of the form "0000 1100 1";

- in FIG. 13 is a table of decoding states of an alternative received sequence of the form "0000 1100 1001 0001";

- in FIG. 14 is a table of decoding conditions of an alternative received sequence of the form "0000 1100 0101 0001 001".

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 (IP) is performed, and on the receiving side, joint arithmetic and noise-resistant decoding of the received sequence is performed with error correction of the transmission channel.

On the transmitting side, the shaper of the current encoding interval 1 generates the current arithmetic encoding interval depending on the received information sequence. From the current arithmetic coding interval, the shaper of the current allowed coding interval 2 extracts a shorter current allowed coding interval. The shaper of the current zero sub-interval 3 and the shaper of the current single sub-interval 4 divide the current allowed encoding interval into the current zero-character encoding sub-interval and the current single-character encoding sub-interval, respectively. Upon receipt of the next part of the information sequence from the sender of the null character, the current null character encoding interval increases and the current coding sub-interval of the single character is proportionally reduced, and when the next part of the information sequence is received from the sender the next character of the information sequence, the current single character coding interval is increased and the current zero character coding interval is proportionally reduced . Based on the data of the current sub-intervals, the next binary characters of the next part of the information sequence are arithmetically encoded in the arithmetic encoder 5 into the next part of the encoded sequence, which is transmitted via the transmission channel 6 to the receiving side.

At the receiving side, in Z decoding units 7, the next bits of the received sequence are received. A diagram of the decoding unit 7 is shown in FIG. 2. In each decoding unit 7, an alternative received sequence generator (APT) with a zero continuation of 7.1 and an APT generator with a single continuation of 7.9 form alternative received sequences with corresponding sequence extensions, which in arithmetic decoder 7.2 and arithmetic decoder 7.10, respectively, are arithmetically decoded into the next parts of the corresponding alternative reconstructed information sequences.

When decoding binary symbols from the APT with zero continuation, the current arithmetic decoding interval is formed in the former of the current decoding interval 7.3 from the decoding result of the next restored information symbol, from which the current resolving decoding interval 7.4 produces a shorter current allowed decoding interval. From the current allowed decoding interval in the former of the current zero decoding subinterval 7.6 and in the former of the current single decoding subinterval 7.7, respectively, the current zero decoding subinterval and the current single decoding subinterval are formed. When arithmetic decoding in arithmetic decoder 7.2 of the zero character of the next part of the restored information sequence from the APT with zero continuation in the shaper of the current zero decoding subinterval 7.6 and the shaper of the current single decoding subinterval 7.7 increases the current decoding subinterval of the zero character and proportionally reduces the current decoding subinterval of a single character for this AP , and when decoding a single character - increase the current hearth erval symbol decoding unit and proportionally reduces the current subinterval zero symbol for decoding this APP.

Similar actions are performed when decoding binary characters from an APT with a single continuation using an APT generator with a unit extension of 7.9, an arithmetic decoder 7.10, a shaper of the current decoding interval 7.11, a shaper of the currently allowed decoding subinterval 6.12, a shaper of the current zero decoding subinterval 6.14 and a shaper of the current single decoder subinterval 7.15.

In the block for calculating the metric of AMS 7.8, for each alternative received sequence with its continuation, the value of its metric is calculated by summing the metric of the sequence itself and the metric of its continuation, where the values of the continuation metric are set to the appropriate value depending on the relationship between the binary value of the continuation of the sequence and the value of the next bit received sequence. From the APT 7.8 metric calculation block, the calculated metric value of each alternative received sequence, with its continuation, is passed to the block of the alternative received APP 8 sequence selection.

If during the check in the block for checking the interval 7.5, respectively, in the block for checking the interval 7.13, the current value of the alternative received sequence is within the current allowed interval of arithmetic decoding of the corresponding alternative received sequence with its continuation, then the next parts of the alternative restored information sequences corresponding to the alternative accepted sequence with its continuation, nache erase this alternative received sequence with its continuation.

In the selection block APP 8, the metric values of the alternative received sequences are compared with their sequence extensions and no more than the maximum number Z of alternative received sequences having the smallest metric values that complement the corresponding sequence extensions is selected from them, the next parts are stored for these alternative received sequences the corresponding alternative reconstructed information sequence and metric value.

After all bits of the received sequence are received on the receiving side, the metric of the alternative received sequences is compared to each other in the APP 8 selection block and the only alternative received sequence with the lowest metric value is selected from them and the alternative restored received information corresponding to the selected alternative received sequence is transmitted to the recipient as the restored information sequence 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.

Ways of presetting on the transmitting side of the initial arithmetic coding interval of length D> 2 and on the receiving side of the corresponding initial arithmetic decoding interval of length DD> 2 are known and described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Methods of data compression. The device archivers, 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 of this interval. For example, when representing the values of the encoding interval with eight binary characters (the bit depth of the intervals N _R = 8 bits), the initial lower value of the encoding interval of the arithmetic encoding L [0] at time t = 0 is set to the minimum value equal to a zero value in decimal representation or 0000 0000 in binary representation, where high-order binary characters are written to the left, and the initial upper value of the coding interval of the arithmetic coding H [0] is set to a maximum value of 2 55 in decimal or 1111 1111 in binary representation. An example of an initial arithmetic coding interval of length D [0] = 256 is shown in FIG. 4 at t = 0 (first row) and in FIG. 5 at t = 0.

The limit number Z≥2 of the alternative received sequences and the metric value of the alternative received sequences are also pre-set to zero. Methods for pre-setting the limit number Z of alternative received sequences are known and described, for example, in the book D. Prokis "Digital Communication". - M., Radio and Communications, 2000, pp. 328-349. For example, to correct twofold errors, it is recommended to select the limit number Z of alternative received sequences from a range of values 8 ... 16, to correct three-fold errors, it is recommended to choose a limit number Z of alternative received sequences from a range of values 17 ... 32, given that when the selected number Z increases a larger number of transmission errors can be corrected, but the complexity of error correction implementation devices is increasing linearly. For example, for the example considered below, we set the limit number Z of alternative received sequences to Z = 12.

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. Initially, before receiving a sequence at the receiving side, the alternative received sequences are of zero length.

On the transmitting side from the source of the information sequence, the next part of the information sequence of length k≥1 bits is received. An exemplary view of the first 13 consecutive parts of a binary IP of length k = 1 bit is shown in FIG. 6 (a). For example, the first part of the IP has the form "0", the second part is "0", the fourth part is "1", etc. Single bit values in the figures are shown as shaded pulses, zero bits are shown as open shaded pulses.

From the current arithmetic coding interval of length D> 2, the current allowed coding interval of length D _β > 2 is extracted, and the length D _{β of the} current allowed encoding interval is selected as D _β = β⋅D, where the noise immunity coefficient β is selected in the range 0 <β <1, the currently allowed encoding interval is divided into the current null symbol encoding sub-interval and the single symbol encoding current sub-interval. In the inventive method for joint arithmetic and error-correcting coding and decoding, the noise immunity coefficient β is the equivalent of the error-correcting code rate R, defined as the ratio of the length of information symbols to the length of the encoded symbols R = k / n, where the speed of the error-correcting code is selected within 0 <R <1. The smaller the value of the noise immunity coefficient β, the greater the number of errors of the transmission channel can be corrected in the inventive method of joint arithmetic and noise immunity coding and decoding. For the following example, we choose β = 0.6. For example, for the initial arithmetic coding interval of length D = 256, the initial permitted coding interval of length D _β = 256 × 0.6 = 154 is allocated (calculations are performed with rounding to the nearest integer). As a result, the arithmetic coding interval is divided into the allowed coding interval and the unresolved coding interval. Similarly, in error-correcting error-coding coding, the set of all code combinations is divided into a set of allowed code combinations, consisting of undistorted transmission of code sequences, and a set of unresolved code combinations, consisting of distorted transmission of code sequences. If, at reception, the received sequence belongs to a plurality of unresolved code combinations, then using error-correcting coding an error has been detected in the received data. In contrast, in the proposed method for joint arithmetic and error-correcting coding and decoding, an error in the received sequence is detected if the current state of arithmetic decoding does not correspond to the allowed decoding interval.

The separation of the currently allowed encoding interval from the current arithmetic encoding interval can be performed in various ways: starting from the lower or upper values of the encoding interval, or in the central part of the current arithmetic encoding interval, as a continuous interval or as a set of subintervals interspersed by subintervals from an unresolved arithmetic interval coding. The ability to detect and correct transmission errors in this case in the inventive method does not change. For example, for convenience of implementation, it is proposed to extract the current allowed coding interval of length D from the current arithmetic coding interval in the form of two sub-intervals, the first sub-interval, called the current zero-character encoding sub-interval, starts from the lower value of the encoding interval L, the second sub-interval, called the current character encoding sub-interval , starts from the upper value H of the encoding interval. Accordingly, between the current null-character encoding sub-interval and the current zero-character coding sub-interval is the remainder of the current arithmetic coding interval, referred to the current unresolved coding interval. The lower value L0 of the current null-character encoding subinterval coincides with the lower value of the arithmetic coding interval L0 = L, and the upper value H1 of the current null-character encoding subinterval coincides with the upper value of the arithmetic coding interval H1 = H.

Methods of dividing the current allowed interval of arithmetic coding 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 device” by D. Vatolin, 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 D _{β of the} current allowed interval of arithmetic coding, equal to D _β = β⋅D, where D = H1-L0, is divided by the length D ₀ the current sub-interval of the encoding of the null character and the length D _{1 of the} current sub-interval of the coding of a single character D ₁ . To do this, calculate the current number of zero characters SP N ₀ and the current number of unit characters SP N ₁ encoded in an arithmetic encoder. For example, at the initial moment at t = 0, the current number of zero characters of PI N ₀ [0] is set to 1 and the current number of unit characters of PI N ₁ [0] is set to 1. Ways to set the number of zero and one at the initial moment of arithmetic coding IP symbols in a single value 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. 124-130. For example, as shown in FIG. 4, in the first line at t = 0, the unit number of zero symbols of the PI (column N0) and the unit number of unit symbols of the PI (column N1) are indicated. Column N indicates the total number of received symbols, taking into account the zero and single symbols of the IP set at the initial moment.

The current probability of encoding the null symbols of the IP p ₀ [t] is calculated according to the rule: p ₀ [t] = N ₀ [t] / (N ₀ [t] + N ₁ [t]) and the current probability of encoding the individual symbols of the IP p ₁ [ t] by the rule: p _l [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 value of the current probability of coding of zero symbols of PI (column p0) and the value of the current probability of coding of single symbols of PI (column p1), where the initial values are 0.5, are indicated.

The length of the current coding sub-interval of the zero character D ₀ [t] is determined by a formula of the form D ₀ [t] = D _β [t] × p ₀ [t], and the length of the current coding sub-interval of a single character D ₁ [t] is determined by a formula of the form D ₁ [t] = D _β [t] -D ₀ [t]. For example, the length of the initial encoding interval D [0] has a decimal value of 256, the length of the initial allowed encoding interval D _β = 256 × 0.6 = 154, the length of the initial null-character encoding sub-interval D ₀ [0] has a decimal value of 77, and the length of the initial the unit-character encoding sub-interval D ₁ [0] has a decimal value of 77. The unit-character-encoding sub-interval is located at the top of the zero-character encoding sub-interval, as shown, for example, in FIG. 5. The lower boundary of the current null-symbol encoding subinterval is designated as the value L0, and its upper boundary is denoted as Lk, and this subinterval starts from the bottom of the lower boundary of the current arithmetic coding interval inclusively to the Lk value exclusively. The lower boundary of the current coding subinterval of a single symbol is denoted as the value of Hk, and its upper boundary is denoted as H1, and this subinterval starts from the top of the upper boundary of the current arithmetic coding interval exclusively to the value of Hk inclusive. For example, at time t = 0, the current null character coding interval starts from the lower value of the current coding interval and has a lower value in decimal 0 or 0000 0000 in binary representation and has an upper value in decimal 76 or 0100 1100 in binary representation. Accordingly, the current encoding sub-interval of a single character has an upper value matching the upper value of the encoding interval, and has an upper value in decimal 255 or 1111 1111 in binary and lower value in decimal 178 or 1011 0010 in binary, as shown in FIG. . 4 in the second row and in FIG. 5 at t = 0 in the line, highlighting the allowed encoding interval "Highlighted. Resolution Int."

The methods of arithmetic coding of the next part of the IP into the next part of the encoded sequence (KP) 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 characters of the next part of the IP into the next part of the KP in accordance with the current values of the sub-interval of encoding the zero character and the sub-interval of encoding a single character. When the next binary symbol of the next part of the IP, which is a single binary symbol, is received at the input of arithmetic coding, the current interval of arithmetic coding of this symbol is set equal to the coding sub-interval of a single symbol, and when the input receives arithmetic coding of a zero binary symbol, the current interval of arithmetic coding of this symbol is set equal to null character encoding subinterval.

For example, when a binary character of the first part of an IP, which is a binary binary character, enters the encoding input, the current encoding interval is set equal to the encoding subinterval of the zero symbol, and the lower value L0 [1] of the current arithmetic encoding interval is set to 0, and the upper value H1 [1 ] to the decimal value 76, as shown in FIG. 4 and in FIG. 5 at t = 1.

In arithmetic coding, the leftmost bit of the binary representation of the value L0 [1] is compared with the leftmost bit of the binary representation of the value H1 [1], for example, of the form 0000 0000 and 0100 1100, respectively, as shown in FIG. 4 at t = 1. When they coincide, the value of the leftmost bit of the binary representations of the values L0 [1] and H1 [1] is read as the next bit of the next part of the encoded sequence (Code symbol, as shown in Fig. 4). For example, when encoding the first part of the IP, the first bit of the first part of the KP is the zero binary symbol that coincides when comparing, as shown in FIG. 4, the fourth line from the top. The read bit is removed from the binary representations of the values L0 [1] and H1 [1], which are reduced to a length of 7 bits of the form 0000 000 and 100 1100, respectively. The binary symbols of the binary representations of the values L0 [1] and H1 [1] are shifted from right to left by one digit and are appended to them with a zero binary symbol from the right. For example, binary representations of the values L0 [1] and H1 [1] take the form 0000 0000 and 1001 1000, 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 operations of shifting from right to left by one bit and appending a binary binary symbol to the right increase L0 [t] and H1 [t] by 2 times and are called normalization of arithmetic coding parameters. The 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 a multiplication by two decimal values of the lower and upper values of the arithmetic coding 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. 4.

As a result of encoding the first part of the information sequence of the form “0” shown in FIG. 6 (a), the first part of the encoded sequence of the form “0” shown in FIG. 6 (b), which is transmitted to the receiving side.

Upon receipt of the next part of the IP, its coding in the next part of the KP is performed identically. After arithmetic coding of each successive symbol, the number of encoded zero symbols of the IP and the number of encoded unit symbols of the IP are specified. Since the encoded character in this example is zero, the number of encoded zero characters of the PI is increased by a unit value and it is N ₀ [1] = 2, the number of encoded single characters of the information sequence remains equal to N ₁ [1] = 1, respectively, the total the number of encoded null and single information symbols became equal to 3. Recalculate the current value of the encoding probability of null IP symbols p ₀ [1] = 2/3 and the current value of the encoding probability of single IP symbols p ₁ [1] = 1/3.

Before performing the arithmetic coding of the next character again from the current arithmetic coding interval, the currently allowed coding interval is selected, which is divided into the current coding subinterval of the null character and the current encoding subinterval of a single character. For example, before encoding the second IP symbol in a row

а длина текущего подинтервала единичного символа D₁[2]=D_β[2]-D₀[2]=92-61=31. Поэтому текущий подинтервал нулевого символа находится в промежутке десятичных значений от 0 до 61 или в промежутке двоичных значений от 0000 0000 до 0011 1101, а текущий подинтервал единичного символа находится в промежутке от 121 до 152, как показано на фиг. 4 в пятой строке "Выделен. разреш. инт".the length of the current interval of arithmetic coding is D = 152, the length of the current allowed interval of coding D _β = 152 × 0.6 = 92. The length of the current sub-interval of the null character is

and the length of the current sub-interval of a single symbol is D ₁ [2] = D _β [2] -D ₀ [2] = 92-61 = 31. Therefore, the current null character interval is in the range of decimal values from 0 to 61, or in the range of binary values is 0000 0000 to 0011 1101, and the current interval of a single character is in the range of 121 to 152, as shown in FIG. 4 in the fifth line "Highlighted. Resol. Int."

Arithmetic coding of the second and subsequent binary symbols of the PI is performed, as shown in FIG. 4 and in FIG. 5. When normalization is performed, binary characters are read into the next part of the encoded sequence. An exemplary type of arithmetic coding of the first 12 consecutive IP parts of the form "0001 0010 1001" into the corresponding next KP parts of the form "0", "00", "0", "110", "0" and so on is shown in FIG. 6 (b). Note that with a fixed length of the next parts of the IP as a result of their arithmetic coding, the next parts of the CP of variable length are formed, which, in particular, is determined by the variable redundancy of the compressible parts of the IP. For example, the eighth of the CP has zero length (do not contain transmitted characters). In general, the CP of 19 bits in length has the form "0000 1100 0101 0001 001".

Methods of transmitting to the receiving side of the next part of the KP 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 12 parts of the received sequence (Pr. P) is shown in FIG. 7 (a). Let the received sequence with a total length of 19 bits during transmission be distorted in the ninth and tenth bits of the received sequence and have the form "0000 1100 1001 0001 001".

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 Ave. P, where N _R is the number of binary symbols representing the values of the encoding intervals and, accordingly, the decoding intervals. For example, when presenting the values of the coding interval and the decoding interval with eight binary characters (N _R = 8 bits), the first eight bits of Pr.P are received of the form “0000 1100”, as shown in FIG. 11 in the column read binary characters "Count" at the initial time t = 0. The received sequence "0000 1100" has a current value of 12, calculated as the decimal value of this binary sequence, in which the most significant bit is on the left (at the beginning of the sequence) and the least significant bit is on the right (at the end of the sequence).

Let us describe in general terms the joint arithmetic and noise-resistant decoding of Pr.P on the receiving side. The actions of joint arithmetic and noise-correcting decoding of Pr.P on the receiving side are performed by decoding several alternative received sequences (APP). For example, at the initial moment of time, there is a single alternative received sequence coinciding with the first eight bits of Pr. P of the form "0000 1100". At the time of reading the first bit after the initial N _R bit of the next bit of the received sequence, denoted by the time t = 1, for the initial received sequence consisting of the first N _R binary symbols of the received sequence, the continuation of the AMS in the form of a null character and the continuation of the sequence in as a single character, as shown in FIG. 9. When reading the next bit of the received sequence (time moment t = 2), for each of the two APTs, extensions are formed in the form of a zero character and a continuation in the form of a single character, as a result, at the time t = 2, the number of APPs becomes 4, at the time t = 3 the number of AMS reaches 8, etc. A representation of the alternative received sequences in the form of the described tree structure is shown in FIG. 9. This structure of the AMS potentially allows you to correct multiple transmission errors in the adopted sequence, and the place of errors in Pr. May be arbitrary. For each APP, the following actions are performed together arithmetic and noise-free decoding.

For example, with a preset limit number Z = 12 AMP, 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 the truncated tree of alternative received sequences, the number of continued APPs at each moment t does not exceed a given value of Z. For example, for the initial alternative received sequence of the form "0000 1100", 2 continuations are formed: the APT with the continuation of the sequence in in the form of the null character "0000 1100 0", and the APT with the continuation of the sequence in the form of a single character "0000 1100 1". For an APT with the continuation of the sequence in the form of a null character "0000 1100 0", the value of the metric of the continuation of the sequence in the form of a null character relative to the next single, ninth in FIG. 10 bits of the received sequence are set to a single value. Since the metric of the initial alternative received sequence is preset to zero, the APT with the continuation of the sequence in the form of a null character "0000 1100 0" has a metric value of M = 1, as shown in FIG. 10. For an APT with the continuation of the sequence in the form of a single symbol "0000 1100 1", the value of the metric of the continuation of the sequence in the form of a single symbol relative to the next single, ninth in FIG. 10. The bits of the received sequence are set to zero. Accordingly, the APT with the continuation of the sequence in the form of a single symbol “0000 1100 1” has a metric value of M = 0, as shown in FIG. 10.

As a result, the number of continued APTs when decoding the ninth character of the received sequence is 2, this number does not exceed the limit number Z = 12 APTs and both alternative received sequences continue, forming, when decoding, the next tenth in FIG. 10 bits, the received sequence four sequences with metric values from M = 0 to M = 2, which when decoding the next, eleventh in a row in FIG. 10 bits of the received sequence form 8 sequences with metric values from M = 0 to M = 3, which when decoding the next, twelfth in a row in FIG. 10 bits of the received sequence form 16 sequences with metric values from M = 0 to M = 4. Since the number of APPs with their extensions already exceeds the limiting number Z of APPs, then Z = 12 alternative accepted sequences with their extensions with the smallest metric values are selected from these sequences. For example, an APT with its continuation with a metric of M = 4 and three APP with their extensions with a metric of M = 3 are erased, which is indicated by the symbol "X" in FIG. 10. According to the principle of maximum likelihood in the theory of error-correcting coding, as described in the book B. Sklyar "Digital Communication. Theoretical Foundations and Practical Applications". - M., Williams Publishing House, 2003, pp. 422-431, the larger the alternative accepted sequence with its continuation differs from the accepted sequence in terms of the value of the metric M, the less likely it is that it will correct transmission errors, which gives the basis of such a sequence to wash.

на фиг. 10. При этом оказалась стертой альтернативная принятая последовательность с ее продолжением вида "0000 1100 1001 000" со значением метрики М=0, которая по этой причине ранее считалась наиболее предпочтительной при выборе среди альтернативных принятых последовательностей.Further, the number of continued AMS when decoding the thirteenth, fourteenth and fifteenth symbols of the AMS in the order of characters of the received sequence remains equal to the limit number Z = 12 AMP, and when decoding the sixteenth character according to the characters of the received sequence, the number of continued AMS with their extensions decreases to nine. This happened because in many previously continued AMSs, the current value of the alternative received sequence turned out to be outside the current allowed arithmetic decoding interval of these AMSs, that is, such sequences could not be formed on the transmitting side and, accordingly, they should be erased and they would not continue further, as indicated by

in FIG. 10. At the same time, the alternative accepted sequence with its continuation of the form "0000 1100 1001 000" with the value of the metric M = 0, which for this reason was previously considered the most preferable when choosing among the alternative accepted sequences, was erased.

Further, the number of continued APTs when decoding the seventeenth character of the APTs according to the characters of the accepted sequence decreased to five, and when decoding the eighteenth and nineteenth characters of the APTs to four, and among which one APT has a metric of M = 2, two APTs have M = 3 and one APP - M = 4. During further decoding, the best metric value will be the alternative received sequence that continues the identified APT with the metric M [19] = 2, therefore, at the end of receiving the symbols on the receiving side, the alternative with the lowest metric value is chosen among the alternative received sequences. In our case, an APT of the form "0000 1100 0101 0001 001" is selected with a metric value of M = 2, for which two transmission errors are corrected in the received sequence. An alternative restored received information sequence corresponding to the selected alternative received sequence is transmitted to the recipient as a restored information sequence.

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

The methods for extracting the currently allowed decoding interval with a length of DD _β > 2 from the current arithmetic decoding interval with a length of DD> 2 of each alternative received sequence at the receiving side and dividing it into the current decoding interval of a null symbol and the current decoding interval of a single symbol are identical to the methods of extracting the current allowed encoding interval of length D _β > 2 from the current arithmetic coding interval of length D> 2 and its division into the current subinterval is encoded ni character and the current sub-coding interval of a single character on the transmitting side. The length DD _{β of the} current allowed decoding interval of each alternative received sequence is selected as DD _β = β⋅DD. For example, for the selected value β = 0.6 for the initial arithmetic decoding interval of length DD = 256, the initial allowed decoding interval of length DD _β = 256 × 0.6 = 154 is extracted, as shown in FIG. 11 in the first row at the initial time t = 0. At the initial moment of time, there is only one alternative accepted sequence of the form “0000 1100” with a value of 12, as shown in Pr. P.

For each alternative received sequence, the separation of the current allowed decoding interval from the current arithmetic decoding interval is performed in the form of two sub-intervals. The first sub-interval, called the current zero symbol decoding sub-interval, starts from the lower value of the LL decoding interval, the second sub-interval, called the current zero symbol decoding sub-interval, starts from the upper value of the HH decoding interval. Accordingly, between the current null-symbol decoding sub-interval and the current single-symbol decoding sub-interval, there is the remainder of the current arithmetic decoding interval, referred to the current unresolved decoding interval. The lower value of the current null-symbol decoding subinterval LL0 coincides with the lower coding interval value LL0 = LL, and the upper value of the current coding subinterval LL0 H1 coincides with the upper value of the coding interval HH1 = HH.

The length of the current allowed interval of arithmetic decoding DD _{β of} each APT is divided by the length of the current sub-interval of the zero symbol DD ₀ and the length of the current sub-interval of a single symbol DD ₁ . To do this, calculate the current number of zero decoded characters NN ₀ and the current number of unit decoded characters NN _{1 of} this APT restored in the arithmetic decoder. For example, for each APT at the initial moment at t = 0, the current number of zero decoded symbols NN ₀ [0] is set to 1 and the current number of single decoded symbols NN ₁ [0] is set to 1. For example, as shown in FIG. 11, the first line at t = 0 indicates the unit number of null decoded symbols (column NN0) and the unit number of unit decoded symbols (column NN1). The column NN indicates the total number of received symbols, taking into account the zero and single decoded symbols established at the initial moment.

For each APT, the current probability of zero decoded 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 decoded symbols pp ₁ [t] by 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 initial values of the probability of zero decoded symbols (column pp0) and the probabilities of single decoded symbols (column pp1) are 0.5.

For each APT, the length of the current sub-interval of the null decoded symbol DD ₀ [t] is determined by a formula of the form DD ₀ [t] = DD _β [t] × pp ₁ [t], and the length of the current sub-interval of a single decoded symbol DD ₁ [t] is determined by a formula of the form DD ₁ [t] = DD _β [t] -DD ₀ [t]. For example, the length of the initial decoding interval DD [0] has a decimal value of 256, the length of the initial allowed decoding interval of DD _β [0] = 256 × 0.6 = 154, the length of the initial decoding sub-interval of the null character DD ₀ [0] has a decimal value of 77, and the length of the initial decoding interval of a single symbol decoding D ₁ [0] has a decimal value of 77. The decoding interval of a single symbol is located above the decoding interval of a null symbol. The lower boundary of the current decoding interval of the null symbol is denoted as the value LL0, and its upper boundary is denoted as LLk, and this subinterval starts from the bottom of the lower boundary of the current decoding interval of arithmetic decoding inclusively to the LLk value exclusively. The upper boundary of the current decoding sub-interval of a single symbol is denoted as HH1, and its lower boundary is denoted as HHk, and this sub-interval begins from the top of the upper boundary of the current arithmetic decoding decoding interval exclusively up to and including HHk. For example, at time t = 0, the null symbol decoding interval has a lower decimal value of 0 or 0000 0000 in binary representation, and has an upper decimal value of 76 or 0100 1100 in binary representation, as shown in FIG. 11 in the line highlight the allowed interval "Highlighted. Resol. Int". Accordingly, the current single character encoding sub-interval has an upper decimal value of 255 or 1111 1111 in binary representation and a lower decimal value of 178 or 1011 0010 in binary representation.

For each APT form the continuation of the sequence in the form of a null character and the continuation in the form of a single character. For example, from the initial APP of the form “0000 0110”, an APP is formed with a continuation in the form of a zero character of the form “0000 0110 0”, and an APP with a continuation in the form of a single character of the form “0000 0110 1”, as shown in FIG. 10. The top edge of the graphic representation of each APT in the figure is designated as a continuation of the sequence in the form of a null character "0", and the lower edge - as a continuation of the sequence in the form of a single character "1".

After the continuation of the sequence is formed, the continuation metric value is calculated in the form of a null character and the continuation metric value is in the form of a single character relative to the next bit of the received sequence, while the continuation metric value in the form of a zero character relative to the next bit of the received sequence is calculated as zero if the next bit of the next part the received sequence is a zero bit, otherwise it is calculated as a unit value, as well as the value of the metric services in the form of a single symbol relative to the next bit of the received sequence are calculated as a zero value if the next bit of the received sequence is a single bit, otherwise calculated as a single value. For example, as shown in FIG. 10, the next bit of Pr.P, the next after reading eight bits of the initial decoding path, has a single value. Therefore, with respect to this bit, the sequence continuation metric in the form of a null character has a unit value, and the sequence continuation metric in the form of a single character has a null value.

Then, for each APT with its continuation of the sequence, the value of its metric is calculated, for which the values of the metrics of this sequence and the metrics of its continuation are summed. For example, taking into account the fact that the initial APT metric of the type “0000 0110” has a zero value, the APP metric of the type “0000 0110 0” with the continuation in the form of a zero character gets a single value (M = 1), and the APT metric is “0000 0110 1” continued with a single character, it receives a null value (M = 0), as shown in FIG. 10.

The methods of arithmetic decoding of each APP with its continuation into the next parts of the corresponding alternative reconstructed information sequence (WUA) are known and described, for example, in the book “Data compression methods. Device by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin. archivers, image and video compression. " - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequential decoding of each APT with its continuation in accordance with the current values of the decoding sub-interval of the zero symbol and the sub-interval of decoding a single symbol of this APP.

An exemplary arithmetic decoding of an initial AMS of the form “0000 0110” with its subsequent zero extension into the symbols of the next part of the corresponding WUA is shown in FIG. 11. To decode the first character of the next part of the WUA, the current value of the alternative received sequence equal to 12 is compared with the boundaries of the current value of the decoding sub-interval of the APT zero symbol DD ₀ [0], which are, for example, in the range from 0 to 76, and with the boundaries of the current value the sub-interval of decoding a single symbol of the APT DD ₁ [0], for example, ranging from 178 to 255, as shown in FIG. 11 in the second line at t = 0. The current value of the alternative received sequence is defined as the decimal value of this sequence and is indicated in the column "Ave P". Depending on the extent to which the character decoding subinterval turned out to be the current value of the alternative received sequence, a decision is made on the value of the current character (Dec. Sim.) Of the alternative restored information sequence indicated in the right column of FIG. 11. Since in this example, the current value of the alternative received sequence is within the decoding sub-interval of the zero symbol, the first decoded symbol is zero and the following boundaries of the current decoding interval are set to the corresponding boundaries of the decoding sub-interval of the zero symbol of this APT DD ₀ [0]. As a result of decoding the first symbol, the lower value of the arithmetic decoding decoding interval LL is set to LL0 [0], for example, LL0 [1] = 0, and the upper value of the arithmetic decoding decoding interval LL is set to LLk [01] = 76, as shown in FIG. 11 in the third row at t = 1.

After decoding each symbol, the current probability value of the WUA zero symbol and the current probability value of a single symbol of the same sequence are recalculated, for example, after decoding the first symbol that is zero, according to the formula 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, as shown in FIG. 11 in the third row at t = 1.

After each change in the arithmetic decoding state, the leftmost bit of the binary representation of the LL value of the decoding interval is compared with the leftmost bit of the binary representation of the LV value, for example, at t = 1, the LL value is of the form “0000 0000” and the LV value of the form “0100 1100”, respectively. If they coincide, the arithmetic decoding is normalized: the value of the leftmost bit of the binary representations of the LL and LV values is deleted and the binary representations of the LL and LV 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. For example, while the variable LL saved the decimal value 0, and HH received the decimal value 152 and the binary representation "1001 1000", as shown in FIG. 11 in the line "normalization". At the same time, the leftmost bit of the current value of the alternative received sequence is deleted and the binary characters of this sequence are shifted from right to left by one bit, and the next binary symbol of the alternative received sequence is added to them from the right. For example, the next binary character read is the ninth alternative received sequence character having a zero value. Based on the read binary character, the current value of the AMS has received the decimal value 24 and the binary representation "0001 1000", as shown in FIG. 11 in the line "normalization".

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 match again, they will normalize again in the same way, etc.

Next, from the current arithmetic decoding interval, the current allowed decoding interval of each alternative received sequence is extracted, which in turn is divided into the current decoding subinterval of the null symbol and the current decoding subinterval of a single symbol. For example, from the current interval of arithmetic decoding in the range from 0 to 152 of this APT, the current allowed decoding interval of length DD _β = 92 is selected, which is divided into the current sub-interval of decoding a zero character in the range from 0 to 61 and the current sub-interval of decoding a single character ranging from 121 to 152. Since the current value of the probability of the zero character of this APP is 2 times greater than the current value of the probability of a single character of this APP, then, accordingly, the length of the current sub-interval of decoding zeros th symbol is 2 times greater than the current subinterval decoding unit symbol of APP, as shown in FIG. 11 in the penultimate line "highlighted. Resol. Int."

Arithmetic decoding of this APP is performed with its continuation of the sequence of the form "0000 0110 0" into the symbol of the next part of the corresponding WUA. Since the current value of the AMS equal to 24 is within the current sub-interval of decoding the zero symbol, the zero symbol is decoded. As a result of the arithmetic decoding of the APT with the continuation of the sequence in the form of a null character of the form “0000 0110 0” shown in FIG. 7 (b), decode, for example, the symbols of the first two parts of its corresponding WUA, having the form “0 0”, as shown in FIG. 7 (c) and in FIG. eleven.

The actions for the alternative received sequence of the form "0000 1100 1", formed from the initial AMS of the form "0000 1100" with the continuation of the sequence as a single symbol, are shown in FIG. 12. The difference from the previously considered actions for the APT of the form "0000 1100 0" is only the current value of this APP, equal to 25, obtained after reading a single character. As a result of the arithmetic decoding of the APT with the continuation of the sequence in the form of a single symbol of the form “0000 0110 1” shown in FIG. 7 (d), decode, for example, the symbols of the first two parts of its corresponding WUA, having the form “0 0”, as shown in FIG. 7 (e) and in FIG. 12.

If the current value of the alternative received sequence is within its current allowed decoding interval, then the next parts of the alternative restored information sequence corresponding to this sequence are memorized; otherwise, this alternative received sequence is deleted with its continuation. For example, at the time of receiving the ninth character of the received sequence for an APT of the form “0000 1100 0” and an APT of the form “0000 1100 1”, the first two successive parts of the corresponding alternative restored information sequences are stored.

Compare the metric values of the alternative received sequences with their sequence extensions and choose from them no more than the maximum number Z of alternative accepted sequences having the smallest metric values that complement their corresponding sequence extensions. These methods are known and described, for example, in the book of 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, at the time of the reception of the ninth character of the received sequence, there are only two APTs: APP with the continuation of the sequence in the form of a null character of the form “0000 1100 0” and APT with the continuation of the sequence in the form of a single character of the form “0000 1100 1” with the metric values M = 0 and M = 1, respectively. Since the number of these APPs does not exceed the limit number Z = 12 of alternative accepted sequences having the smallest metric values, both sequences are selected and stored. As a result of their addition to the corresponding continuations of the sequence, the first AMS takes the form "0000 1100 0", and the second AMS - "0000 1100 1". For AMS of the type "0000 1100 0", the next parts of the corresponding WUA of the type "0 0" and the value of the metric M = 1 are stored. For AMS of the type "0000 1100 1" remember the next part of the corresponding WUA of the type "0 0" and the value of the metric M = 0.

Upon receipt of the next bit of the received sequence, each of the two stored APT receives two continuation sequences, etc.

When decoding the next tenth in FIG. 10 bits of the received sequence are four APPs with metric values from M = 0 to M = 2, which, when decoding the next, eleventh in a row in FIG. 10 bits of the received sequence form 8 sequences with metric values from M = 0 to M = 3, which when decoding the next, twelfth in a row in FIG. 10 bits of the received sequence form 16 sequences with metric values from M = 0 to M = 4. Since the number of APPs with their extensions already exceeds the limiting number Z of APPs, then Z = 12 alternative accepted sequences with their extensions with the smallest metric values are selected from these sequences.

For example, one APP with its continuation with the metric M = 4 and three APP with their extensions with the metric M = 3 are erased, which is indicated by the symbol "X" in FIG. 10. According to the principle of maximum likelihood in the theory of error-correcting coding, as described in the book B. Sklyar "Digital Communication. Theoretical Foundations and Practical Applications". - M., Williams Publishing House, 2003, pp. 422-431, the larger the alternative accepted sequence with its continuation differs from the accepted sequence in terms of the Hamming metric, the less likely it is that it will correct transmission errors, which gives reason discard such a sequence.

на фиг. 10.Further, the number of continued APTs when decoding the thirteenth, fourteenth, and fifteenth characters according to the character count of the received sequence remains equal to the limit number Z = 12 due to the erasure of the part of the APT, and when decoding the sixteenth character according to the count of the received sequence, the number of continued APPs with their extensions decreases to nine. This happened because in many previously continued AMSs, their current value was outside the current allowed arithmetic decoding interval of these AMSs, that is, such sequences could not be formed on the transmitting side and, accordingly, they should be erased and they would not continue further, as shown a symbol

in FIG. 10.

For example, an alternative accepted sequence was deleted with its continuation of the form “0000 1100 0110 0110” with a metric value of M = 0, which for this reason was previously considered the most preferable when choosing among alternative accepted sequences. Actions for an alternative received sequence of the form "0000 1100 1001 0001" identical to the received sequence are shown in FIG. 13. As a result of decoding the first sixteen characters of the sequence shown in FIG. 7 (e), a WUA of the form “000 1 0” shown in FIG. 7 (g). For example, when decoding the fourth symbol of the next part of the WUA, the current value of the alternative accepted sequence, equal to 201, is compared with the boundaries of the current value of the decoding subinterval of the APT zero symbol DD ₀ , ranging from 0 to 106, and with the boundaries of the current value of the decoding subinterval of a single character APP DD ₁ ranging from 193 to 220, as shown in FIG. 13 in the ninth line. Since the current value of the alternative received sequence was within the decoding sub-interval of a single symbol, the fourth decoded symbol is single and the following boundaries of the current decoding interval are set to the corresponding boundaries of the decoding sub-interval of a single symbol of this APT DD ₁ . As a result of decoding, the lower value of the arithmetic decoding decoding interval LL is set to the lower boundary value of the current unit symbol decoding sub-interval, and the upper value of the arithmetic decoding decoding interval HH is equal to the upper boundary of the current unit symbol decoding sub-interval, as shown in FIG. 13 per line at t = 4.

на фиг. 10.Upon receipt of the sixteenth character of the received sequence, the current value of the alternative received sequence equal to 145 is compared with the limits of the current allowed decoding interval of the APT, which consists of the current decoding sub-interval of the APT zero symbol DD ₀ ranging from 16 to 91, and from the current value of the decoding sub-interval of a single symbol APP DD ₁ ranging from 160 to 190, as shown in FIG. 13 in the penultimate line. Since the current value of the APT is not within the current allowed decoding interval of this APT, this alternative received sequence is erased with its continuation. The fact of erasing this alternative accepted sequence with its continuation is marked with a symbol

in FIG. 10.

Upon receipt of the sixteenth and subsequent characters of the received sequence, the set of alternative received sequences has a current value outside the current allowed decoding interval of this APT and, accordingly, must be erased as alternative received sequences, which, taking into account the possible impact of various combinations of transmission channel errors, cannot be generated on the transmitting side joint arithmetic and noise-resistant coding. As a result of this, in this example, the number of continued APPs when decoding the eighteenth character in the count of characters of the received sequence decreased to four, among which one APP has a metric of M = 2, two APPs - M = 3, and one APP - M = 4.

Decoding APP of the form "0100 0000 0101 0001 001" with the metric value M = 2 is shown in FIG. 14. In the arithmetic decoding of nineteen characters of a given APP shown in FIG. 7 (h), the first nine parts of the alternative reconstructed information sequence of the form “000100101” shown in FIG. 7 (s). As shown in FIG. 10, this APP has a metric of M = 2 and is one of four APPs preserved from all APPs upon receipt of the first nineteen bits of the received sequence. However, the other three APPs have the metric values M = 3 and M = 4. In the course of further decoding, the alternative accepted sequence will continue to have the smallest metric value, continuing the identified APT with the metric M [19] = 2, since the other three APPs cannot provide a metric value less than M = 3 for any possible extensions.

After the receipt of the next bits of the received sequence stops, the metric values of the alternative received sequences are compared and the sequence with the lowest metric value is selected from them. In the given example, the continuation of the AMS of the form “0100 0000 0101 0001 001” with the metric value on the nineteenth received bit M [19] = 2, for which two transmission errors are corrected on the first nineteen bits of the received sequence, will be selected.

Next, the recipient, as the reconstructed information sequence, corresponds to the selected alternative received alternative sequence, the reconstructed alternative information sequence. The first continuation of the AMS of the type “0100 0000 0101 0001 001” selected in the example corresponds to the first nine parts of the alternative reconstructed information sequence of the form “000100101” shown in FIG. 7 (s).

In this example, joint arithmetic and noise-correcting coding and decoding provides the correction of two transmission errors in the received sequence.

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

Joint arithmetic and noise-resistant coding and decoding of the next parts of length k = 1 bit of the excess information sequence with a total length of 1024 bits was performed using the prototype method for which the error-correcting code speed values R = 1/2 and R = 2/3 were selected. We also performed joint arithmetic and noise-resistant coding and decoding of the next parts of length k = 1 bit of the same redundant information sequence with a total length of 1024 bits using the proposed method when choosing the value of the noise immunity coefficient β equal to the speed of the error-correcting code R = 1/2 and R = 2 / 3. It was revealed that when transmitting encoded sequences over the communication channel with errors, in all cases, correction of a larger number of transmission errors using the proposed method is provided in comparison with the prototype method. Moreover, with an increase in the limiting number Z of alternative received sequences to 17 ... 32, in addition to single and double errors, they provide the correction of triple transmission errors.

The conducted studies confirm that when using the proposed method of joint arithmetic and noise-resistant coding and decoding, the noise immunity of the transmission of the next parts of the encoded sequence under the influence of multiple transmission errors is increased.

Claims (4)

1. The method of joint arithmetic and error-correcting encoding and decoding, which consists in first setting the initial interval of arithmetic encoding on the transmitting side and the initial arithmetic decoding interval corresponding to it, on the transmitting side, the next part of the information sequence of length k ≥1 bit, divide the current arithmetic coding interval into the current coding interval nulling the character and the current sub-encoding interval of a single character, perform arithmetic coding of the next part of the sequence into the next part of the encoded 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 at the receiving side receive a sequence, divide the current interval of arithmetic decoding into the current sub-interval decoding of the null character and the current sub-interval of decoding a single character, arithmetically decode the next part of the received sequence into the next part of the sequence, perform the above actions on the receiving side until the received sequence arrives, transmit the restored information sequence, characterized in that the limit number is preset Z≥2 alternative accepted sequences and the value of the alternative accepted metric after sequences to zero, on the transmitting side, after receiving the next part of the information sequence from the current arithmetic coding interval of length D> 2, the current allowed coding interval of length D _β > 2 is distinguished, which is divided into the current null symbol encoding subinterval and the current character encoding subinterval, and perform arithmetic coding of the next part of the information sequence into the next part of the encoded sequence, which is transmitted to on the receiving side, the next bit of the sequence is received, from the current arithmetic decoding interval of length DD> 2 of each alternative received sequence, the current allowed decoding interval of length DD _β > 2 is separated, which is divided into the current decoding subinterval of the zero symbol and the current decoding subinterval of a single symbol of this sequence, for each alternative received sequence form the continuation of the sequence in the form of a null character and the continuation of the sequence in the form of a single symbol, the metric of the continuation of the sequence in the form of a zero symbol is set and the metric of the continuation of the sequence in the form of a single symbol relative to the next bit of the received sequence, for each alternative received sequence with its continuation of the sequence, its metric value is calculated, for which the values are summed metrics of the given sequence and metrics of its continuation of the sequence, arithmetically decode each alternate received sequence with its continuation into the next parts of the corresponding alternative restored sequence, if the current value of the received sequence is within the current allowed decoding interval of the alternative received sequence, then the next parts of the alternative restored information sequence corresponding to this sequence are stored, otherwise this alternative accepted research with its continuation of the sequence, compare the metric values of the alternative received sequences with their sequence extensions and choose from them no more than the maximum number Z of alternative received sequences having the smallest metric values that complement their corresponding sequence extensions, remember the next for these alternative received sequences parts of the corresponding alternative restored informational effects values and metric values, perform the above actions on the receiving side until the next bits of the received sequence arrive, compare the metric values of the alternative received sequences and select the sequence with the lowest metric value from them, and then transfer the corresponding selected alternative received sequence; alternative reconstructed information sequence. 2. The method according to p. 1, characterized in that on the transmitting side, the length D _{β of the} current allowed coding interval is selected as D _β = β⋅D, where the noise figure β is set within 0 <β <1, and on the receiving side, the length DD _{β of the} current allowed decoding interval is selected from the condition DD _β = β⋅DD. 3. The method according to p. 1, characterized in that the value of the continuation metric in the form of a zero symbol relative to the next bit of the received sequence is set to zero if the next bit of the received sequence is a zero bit, otherwise set to 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 received sequence is set to zero if the next bit of the received sequence is a single bit, otherwise set to a single value.

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