CA1230396A - Method of synchronization in a data transmission system using a linear block code - Google Patents
Method of synchronization in a data transmission system using a linear block codeInfo
- Publication number
- CA1230396A CA1230396A CA000456064A CA456064A CA1230396A CA 1230396 A CA1230396 A CA 1230396A CA 000456064 A CA000456064 A CA 000456064A CA 456064 A CA456064 A CA 456064A CA 1230396 A CA1230396 A CA 1230396A
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- code
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- data
- Prior art date
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Links
- 230000005540 biological transmission Effects 0.000 title claims abstract description 34
- 238000000034 method Methods 0.000 title claims description 15
- 230000004224 protection Effects 0.000 claims abstract description 39
- 238000007792 addition Methods 0.000 description 6
- 238000011156 evaluation Methods 0.000 description 3
- 238000003860 storage Methods 0.000 description 3
- 230000009897 systematic effect Effects 0.000 description 3
- 229940000425 combination drug Drugs 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 241000276438 Gadus morhua Species 0.000 description 1
- 229910052729 chemical element Inorganic materials 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000014759 maintenance of location Effects 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- VOVZXURTCKPRDQ-CQSZACIVSA-N n-[4-[chloro(difluoro)methoxy]phenyl]-6-[(3r)-3-hydroxypyrrolidin-1-yl]-5-(1h-pyrazol-5-yl)pyridine-3-carboxamide Chemical compound C1[C@H](O)CCN1C1=NC=C(C(=O)NC=2C=CC(OC(F)(F)Cl)=CC=2)C=C1C1=CC=NN1 VOVZXURTCKPRDQ-CQSZACIVSA-N 0.000 description 1
- 230000001360 synchronised effect Effects 0.000 description 1
- 208000011580 syndromic disease Diseases 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L7/00—Arrangements for synchronising receiver with transmitter
- H04L7/04—Speed or phase control by synchronisation signals
- H04L7/048—Speed or phase control by synchronisation signals using the properties of error detecting or error correcting codes, e.g. parity as synchronisation signal
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
Abstract
ABSTRACT:
In a data transmission system data, more spec-ifically messages can be transmitted in the form of sequentially linked modified code words of a linear block code. The modified code words are obtained by combining the code words formed from the data with a protection word.
When modified code words are interleaved bit-wise the sequence of code words of a message can be changed after de-interleaving at the receiver end, by bit shift. So as to make it possible to recognize faulty synchronization, each code word is linked to a protection word which char-acterized its position within the message. The modified code words thus obtained are interleaved bit-wise, trans-mitted and de-interleaved again and each word thus obtained is combined at the receiver end with a check word charac-terizing its position within the message. The protection words and the check words are chosen such, that the key words obtained by combining the protection words and the check words are preferably located in sub-classes which are not used for decoding.
In a data transmission system data, more spec-ifically messages can be transmitted in the form of sequentially linked modified code words of a linear block code. The modified code words are obtained by combining the code words formed from the data with a protection word.
When modified code words are interleaved bit-wise the sequence of code words of a message can be changed after de-interleaving at the receiver end, by bit shift. So as to make it possible to recognize faulty synchronization, each code word is linked to a protection word which char-acterized its position within the message. The modified code words thus obtained are interleaved bit-wise, trans-mitted and de-interleaved again and each word thus obtained is combined at the receiver end with a check word charac-terizing its position within the message. The protection words and the check words are chosen such, that the key words obtained by combining the protection words and the check words are preferably located in sub-classes which are not used for decoding.
Description
F~
The invention relates to a method of synchroniz-ing a data sink with a data source of a data transmission system, in which messages consisting of sequentially linked, modified code words of a linear block code which are formed by linking a code word to a protection word are transm-tted v a transmission channel between the data source and the data sink.
In a data transmission system having data sinks and data sources messages can be exchanged between the sinks and the sources vla transmission channels. These messages may have a word structure and consist, for example, of linked code words of a linear block code. A block code is a code having code words of equal lengths, in which a sequence of symbols (or source words) to be encoded are divided into blocks of e~ual lengths. A code word is assigned to the symbols or words of the data source. With a linear block code each linear combination of code words results again in a code word.
When code words are linked and transmitted in a continuous sequence via the transmission channel, this sequence must be broken up at the receiving side to form code words, that is to say synchronization must be effected.
When the word synchronization is lost, combinations of code elements are applied to a decoder, these elements origina-ting from two consecutive code words. Decoding is not possible when no code words from the code word stock can be assigned.
In "Fehlerkorrigierende Block-Codierung fur die Datenubertragung" by F.J. Furrer, Birkhauser Verlag~ 1981~
pages 238 to 250 a description is given of methods of word synchronization for consecutively transmitted code words using synchronization samples, codes with binary prefixes, separable codes and synchronizable codes. Which synchro-nization method is chosen, as does also the choice of the encoding of the encoding method depends on the properties of the transmission channel. For the purpose of synchron-ization, a synchronization sample can be used which is a bit sequence of a predetermined length and a fixed sample which is known to the receiver (for example ISO 3309-1979).
Inserting a synchronization sample at the beginning of the message or repeating it at predetermined distances within the message reduce the effective data speed of a data transmission channel.
~ further method of word synchronization is dis-closed in "Error-Correcting Codes" by Peterson/Weldon, 2nd Edition 1972, more specifically on pages 374 to 390.
In this method all the sequentially transmitted code words are linked to one and the same protection word, whereby a bit-wise shift of the code words of a message can be recog-nized. The protection word, which is no code word, isadded at the transmitter end and subtracted at the receiver ~nd. On page 379 an example is described in which the pro-tection word for a binary code is chosen to be equal to "1", as a result of which each last bit of the code words is inverted. If the code words are shifted through one or more bit positions, then, because of the fact that the encoding instruction is violated, this bit shift can be recognized and possibly corrected at the receiver end.
So as to render it possible to use codes which recognize or correct randomly occurring errors, for trans-mission via channels which are susceptible to interferences and have error bursts, for example radio transmission channels in a radio transmission system, the individual code words are interleaved bit-wise prior to transmission. For the purpose o~ bit-sequential interleaving the first bit of the code words, then the second bit of the code words and so on until the last bit of the code words of the message are joined together (~. Dorsch "Performance and Limits of Coding for Simple Time ~arying Channelsl', 1980, Interna-tional Zurich Seminar on Digital Communications, Proceed-ings IEEE Catalog No. 80 C~I 1521-4, left-hand column of ~2~
paye G 1.1). The invention is based on the recognition that a faulty synchronization in bit-wise interleaved code words evidences itself as a change in the sequence of the interleaved code words at the receiver.
The invention has for its object to provide a method of word synchronization with which the changes in the sequence of words of a message can be recognized.
In a method of word synchronization of the type set forth in the opening paragraph, which is known from Peterson/Weldon this object is accomplished in that the protection word (WL) characterizes the position of the code word (CL) within the message (M), that the code words (C'L) thus modified are interleaved bit-sequentially, are trans-mitted and de-interleaved again and that after de-inter-leaving each word (CK) is linked to a check word (WK) whichcharacteri~es its position within the message (M).
If code words of a linear block code are bit-wise interleaved and transmitted via a disturbed transmission channel, then a change in the sequence of the code words of a message as compared with the original sequence may occur.
By linking code uords or words with protection words or check words which are characteristic of their position with-in the message a change in the sequence can be recogni2ed unambiguously. Taking account of the prede-termined encoding instructions the choice of the protection words or the check words is easy. During the transmission of code words vla a disturbed transmission channel an error burst may occur in a code word. By bit-wise interleaving the code words the error burst is distributed over several code words. The word error probability,and the residual error probability are less compared wi,th a block-sequential transmission of code words.
Pre~erred embodiments of the invention are des-cribed in the sub-Claim.
If a linear, systematic code is used the length of the protection or check words may be limited to the PHD 83308 3a check portions of the code words or words. This renders it possible -to reduce with simple means and in a simple way the cost and designing efforts of the circuitry at the receiving and at the transmission sides for putting the method into effect.
PHD 83308 4 1~J.5,1~84 The check words and protection words are stored at the receiving and the transmitting ends. For duplex transmiSSion sys-tems the required storage capacity can be reduced to 50% when the protection words are at the same time employed as the check words. The required stor-age capacity can be reduced when the protection words and check words are chosen to be code words of a linear code, -the generator matrix, ~or example9 being stored.
Linking code words with protection words or words with check words by bit-sequential modulo-2 addi-tion is easy to effect and has the advantage that the circuit cost is low.
The invention will now be described in greater detail by way of example with reference to the accompany-lS ing drawings, in which Fig. 1 shows a block diagram of a data transmis-sion system, Fig. 2 shows a message which is mutilated by a faulty synchronization, Fig. 3 shows the change in the position of code words in dependence on a shift through f bit positions, Fig. 4 shows in the form of a Table protection words or check words chosen for a predetermined code, and Fig. 5 shows in the form of a Table for this code all the key words obtained in the event of faulty synchronization on the basis of linking the protection words to the check wordsO
In a data transmission system as shown in Fig.
1 a data source 1 is connected to a data sink 3 via a transmission channel 2. At the transmitter end an encoder 4, an adder circuit 6 and a first arrangement 8 for the bit-wise interleaving of modified code words cL are ar-ranged. At the receiving end there are provided a second arrangement 9 for de-interleaving the modified code words cL transmitted via the transmission channel 2, a subtraction circuit 7 and a decoder 5. In accordance with an encoding instruction code words cL are assigned to the symbols (data) or words produced by the data source 1. In the adder circuit 6 a protection word wL, which is charac-teristic of its position within a message N is linked to each code word cL. The protection words wL are stored in 5 a store 10. The modified code words cL thus formed are interleaved bit-wise, transmitted and de-interleaved again at the receiver end. After the de-interleaving operation a word cK occurring at the receiving end is linked in the subtraction circuit 7 to a check word wK which is charac-lG teristic of a position within the message ~. The checkwords wK are stored in a store 11.
When the data source 1 and the data sink 3 are in synchronization with each other, the code word cK at the output of the subtraction circuit 7 is identical to the 15 code word cL at the transmitter end. The code word cK is converted into a word or into data in the decoder 5 and applied to the data sink 3 for message evaluation. An apparent block synchronization may result in a faul-ty mes-sage evaluation in -the data sink 3.
In a radio transmission system radio subscribers' numbers are, for example, transmitted as messages M via a transmission channel 2 between a mobile subscriber station (data source 1) and a fixed radio station (data sink 3).
In the direction from the mobile subscriber station 1 to 25 the fixed radio station 3 the message M comprises, for example, ten code words and eight code words in the oppos-ite direction. A faulty message evaluation may, for example, result in call charges being charged to the wrong account.
Fig. 2 shows in the form of a Table the bit-wise interleaving of modified code words CL and the bit-wise de-interleaving of the words c~K. In the event of faulty synchronization, for example when the modified code words cL are shifted through two bit positions, an 35 interchanging of code words occurs. The Table shows a mes-sage M consisting of sixteen code elements, to which four code words (cL, aK) wi-th a number of positions equal to ~7 PHD 8330~ 6 1~
four are assigned. The sixteen positions of the bit se-quence of the transmitted and received message M are in-dicated at the head of the Table. In the column on the left in the Table the modified code words cL and also the words cK are arranged according to their sequence in the message ~l. Because of the faulty synchronization by two bi-t positions, the sequence of the transmitted words (c'1, c~2, cl3, c'~) is interchanged, that is to say the code words cK are received in a different sequence (c'3, C~4, c'1, c'2). Providing the code elements in the Table with indices, for example c'2 4 must make it clear that as regards this specific code element the code element arranged in the fourth position of the secon~
modified code word clL is involved. The crosses (x) in the fifteenth and sixteenth bit positions within the re-ceived message M indicate that as regards these code ele-ments code elements are involved which do not belong to the code elements of the transmitted message M. A shift through two bit positions causes a change by two positions in the sequence of the words 8K.
Fig. 3 shows the sequence of the received words CK in dependence on a shift through f bit positions. The message M must comprise four code words cL or four words CK. In the Table the left-hand column illustra-tes the shift through up to three bit positions, the sign in-dicating the direction of shift. In -the case of a negative sign the word cK is received too late or in the case of a positive sign received too early compared with the trans-mitted sequence of the code words cL (or the modified code words c~L)~ `
Because of the faulty synchronization, the re-ceived words cK are cyclically changed relative to the -transmitted code words cL and additional shifts occur in the last f or first f words CK. In the Table on Fig. 3 words cK in which this additional shift occurs are in-dicated by an asterisk added to the number.
The probability that a message M is evaluated PHD 83308 7 1G.~ X~
incorrectly because of the faulty synchronization is ve~J
great, more specifically in the event of a shift through only a few bit positions. In a linear code it is possible that owing to the bit shift in each of the words cK a bi-nary sample is produced which is a code word from thestock of code words of the code.
To recognize the faulty synchronization, the sequence of the code words cL to be transmitted is la-belled in accordance with the invention. Each code word CL is linked to the protection word wL in accordance with the linking instruction C~L = CL 0 WL
a bit-wise modulo-2 addition being preferably used as the linking instruction.
After a bit-wise interleaving, transmission and de-interleaving the check word wK is linked to the receiv-ed word 8K~ in accordance with the linking instruction CK = CK Q wK
preferably by means of modulo-2 addition. A key word wKL
which is formed in accordance with the linking instruc-tion wKL = wK 0 wL
is obtained at the receiver end.
If -the data sink 3 (receiver) is in the syn-chronized state, then the sequence of the transmitted, 30modified code words clL corresponds to the sequence of the received words c , that is to say K = L. The code violation caused at the transmitter end by the addition of the protection words wL is then eliminated at the re-3 ceiving end by the repeated addition of the check word WK-To ensure unambiguous recognition of the faulty synchronization for a linear block code with e-error cor-P~ 83308 8 1~.~.19 rection, the protection or check words wL or w~ must bechosen such, -chat the key words WKL are allocated in a secondary class, which is not used for decoding. The se-condary class can, for example, be determined by syndrome S formatioll.
For a linear, systema-tic (16, 8, ~) block code with the generator polynomial g(x) = x + x7 + x + x +
x ~ x + 1, which is capable of correcting up to two er-rors, Fig. 4 shows a message M having ten code words which indicate selected pro-tection words WL (which are the same as the check words WK). The decimal representation ZL f the bit samples of the associated protection words wL
(check words WK~ and their positions are indicated in the left hand columns of the table.
The bit samples are then chosen such ~hat when the protection words WL or check words wK are linked, a key word WKL is obtained which has a greater Hamming distance than the number e of the corrected errors of each code word. The bit samples of the protection word 20 WL or the check word WK should be chosen such tha-t the key word WKL produced for K ~ L is not a code word from the stock of code words. It can be demonstrated that the bit samples searched for must be elements from different secondary classes Nt. The object aimed at is to choose the bit samples searched for such that the key word wKL
produced for K ~ L are located in secondary classes which are not used for decoding.
In case of a faulty synchronization the bit samples of WL and wK do not agree. In addi-tion to the ~ode violation caused at -the transmitter end by adding together the bit samples of protection word WL there are further code violations caused by adding the bit samples of check word WK at the receiving end. The sum of the bi-nary positions (code elements) thus invalidated in the word CK exceeds the number e of correctable errors.
Fig. 5 shows for the linear, systematic (16, ~, 5~ block code having 2-error-correction (e = 2) the matriY
:~3~
PHD 83308 9 10.~.19Xi of key words wKL which is obtained by linking the bit samples of the protection words wK or check words r~L of Fig. 4. From the specified secondary class conditions a quadrapole (25, 44, 138, 201) can be determined as a bit sample, which quadrapole covers a sub-storage area having sixteen bit samples. From these sixteen bit samples ten samples are chosen which are indicated in the table of Fig. 4. The table of Fig. 5 shows all the possible com-binations of these ten bit samples.
The key words wKL obtained during the combina-tion and having the decimal representations 111 and 118 are elements of a secondary class Nt for a code having a minimum distance equal to two. For example, on the ba-sis of the faulty synchronization, the key word wKL hav-ing the decimal number 25 is combined with check word wL
having the decimal number 111. The key word wKL which is obtained as the result of a bit shift through seven po-sitions and which has -the decimal number 118 (code word) con-tains two errors and is consequently capable of error correction. Key words wKL of such secondary classes Nt are provided with a negative sign in Fig. 5. Such key words wKL occur only at a shift through more than seven bit positions, the probability of such a shift being very small.
Consequently, the probability that faulty syn-chronization is not recognized can be reduced by the methcd according to -the invention. Therewith 9 a mutilation of messages (messages M on a higher protocol level) caused by such a faulty synchronization can be avoided.
The invention relates to a method of synchroniz-ing a data sink with a data source of a data transmission system, in which messages consisting of sequentially linked, modified code words of a linear block code which are formed by linking a code word to a protection word are transm-tted v a transmission channel between the data source and the data sink.
In a data transmission system having data sinks and data sources messages can be exchanged between the sinks and the sources vla transmission channels. These messages may have a word structure and consist, for example, of linked code words of a linear block code. A block code is a code having code words of equal lengths, in which a sequence of symbols (or source words) to be encoded are divided into blocks of e~ual lengths. A code word is assigned to the symbols or words of the data source. With a linear block code each linear combination of code words results again in a code word.
When code words are linked and transmitted in a continuous sequence via the transmission channel, this sequence must be broken up at the receiving side to form code words, that is to say synchronization must be effected.
When the word synchronization is lost, combinations of code elements are applied to a decoder, these elements origina-ting from two consecutive code words. Decoding is not possible when no code words from the code word stock can be assigned.
In "Fehlerkorrigierende Block-Codierung fur die Datenubertragung" by F.J. Furrer, Birkhauser Verlag~ 1981~
pages 238 to 250 a description is given of methods of word synchronization for consecutively transmitted code words using synchronization samples, codes with binary prefixes, separable codes and synchronizable codes. Which synchro-nization method is chosen, as does also the choice of the encoding of the encoding method depends on the properties of the transmission channel. For the purpose of synchron-ization, a synchronization sample can be used which is a bit sequence of a predetermined length and a fixed sample which is known to the receiver (for example ISO 3309-1979).
Inserting a synchronization sample at the beginning of the message or repeating it at predetermined distances within the message reduce the effective data speed of a data transmission channel.
~ further method of word synchronization is dis-closed in "Error-Correcting Codes" by Peterson/Weldon, 2nd Edition 1972, more specifically on pages 374 to 390.
In this method all the sequentially transmitted code words are linked to one and the same protection word, whereby a bit-wise shift of the code words of a message can be recog-nized. The protection word, which is no code word, isadded at the transmitter end and subtracted at the receiver ~nd. On page 379 an example is described in which the pro-tection word for a binary code is chosen to be equal to "1", as a result of which each last bit of the code words is inverted. If the code words are shifted through one or more bit positions, then, because of the fact that the encoding instruction is violated, this bit shift can be recognized and possibly corrected at the receiver end.
So as to render it possible to use codes which recognize or correct randomly occurring errors, for trans-mission via channels which are susceptible to interferences and have error bursts, for example radio transmission channels in a radio transmission system, the individual code words are interleaved bit-wise prior to transmission. For the purpose o~ bit-sequential interleaving the first bit of the code words, then the second bit of the code words and so on until the last bit of the code words of the message are joined together (~. Dorsch "Performance and Limits of Coding for Simple Time ~arying Channelsl', 1980, Interna-tional Zurich Seminar on Digital Communications, Proceed-ings IEEE Catalog No. 80 C~I 1521-4, left-hand column of ~2~
paye G 1.1). The invention is based on the recognition that a faulty synchronization in bit-wise interleaved code words evidences itself as a change in the sequence of the interleaved code words at the receiver.
The invention has for its object to provide a method of word synchronization with which the changes in the sequence of words of a message can be recognized.
In a method of word synchronization of the type set forth in the opening paragraph, which is known from Peterson/Weldon this object is accomplished in that the protection word (WL) characterizes the position of the code word (CL) within the message (M), that the code words (C'L) thus modified are interleaved bit-sequentially, are trans-mitted and de-interleaved again and that after de-inter-leaving each word (CK) is linked to a check word (WK) whichcharacteri~es its position within the message (M).
If code words of a linear block code are bit-wise interleaved and transmitted via a disturbed transmission channel, then a change in the sequence of the code words of a message as compared with the original sequence may occur.
By linking code uords or words with protection words or check words which are characteristic of their position with-in the message a change in the sequence can be recogni2ed unambiguously. Taking account of the prede-termined encoding instructions the choice of the protection words or the check words is easy. During the transmission of code words vla a disturbed transmission channel an error burst may occur in a code word. By bit-wise interleaving the code words the error burst is distributed over several code words. The word error probability,and the residual error probability are less compared wi,th a block-sequential transmission of code words.
Pre~erred embodiments of the invention are des-cribed in the sub-Claim.
If a linear, systematic code is used the length of the protection or check words may be limited to the PHD 83308 3a check portions of the code words or words. This renders it possible -to reduce with simple means and in a simple way the cost and designing efforts of the circuitry at the receiving and at the transmission sides for putting the method into effect.
PHD 83308 4 1~J.5,1~84 The check words and protection words are stored at the receiving and the transmitting ends. For duplex transmiSSion sys-tems the required storage capacity can be reduced to 50% when the protection words are at the same time employed as the check words. The required stor-age capacity can be reduced when the protection words and check words are chosen to be code words of a linear code, -the generator matrix, ~or example9 being stored.
Linking code words with protection words or words with check words by bit-sequential modulo-2 addi-tion is easy to effect and has the advantage that the circuit cost is low.
The invention will now be described in greater detail by way of example with reference to the accompany-lS ing drawings, in which Fig. 1 shows a block diagram of a data transmis-sion system, Fig. 2 shows a message which is mutilated by a faulty synchronization, Fig. 3 shows the change in the position of code words in dependence on a shift through f bit positions, Fig. 4 shows in the form of a Table protection words or check words chosen for a predetermined code, and Fig. 5 shows in the form of a Table for this code all the key words obtained in the event of faulty synchronization on the basis of linking the protection words to the check wordsO
In a data transmission system as shown in Fig.
1 a data source 1 is connected to a data sink 3 via a transmission channel 2. At the transmitter end an encoder 4, an adder circuit 6 and a first arrangement 8 for the bit-wise interleaving of modified code words cL are ar-ranged. At the receiving end there are provided a second arrangement 9 for de-interleaving the modified code words cL transmitted via the transmission channel 2, a subtraction circuit 7 and a decoder 5. In accordance with an encoding instruction code words cL are assigned to the symbols (data) or words produced by the data source 1. In the adder circuit 6 a protection word wL, which is charac-teristic of its position within a message N is linked to each code word cL. The protection words wL are stored in 5 a store 10. The modified code words cL thus formed are interleaved bit-wise, transmitted and de-interleaved again at the receiver end. After the de-interleaving operation a word cK occurring at the receiving end is linked in the subtraction circuit 7 to a check word wK which is charac-lG teristic of a position within the message ~. The checkwords wK are stored in a store 11.
When the data source 1 and the data sink 3 are in synchronization with each other, the code word cK at the output of the subtraction circuit 7 is identical to the 15 code word cL at the transmitter end. The code word cK is converted into a word or into data in the decoder 5 and applied to the data sink 3 for message evaluation. An apparent block synchronization may result in a faul-ty mes-sage evaluation in -the data sink 3.
In a radio transmission system radio subscribers' numbers are, for example, transmitted as messages M via a transmission channel 2 between a mobile subscriber station (data source 1) and a fixed radio station (data sink 3).
In the direction from the mobile subscriber station 1 to 25 the fixed radio station 3 the message M comprises, for example, ten code words and eight code words in the oppos-ite direction. A faulty message evaluation may, for example, result in call charges being charged to the wrong account.
Fig. 2 shows in the form of a Table the bit-wise interleaving of modified code words CL and the bit-wise de-interleaving of the words c~K. In the event of faulty synchronization, for example when the modified code words cL are shifted through two bit positions, an 35 interchanging of code words occurs. The Table shows a mes-sage M consisting of sixteen code elements, to which four code words (cL, aK) wi-th a number of positions equal to ~7 PHD 8330~ 6 1~
four are assigned. The sixteen positions of the bit se-quence of the transmitted and received message M are in-dicated at the head of the Table. In the column on the left in the Table the modified code words cL and also the words cK are arranged according to their sequence in the message ~l. Because of the faulty synchronization by two bi-t positions, the sequence of the transmitted words (c'1, c~2, cl3, c'~) is interchanged, that is to say the code words cK are received in a different sequence (c'3, C~4, c'1, c'2). Providing the code elements in the Table with indices, for example c'2 4 must make it clear that as regards this specific code element the code element arranged in the fourth position of the secon~
modified code word clL is involved. The crosses (x) in the fifteenth and sixteenth bit positions within the re-ceived message M indicate that as regards these code ele-ments code elements are involved which do not belong to the code elements of the transmitted message M. A shift through two bit positions causes a change by two positions in the sequence of the words 8K.
Fig. 3 shows the sequence of the received words CK in dependence on a shift through f bit positions. The message M must comprise four code words cL or four words CK. In the Table the left-hand column illustra-tes the shift through up to three bit positions, the sign in-dicating the direction of shift. In -the case of a negative sign the word cK is received too late or in the case of a positive sign received too early compared with the trans-mitted sequence of the code words cL (or the modified code words c~L)~ `
Because of the faulty synchronization, the re-ceived words cK are cyclically changed relative to the -transmitted code words cL and additional shifts occur in the last f or first f words CK. In the Table on Fig. 3 words cK in which this additional shift occurs are in-dicated by an asterisk added to the number.
The probability that a message M is evaluated PHD 83308 7 1G.~ X~
incorrectly because of the faulty synchronization is ve~J
great, more specifically in the event of a shift through only a few bit positions. In a linear code it is possible that owing to the bit shift in each of the words cK a bi-nary sample is produced which is a code word from thestock of code words of the code.
To recognize the faulty synchronization, the sequence of the code words cL to be transmitted is la-belled in accordance with the invention. Each code word CL is linked to the protection word wL in accordance with the linking instruction C~L = CL 0 WL
a bit-wise modulo-2 addition being preferably used as the linking instruction.
After a bit-wise interleaving, transmission and de-interleaving the check word wK is linked to the receiv-ed word 8K~ in accordance with the linking instruction CK = CK Q wK
preferably by means of modulo-2 addition. A key word wKL
which is formed in accordance with the linking instruc-tion wKL = wK 0 wL
is obtained at the receiver end.
If -the data sink 3 (receiver) is in the syn-chronized state, then the sequence of the transmitted, 30modified code words clL corresponds to the sequence of the received words c , that is to say K = L. The code violation caused at the transmitter end by the addition of the protection words wL is then eliminated at the re-3 ceiving end by the repeated addition of the check word WK-To ensure unambiguous recognition of the faulty synchronization for a linear block code with e-error cor-P~ 83308 8 1~.~.19 rection, the protection or check words wL or w~ must bechosen such, -chat the key words WKL are allocated in a secondary class, which is not used for decoding. The se-condary class can, for example, be determined by syndrome S formatioll.
For a linear, systema-tic (16, 8, ~) block code with the generator polynomial g(x) = x + x7 + x + x +
x ~ x + 1, which is capable of correcting up to two er-rors, Fig. 4 shows a message M having ten code words which indicate selected pro-tection words WL (which are the same as the check words WK). The decimal representation ZL f the bit samples of the associated protection words wL
(check words WK~ and their positions are indicated in the left hand columns of the table.
The bit samples are then chosen such ~hat when the protection words WL or check words wK are linked, a key word WKL is obtained which has a greater Hamming distance than the number e of the corrected errors of each code word. The bit samples of the protection word 20 WL or the check word WK should be chosen such tha-t the key word WKL produced for K ~ L is not a code word from the stock of code words. It can be demonstrated that the bit samples searched for must be elements from different secondary classes Nt. The object aimed at is to choose the bit samples searched for such that the key word wKL
produced for K ~ L are located in secondary classes which are not used for decoding.
In case of a faulty synchronization the bit samples of WL and wK do not agree. In addi-tion to the ~ode violation caused at -the transmitter end by adding together the bit samples of protection word WL there are further code violations caused by adding the bit samples of check word WK at the receiving end. The sum of the bi-nary positions (code elements) thus invalidated in the word CK exceeds the number e of correctable errors.
Fig. 5 shows for the linear, systematic (16, ~, 5~ block code having 2-error-correction (e = 2) the matriY
:~3~
PHD 83308 9 10.~.19Xi of key words wKL which is obtained by linking the bit samples of the protection words wK or check words r~L of Fig. 4. From the specified secondary class conditions a quadrapole (25, 44, 138, 201) can be determined as a bit sample, which quadrapole covers a sub-storage area having sixteen bit samples. From these sixteen bit samples ten samples are chosen which are indicated in the table of Fig. 4. The table of Fig. 5 shows all the possible com-binations of these ten bit samples.
The key words wKL obtained during the combina-tion and having the decimal representations 111 and 118 are elements of a secondary class Nt for a code having a minimum distance equal to two. For example, on the ba-sis of the faulty synchronization, the key word wKL hav-ing the decimal number 25 is combined with check word wL
having the decimal number 111. The key word wKL which is obtained as the result of a bit shift through seven po-sitions and which has -the decimal number 118 (code word) con-tains two errors and is consequently capable of error correction. Key words wKL of such secondary classes Nt are provided with a negative sign in Fig. 5. Such key words wKL occur only at a shift through more than seven bit positions, the probability of such a shift being very small.
Consequently, the probability that faulty syn-chronization is not recognized can be reduced by the methcd according to -the invention. Therewith 9 a mutilation of messages (messages M on a higher protocol level) caused by such a faulty synchronization can be avoided.
Claims (6)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A method of synchronizing a data sink with a data source in a data transmission system in which data provided by the data source is encoded as code words (CL) in a linear block code and such code words are transmitted as messages over a transmission channel in the form of sequen-tially linked modified code words (C'L), the modified code words (C'L) being formed by linking each data code word (CL) to a protection word (WL) which is transmitted over such transmission channel, characterized in that: each protection word (WL) identifies the position within the transmitted message of the code word (CL) linked thereto;
the modified code words (C'L) are interleaved bit-sequen-tially, transmitted, and at the receiver are de-interleaved to derive received code words (?K); and each received code word (?K) is linked to a check word (WK) which character-izes the position of such code word (?K) within the received message.
the modified code words (C'L) are interleaved bit-sequen-tially, transmitted, and at the receiver are de-interleaved to derive received code words (?K); and each received code word (?K) is linked to a check word (WK) which character-izes the position of such code word (?K) within the received message.
2. A method as claimed in Claim 1, further charac-terized in that at the receiver the protection words (WL) of the transmitted code words (C'L) are combined with the check words (WK) of the received code words (?K), the lengths of the protection words and check words being a portion of the length of the code words.
3. A method as claimed in Claim 2, further charac-terized in that linking of each data code word (CL) with a protection word (WL) and linking each received code word (?K) with the check word (WK) is effected by a bit-wise modulo-2 adding operation.
4. A method as claimed in Claim 2, further charac-terized in that the check words (WK) are the same as the protection words (WL) and are selected such that key words (WKL) which result from combining the protection words (WL) with the check words (WK) are in secondary classes of code words other than the code words used for encoding the data provided by the data source.
5. A method as claimed in Claim 4, further charac-terized in that the protection words (WL) and check words (WK) are code words of a linear code.
6. A circuit arrangement for the synchronization of a data sink with a data source of a data transmission sys-tem having a transmission channel via which messages (M) consisting of sequentially linked modified code words (C'L) of a linear block code are transmitted, which are formed by linking a code word (CL) appearing at the output of a coder connected to the data source to a protection word (WL) by means of an adder circuit arranged at the place of the data source, characterized in that a plurality of protection words (WL) which characterize the position of the code word (CL) within the message (M) are stored in a memory at the place of the data source, that at the place of the data source a first device is provided which is connected to the adder circuit and to the transmission channel and which applies the modified code words (C'L) interleaved bit-sequentially to the transmission channel, that the received modified code words (C'L) are again de-interleaved by means of a second device which is arranged at the place of the data sink and which is connected to the transmission chan-nel, that a plurality of check words (WK) which character-ize the position of each word occurring at the output of the second device within the message (M) are stored in a memory provided at the place of the data sink, and that a subtraction circuit is provided at the place of the data sink, which circuit is connected to the second device and to the memory and which interleaves the applied words (?K) and check words (WK) and applies code words (CK) appearing at the output to a decoder which is connected to the data sink, the data source and the data sink being in synchron-ism when the code word (CK) at the output of the subtrac-tion circuit is equal to the code word (CL) at the output of the coder.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DEP3320948.0 | 1983-06-10 | ||
| DE19833320948 DE3320948A1 (en) | 1983-06-10 | 1983-06-10 | METHOD FOR SYNCHRONIZING IN A DATA TRANSFER SYSTEM USING A LINEAR BLOCK CODE |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1230396A true CA1230396A (en) | 1987-12-15 |
Family
ID=6201114
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000456064A Expired CA1230396A (en) | 1983-06-10 | 1984-06-07 | Method of synchronization in a data transmission system using a linear block code |
Country Status (8)
| Country | Link |
|---|---|
| US (1) | US4635262A (en) |
| EP (1) | EP0128624A3 (en) |
| JP (1) | JPS6041833A (en) |
| AU (1) | AU569443B2 (en) |
| CA (1) | CA1230396A (en) |
| DE (1) | DE3320948A1 (en) |
| DK (1) | DK281084A (en) |
| ZA (1) | ZA844404B (en) |
Families Citing this family (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1987006036A1 (en) * | 1986-03-28 | 1987-10-08 | Ampex Corporation | Digital data transmission with detection of errors, including word framing errors |
| FR2608871B1 (en) * | 1986-12-18 | 1992-03-20 | Cit Alcatel | METHOD FOR MULTIPLEXING AND TEMPORAL DEMULTIPLEXING OF SYNCHRONOUS DIGITAL TRAINS |
| US5280484A (en) * | 1989-07-08 | 1994-01-18 | Alcatel N.V. | Time-division multiplex communication system with a synchronizing circuit at the receiving end which responds to the coding of words inserted in the transmitted information |
| FR2673298B1 (en) * | 1991-02-22 | 1995-04-07 | Inst Francais Du Petrole | METHOD AND DEVICE FOR SEISMIC TRANSMISSION WITH VERY LOW ERROR RATES. |
| US5461631A (en) * | 1992-12-15 | 1995-10-24 | International Business Machines Corporation | Method for bit resynchronization of code-constrained sequences |
| DE4408163A1 (en) * | 1994-03-11 | 1995-09-14 | Bosch Gmbh Robert | Method of transferring data |
| US5727004A (en) * | 1995-03-14 | 1998-03-10 | Adaptive Networks, Inc. | Method and apparatus for data encoding and communication over noisy media |
| US7681110B2 (en) * | 2006-08-30 | 2010-03-16 | Microsoft Corporation | Decoding technique for linear block codes |
| US8103934B2 (en) | 2007-12-21 | 2012-01-24 | Honeywell International Inc. | High speed memory error detection and correction using interleaved (8,4) LBCs |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| NL296163A (en) * | 1960-03-02 | |||
| BE656364A (en) * | 1963-11-29 | |||
| JPS5292413A (en) * | 1976-01-30 | 1977-08-03 | Toshiba Corp | Data transfer system |
| JPS5380105A (en) * | 1976-12-24 | 1978-07-15 | Sony Corp | Digital signal transmission method |
| US4271520A (en) * | 1979-06-25 | 1981-06-02 | Motorola, Inc. | Synchronizing technique for an error correcting digital transmission system |
| US4312070A (en) * | 1979-12-07 | 1982-01-19 | Motorola, Inc. | Digital encoder-decoder |
| US4468752A (en) * | 1981-09-21 | 1984-08-28 | Tandy Corporation | Data synchronization apparatus |
| US4466099A (en) * | 1981-12-20 | 1984-08-14 | International Business Machines Corp. | Information system using error syndrome for special control |
| US4541091A (en) * | 1982-06-11 | 1985-09-10 | Hitachi, Ltd. | Code error detection and correction method and apparatus |
-
1983
- 1983-06-10 DE DE19833320948 patent/DE3320948A1/en not_active Withdrawn
-
1984
- 1984-06-07 DK DK281084A patent/DK281084A/en not_active Application Discontinuation
- 1984-06-07 CA CA000456064A patent/CA1230396A/en not_active Expired
- 1984-06-08 EP EP84200816A patent/EP0128624A3/en not_active Withdrawn
- 1984-06-08 AU AU29229/84A patent/AU569443B2/en not_active Ceased
- 1984-06-09 JP JP59117481A patent/JPS6041833A/en active Pending
- 1984-06-11 ZA ZA844404A patent/ZA844404B/en unknown
- 1984-06-11 US US06/618,976 patent/US4635262A/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| DE3320948A1 (en) | 1984-12-13 |
| US4635262A (en) | 1987-01-06 |
| JPS6041833A (en) | 1985-03-05 |
| EP0128624A2 (en) | 1984-12-19 |
| AU569443B2 (en) | 1988-01-28 |
| AU2922984A (en) | 1984-12-13 |
| DK281084A (en) | 1984-12-11 |
| EP0128624A3 (en) | 1987-12-02 |
| ZA844404B (en) | 1986-01-29 |
| DK281084D0 (en) | 1984-06-07 |
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