CA1212437A - Data transmission system with error correcting data encoding - Google Patents

Abstract

IMPROVED DATA TRANSMISSION
SYSTEM WITH ERROR CORRECTING DATA ENCODING

ABSTRACT OF
THE DISCLOSURE

A multi-phase communication system for simultaneously trans-mitting plural binary digits employs one or more error-check bits which perform an encoding on the conveyed information over a plurality of digit intervals. The information and error check digits are then communicated via a transmission channel -as by amplitude modulating phase-orthogonal carriers.
Upon reception, the incoming information and error check digits are decoded, and supplied to error syndrome circuitry which corrects errors which may arise from time to time during data transmission.

Description

I

disclosure of the Invention This invention relates to electronic communications and, more specifically, to an improved data transmission and reception system employing error detection and correction.
It is an object of the present invention to provide an imp proved data transmission system.
More specifically, it is an object of the present invention to provide improved data transmission apparatus which coincident tally transmits plural digits via quadrature phase modulation;
and which encodes the outgoing digital information Jo detect and lo correct errors in the received information data stream.
Roy above and other objects of the present invention are realized in a specific, illustrative multi-phase communication system for simultaneously transmitting plural binary digits which employs one or more error-check to perform an encoding on the conveyed information over a period of time The inform motion and error check digits are then communicated via a trays-mission channel - as by amplitude modulating phase-orthogonal carriers.
Upon reception, the incoming information and error check digits are decoded, and supplied to error syndrome circuitry which corrects errors which may arise from time two time during ' data transmission.
I The above and additional features and advantages of the ! present invention will become more clear from the following detailed description of a specific, illustrative embodiment thereof, presented hereinbelow in conjunction with the accom-paying drawing, in which:
Fig. 1 is a signal space diagram depicting multi-phase transmission of the prior art and of the instant invention;
Fig. 2 is a block diagram of transmitter circuitry of the instant invention;

Fig. 3 schematically depicts receiver circuitry operative in conjunction with the Fig. 2 transmission apparatus;
Fig. 4 represents a specific, illustrative implementation of transmitter convolutional encoder circuitry 13 of Fig. 2; and Fig. 5 illustrates a specific, illustrative implementation for decoder 41 and syndrome error correcting apparatus 43 utile iced in the Fig 3 receiver.
Referring now to the drawing and more particularly Fig. 1, there is shown a signal space diagram for multi-phase, e.g., quadrature, transmission. As is per so well known (e.g., for QPSK or quadrature phase shift keying transmission), two carriers are independently amplitude modulated along orthogonal (i.e., 90 phase shifted) axes. Thus, for conventional QPSK transmission one carrier assumes an orientation along the plus or minus X-axis (0 or 180 phase shift) depending upon one of two bits for the dubiety encoding; while another carrier resides along either the plus or minus Y axis (90 or 270 transmission) in accordance with the binary value of the second bit. Accordingly, an outgoing QPSK radiation will assume one of the points a-d of Fig. 1 depending upon the value of the two information bits to be transmitted. Such QPSK coding is widely employed and basically has a phase error margin of 45. That is, a received QPSK signal may vary from its nominal value and still be properly detected as long as the variation does not exceed 45. Once the 45 limit is exceeded, the received point appears closer to a different QPSK state and thus an error occurs in one of the two information bits.
In QPSK transmission, all carriers have a like nominal amplitude. For purposes of the Fig. 1 description assuming a unit circle sample space (shown dashed in Fig. 1), the relative amplitude of each carrier for QPSK transmission permissible n 3 transmission states a-d) is always + .
In accordance with the principles underlying one aspect of the instant invention, eight possible -transmission states, given by the points a-_ of Fig. 1, are utilized. To determine one of eight states (vis-a-vis, one of four for conventional QPSK
transmission) a third outgoing phase-specifying digit is developed in addition to the two dubiety outgoing information values (herein deemed x2 and Al). This third digit is an error encoding bit stream and is deemed herein Jo. It will now be apparent from Fig. 1 that the error correcting additional bit increases the phase margin for properly recovering a dubiety transmission by 22 1/2 to a total of 67.5 as shown in Fig. 1 (thus effecting approximately a 2 dub improvement in error rejection).
way of overview, the ability to correct for single errors lo is imparted to the apparatus of the instant invention by employ-in at the transmitter an additional bit which performs an en-coding over the two outgoing digital data streams. Moreover, the encoding is effected over a period of time such that each error correcting, encoding digit represents information which is in general descriptive of each of (i) the first (or x2) data bit and the previous such bits over some plural-digit time interval;
; (ii) the second or Al) data bit and the previous such bits over a predetermined interval; and (iii) the coding or error check bit (Jo) data stream over the like interval.
I 11 At the receiver, the recovered information data streams X2 and Xi are delayed for the number of digit intervals over which the encoding was performed (as is also the received coding hit stream Jo). The inverse of the coding operation effected at the transmitter is then accomplished. If the recovered information x2, Xi and Jo suffered no errors, the parity will fully check and the x2 and Al data is simply passed -to an output utili7~tio~ device or circuit. Louvre, if any error in reception or receiver data processing has occurred the parity will not check in the receiver decoding apparatus and then the error syndrome processing structure will then operate in -the manner more fully described below to overcome or cure the error in the received information.
With the above overview in mind, attention will now be directed to the transmission and receiver apparatus of Figs. 2 and 3 which specifically implement the above discussed overall mode of operation. Considering initially the transmitter appear-tug of Fig. 2, a data source 10 supplies two data serial streamsX2 and Al such -that for the instant di-bit-transmission during each digit or bit time, there exists one binary value for each of Al and x2. The x2 and Al values are then supplied to a con-volitional encoder 13 (together with -the internally generated error or check bit stream output x0 which is fed back into the circuit). The convolutional encoder includes a number of delay elements and during each bit time provides a specific output value x0 which is dependent upon the current and/or past values of x2, Al and x0 over some interval. A specific embodiment of the convolutional encoder 13 is shown in Fig. 4 and is discussed below. Again, suffice it for present purposes that the error check output bit stream x0 performs an error correction encoding on both itself and on the x2 and Al data flow. Specific error detecting and correction codes are per so well known to those skilled in the art - see, e.g., Fig. 4 and the discussion below.
During each data interval, the then obtaining x2, Al and I binary values constitute addressing inputs to a read only memory (ROM) 16 which for each one of-eight input address condo---lions supplies three amplitude and one polarity defining input pa to each of digital-to-analog converters 17 and I The outputs of the digital-to-analog converters 17 and I supply an analog level X I

o of one-of-three bipolar states sufficient to give rise to one of the eight permissible transmission points a-h of Fig. 1 depending upon -the input variables x2, Al and Jo.
Roy specifically, with respect to the outgoing quadrature phase transmission, a carrier source 12 supplies a source of carrier directly to a modulator 21 wherein the 0 phase carrier is modulated by the output of -the digital to analog converter 18. The output carrier of source 12 is shifted by 90 in a phase shifter 15 and is supplied to the modulator 19. The output amplitude of modulator 19 is controlled by digital-to-analog converter 17.
Accordingly, in a per so straightforward manner the input variables x2, Al and Jo to ROM 16 specify one of the eight -trays-mission points _-_; and the output of ROM 16 acting in consort with the digital to analog converters 17 and 18 and modulators 19 and 21 generate the requisite two modulated quadrature carrier signals to implement the desired transmission point. It is apparent that instead of the shifted amplitude signals of the QPSK situation considered above, the phase modulated carrier signals of the instant transmission. system have relative values ~`~ of "O" and + "1" for the assumed unit circle of Fig. 1.
The two modulated quadrature carriers Al and Z2 are then combined in a linear summing network 26 and impressed upon a communique lions channel for distribution to any and all intended recipients.
The communications channel may be of any form well known to those skilled in the art, e.g., radio carrier, wire communique-lions or the like.
j! Thus, it will be seen that for each digit period, the two then obtaining characters x2 and x1 - together with the coin-cidentally present error bit Jo define a specific trays-mission point of Fig. 1 - and that the phase and amplitude of the outgoing quadrature carriers in general varies from digit period to digit period in accordance with the incoming data streams and in accordance with the history of -those streams as reflected by the x0 signal.
At each receiver location (Fig. 3), a reconstituted carrier source 29 supplies a carrier in phase with -that of the carrier source 12 at the transmitter. Carrier reconstitution circuitry is per so well known to those skilled in the art and may be implemented, for example, by simply multiplying the incoming carrier signal by a factor of eight to resolve phase ambiguity;
and dividing the eighth harmonic so formed by a factor of eight.
The reconstituted carrier 29 is supplied directly to detector (e.g., a synchronous mixer and low pass filter) 31. Further, the reconstituted carrier from source 29 is shifted in phase by 90 in circuitry 33 and supplied to detector 30. The outputs of the detectors 30 and 31 (which correspond to the analog levels of converters 18 and 17) are respectively supplied to analog-to-digi--tat converters 38 and 36. The output of converter 36 is a three bit digital word which corresponds in the absence of transmission error to the input at the transmitter (Fig. 2) to digital-to-analog converter 18. Similarly, the output of analog-to-digital converter 38 at the receiver corresponds to the three digital bits supplied to the digital-to-analog converter 17.
The read only memory (ROM) 40 at -the receiver provides a , function inverse to that effected by ROM 16 in the transmitter.
In particular, the six bit output of analog-to-digital converters 36 and 38 are address inputs to ROM 40 (and specify the x and the y coordinates of the received signal point). The ROM 40 includes a stored pattern which converts these inputs to the equivalent x2, Al and x0 received versions of the original x2 and Al and x0 outgoing data at the transmitter. The use of the prime designations on the x-underlyiny variables indicates received versions of the outyoiny data. The x', Al and x0 data will identically equal the x2, x1 and x variables in the absence of error. Should a -transmission error or receiver data processing error occur there of course will be a difference between the two and it is the function of the instant apparatus to detect and correct that difference and that error.
The received x2, Al and x0 signals are supplied to a decoder circuit 41 which provides a decoding which is the inverse of that effected by convolutional encoder 13. The decoder 41 includes delay apparatus for delaying between its input and output the x2, Al and x0 signals for an interval corresponding to the encoding period for convolutional encoder 13. assuming that the received signals are identical to the transmitted signals, the decoder 41 supplies on an output lead 42 to a syndrome correcting circuit 43 characterized by an error-free signaling state (e.g., a binary "0") indicating that no errors have occurred. As long as this situation obtains, the delayed x2 and Xi outputs of decoder 41 pass without change through Exclusive-OR gates 79 and 81 such that the recovered x2 and Al signals are available for any desired output utilization purpose. however, when an error does occur, the output lead 42 switches to its alternate (assumed "1") state. Depending upon the nature of the error and the power of the code employed, one or perhaps both of the erroneous I or Xi variables are corrected in the corresponding Exelusive-OR gates 79 or 81 by "1" output signal on leads 44 or 45 (since a "1" input to an Exclusive-OR gate will invert whatever binary level is applied to the other input of an Exclusive-OR gate). A specific implementation for decoder 41 and the syndrome correcting circuit 43 operative with respect to the specific encoder 13 shown in Fig. 4 is discussed below with respect to Fig. 5.

it Turning now to Fig. 4, there is shown a specific convolu-tonal encoder 13 used in the transmitter portion of the instant communication apparatus (Fig. 2). The apparatus includes an array of cascaded unit delay circuits 50, 53, 56, 58, 62, 64, 66, 72 and 73, i.e., delays of one digit period for the data streams I and Al. A plurality of Exclusive-OR gates 52, 55, 60, 63, 65 and 69 are disposed between illustrated ones of the unit delay elements. As above discussed, it is the purpose of the encoder to perform an encoding over the x2, Al and x0 digits over a predetermined number of prior bit intervals. Thus, for the Fig. 4 encoder, the error bit encoding x0 will include a measure of the x2 signal from two bit times prior (effected by delays 72 and 73 through the flow combining effect of Exclusive-OR gate 69), of the x2 digit four digits prior (delays 64, 66, 72 and 73 with the combining and pass through effects of Exile-sever gates 63, 65 and 69); and five bits prior (via delays 62, 64, 66, 72 and 73 and their associated Exclusive-OR gates. Semi-laxly, x0 is also a function of the Al variable occurring 3, 4, 5 and 7 bit times earlier; and of its own error check-encoding character x0 stream 7, 8, and 9 times earlier. Expressed in mathematical terms, x0 = x2 (D + D -I D ) + Al (D + D + Equation 1 D + D + x0 (D + D -I D ) where "D" is an operator representing one unit of delay, "D "
represellts two units of delay, and so forth. Rearranging Equation 1, x0 x0 (Do + Do + Do) = x (D + D + Equation 2 Do) + Al (Do + Do = Do -I Do) and solving for x0, X2 (D -I D Do) -I Al (Do Do -I Do Do) Equation 3 O
l [Do -I Do Do]

Letting operators Go, Go and Go represent the functional depend dunce of x0 on x2, Al and x0, respectively, Equation 3 may be rewritten, Jo - 2G2 + xlGl Equation 4 1 - Go For purposes which will become more clear below when operation of the Fig. 5 decoder 41 is considered, Equation 4 may be rewritten,

2 2 1 1 0 0 ) Equation S
The negative sign in the last parenthetical expression of Equal lo lion 5 may be changed to a positive yielding Equation 6, 0 = x2G2 + xlGl + x0 ( 0 Equation 6 since, for the muddle purpose effected by the Fxclusive-OR
gates of the instant apparatus, subtraction and addition yield identical results. Thus it will be clear from the foregoing in Fig. 4 that the expression for the output encoding bit stream x0 is given by Equation 3 (or 4) above and that x0 in fact is dependent upon events occurring as many as nine digit times earlier A specific implementation for decoder 41 and syndrome correcting circuit 43 operative in conjunction with the Fig.
4 implementation of transmitter encoder 13 is shown in Fig. 5.
The received versions of the transmitted data x2, Al and x0, viz., x2, Xi and x0, are respectively loaded into nine stage shift registers 80, 82 and 85. Nine stages are employed for the shift registers since nine digit times of data must be examined to recheck the parity effected by encoder 13 (Fig. I) which was operative in conjunction with x0 digits occurring nine digit intervals earlier. The shift registers 80, 82 and 85, operative in conjunction with cascaded Exclusive-OR gates 84, 83 and 87 to recheck the accuracy or parity of the received digits - in essence employing the algorithm or expression of Equation 6 above. That is, if the received digits x2, Xi and lo x0 accurately and identically correspond to x2, x and x0, Equation 6 will be satisfied and the output of the final Exclusive-OR gate 87 will be a binary "0" indicating that no error has occurred. Thus, for example, during encoding the x2 variable was sampled with unit delays of Do, Do and Do.
Accordingly, the output of the second, fourth and fifth shift register 80 stages 802, 804 and 805 are utilized. Similarly examining shift registers 82 and 85 i-t will be seen that the Al received signal is sampled with unit delays of Do, D and D
(corresponding to G in Equations 36) while x' is sampled with unit delays Do, Do and D as well as a direct ("l") connection into the final Exclusive-OR gate 87 ("logo" in Equations 3-6).
Again, if no transmission errors were incurred, the output of gate 87 is and will remain a "0". Accordingly, -the output of syndrome error correction circuit 43 and more specifically a error correction pattern storing read only memory (ROM) 89 will have at its output terminals Ho E an array of all "0's"
thus not inverting the outputs of the Exclusive-OR gates 79 and 81. Under this condition, the correct x2 and Al signals flow out of the Exclusive-OR gates 79 and 81 and appear as the desired output data x2 and Al.

Conversely, if an error does occur, -the output of -the Exclusive-OR gate 87 will be a "1" rather than a "0". Earthier as each error occurs, it will flow -through a shift register 87 also having nine stages each formed of an Exclusive-OR gate and following unit delay. The particular pat-tern of "l's" and "0's"
at the output of the shift register 87 stage form address inputs to the correction storing ROM 89 and, for each address input, the appropriate stored correction signals are recovered and imp pressed on the output ports Eye Where a "1" appears on the corresponding ROM 89 output, the output of the respective gate 79 or 81 is inverted thus correcting the desired error. The particular contents of ROM 89 depends upon the correspondence between the pattern of detected errors (if any) stored in the shift register 87 - and the inversion(s) required to correct that error condition. Again, where the shift register 87 stores all "0's" indicating no errors, a "0" appears at each of the out-puts Eye The pattern for Eye for any non-zero address in-put depends on the particular coding and the like used and may be empirically or computational derived. Thus, for example, single or multiple errors may simply be postulated for the no-ceiled variables x2, Al and x0 - and the pattern in shift register 87 computed as the error(s) ripple through register 87.
The necessary correction outputs Eye are then computed for each state of register 87 -- and define the stored three-bit con-tents of the corrective word stored at the corresponding address in ROM 89. The process continues for all errors - and error come binations of interest to define all used address locations in ROM 89.
Accordingly, the apparatus of Figs. 2 and 3 using the specific implementations of Figs. 4 and 5 includes data formed I

over nine digit intervals upon transmission; and rechecks the transmitted parity upon reception, correcting any detected errors. Many forms of codes may be employed depending upon -the hardware, complexity and code pattern desired for any particular application.
In accordance with one aspect of the present invention, stored errors in the shift register stages 87i may be cleared (after output correction) by employing a feed back path from the outputs En Ho to the appropriate inputs of the stages 87io The particular connection patterns of Fig. 5 correspond to that for the assumed encoding and decoding apparatus 13 and 41, and effectively comprises the inverse of the delays effected by the shift registers 80, 82 and 85. Thus, for example, the Ho cornea-lion signal (corresponding to x0 errors) is connected to the first, second and third stages 871, 872 and 873 rather than to the last three stages of shift register 85 in decoder 14. Semi-laxly, the feed back connections for the El and En outputs are the mirror inverse for those of the shift registers 82 and 80.
Exclusive-OR gates (e.g., gates 92-94) are utilized where more than one output resets any particular stage of shift register 87.
Thus, for example, the third stage 873 is reset by both the El and Ho signals (corresponding to connections from shift register stages 827 and 857 in the decoder 41. Note also the correspond in use of the exclusive-OR gates 93 and 94 for the x2 and x stage 804, 805 and 824, 825 connections of decoder 41. The above feed back connection is optional and when employed will increase system performance.
The maximum error correction capability of the code employed can be achieved if the functions of the decoder 41 and I the syndrome correcting circuit 43 are cascaded, i.e., if the structure of Fig. 5 is replicated with outputs x2 j, Al j and x0 j for each stage are supplied as inputs to a just stage.
For this purpose, an Exclusive-OR gate 86 is added (shown dashed in Fig. 5) to correct -the x0~ bit prior -to -the x21 - x0' bitts being fed in-to a cascaded, following Fig. 5-type arrangement.
This cascade may be repeated as many times as is needed. In practice, the full capability is achieved in three or four sea-lions.
The storage pattern for ROM 89 is different for each stage of the cascade. The first ROM corrects only the most easily corrected errors. Later ROM's correct the more difficult to correct errors i.e., multiple clustered errors. This may be thought of as having the earlier ROM's "clear the field" for the final correction stage. The final stage does no-t require the Exclusive-OR gate 86.
The above described arrangement is merely illustrative of the principles of the present invention. Numerous modifica-lions and adaptations thereof may be readily apparent to those skilled in the art. Thus, for example, any number of concurrent data streams zoom be encoded by any number of error correct-on digits Xoj~ it simply requiring a signal space having sufficient transmission conditions to reflect each of the different xi, x Further, as above discussed, -the specific coding and decoding implemented may be as elaborate or straightforward as desired by the user depending upon the economics of any application, con-side ring cost, signal delay time and the like.

Claims (12)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. In combination, quadrature phase modulation data communications apparatus for transmitting digital information by di-bit amplitude and phase modulation on two phase quadra-ture carriers, said communications apparatus including trans-mitter means including convolutional encoding means including means for generating a digital stream performing an encoding on the di-bit digital information to be conveyed by said com-munications apparatus over a period of time exceeding one information digit period, and signalling means modulated by the output of said convolutional encoding means and by the digital information conveyed for disseminating said phase and amplitude modulated two carriers; and receiving means for recovering the digital information and digital encoding stream from the output of said signalling means, said receiver means including decoding means including delay means for performing the inverse of the encoding effected by said encoding means at said transmitter means, and syndrome error detecting and correcting means enabled responsive to the output of said decoding means, said syndrome error detecting and correcting means including a memory supplying error correcting stored out-put signals.

2. A combination as in claim 1 wherein said convolutional encoding means includes a plurality of cascaded Exclusive-OR
gates and delay units, and means for energizing inputs of said convolutional encoding means with the digital information and with the output stream of said convolutional encoding means.

3. A combination as in claim 1 or 2 wherein said signal-ling means includes means for generating amplitude modulated quadrature phase carriers.

4. A combination as in claim 1 or 2 wherein said signal-ling means includes means for generating amplitude modulated quadrature phase carriers and further comprises a first addi-tional memory, first and second modulators supplied with carriers having a phase shift therebetween, and digital-to-analog converter means connecting said first additional memory and said modulators.

5. A combination as in claim 1 or 2 wherein said receiver decoding means includes plural shift registers, and means for checking the encoding effected at the transmitter by said convolutional encoding means responsive to the stored contents of predetermined stages of said shift registers.

6. A combination as in claim 1 or 2 wherein said receiver decoding means includes plural shift registers, and means for checking the encoding effected at the transmitter by said convolutional encoding means responsive to the stored contents of predetermined stages of said shift registers and further comprising Exclusive-OR means connected to the outputs of said decoding means and said syndrome error detecting/correcting means.

7. A combination as in claim 1 or 2 wherein said receiver decoding means includes plural shift registers, and means for checking the encoding effected at the transmitter by said convolutional encoding means responsive to the stored contents of predetermined stages of said shift registers and wherein said memory of said syndrome error detecting and correcting includes address input ports, and an additional plural stage shift register having an input connected to the output of said decoding means and outputs connected to said address input ports of said syndrome detecting and correcting means.

8. A combination as in claim 1 or 2 wherein said receiver decoding means includes plural shift registers, and means for checking the encoding effected at the transmitter by said convolutional encoding means responsive to the stored contents of predetermined stages of said shift registers and further comprising source means for supplying di-bit digital informa-tion to said encoding means and to said signalling means.

9. In combination, in multiphase data communications apparatus for transmitting digital information, transmitter means for supplying at least one digital information data stream xi, convolutional encoding means having an output bit stream xO and performing an error correcting encoding on said data stream xi and on its own output xO given by xO = XiGi + XOGO

where Gi and GO are independent Boolean expressions specifying time values over plural digit intervals of xi and xO when those digits contribute to the formation of xO, and signalling means modulated by the output of said convolutional encoding means and by the digital information xi supplied by said source thereof for disseminating plural carriers of different phases;
and receiving means for receiving the digital information from the output of said signalling means, said receiver means in-cluding decoder means, including delay means, for providing a first output signal if the expression 0 = xiGi + x0 (1 + G0) is satisfied and a different signal if such expression is not satisfied, and syndrome error detecting and correcting means enabled responsive to the output of said decoding means for selectively inverting the output of said received information depending upon the error state reported thereto by said de-coding means.

10. A combination as in claim 1 or 9, further comprising at least one additional decoding means cascaded with said decoding means in said receiver means, and at least one addi-tional syndrome error detecting and correcting means connected to said additional decoding means, said additional syndrome error and detecting means including additional memory means for supplying error correcting stored output signals.

11. In combination, quadrature phase modulation data communications apparatus for transmitting digital information by amplitude and phase modulation on two phase quadrature carriers, said communications apparatus including a source of di-bit information signals, transmitter means receiving the output of said di-bit source means and including encoding means comprising convolutional encoding means for generating a digital encoding bit stream performing an encoding on the di-bit digital information supplied by said di-bit source means to be conveyed by said communications apparatus over a period of time exceeding one information digit period, and means for generating a two digit modulation bit stream from the di-bit output of said source thereof and said encoding bit stream, and signalling means modulating said two quadrature carriers in phase and in amplitude in accordance with said two digit modulation bit streams for disseminating said phase and amp-litude modulated two quadrature carriers; and receiving means for recovering the digital information and digital encoding stream from the output of said signalling means, said receiver means including decoding means including delay means for per-forming the inverse of the encoding effected by said encoding means at said transmitter means, and syndrome error detecting and correcting means enabled responsive to the output of said decoding means, said syndrome error detecting and correcting means including a memory supplying error correcting stored output signals.

12. A combination as in claim 11, wherein said two digit modulation bit stream generating means comprises a read only memory addressed by said di-bit information signals supplied by said information signal source and said encoding bit digital stream.