DE19613382A1 - Error correction method for non-redundant transmission signals - Google Patents

Abstract

The method involves determining a sequence of parity values (ct,v) of the actual phase displacement between time t of a current character and the time of the occurrence of an adjacent phase displacement. A sequence of correction values (pt,v) of the theoretical phase displacement is calculated using character values (dt,dt-v). Characters (st,v) are formed by comparison of parity values with correction values. The formed characters indicate if a parity value equals the corresponding correction value. The formed characters of the current character (dt) are added. When more than half of the formed character differs in the parity value and the corresponding correction value, the current character is erroneous. The erroneous character is corrected.

Description

Conventional methods for detection and correction of Errors in the transmission of data are usually based on a systematic redundancy. This will be either characters coded blockwise according to the parity principle or it becomes a Signal coding performed.

In block-by-block coding, the ones to be transmitted become Data is grouped into blocks and it will be at least one Parity bit added to each block. The parity bit returns whether the block weight is even or odd. It is the block weight is the number of non-zero bits a block.

The parity principle has several disadvantages. For one thing must the parity bit is encoded at the transmitter. In addition, the Transmission rate reduced.

In signal coding, the waveform that is a Sign is assigned in the transmission, from a Subset of possible waveforms depending preceding transmitted sequences of a signal so determines that the energetic distance to other possible Sequences is as large as possible.

In both cases, minor falsifications no plausible blocks or waveforms arise, so that a corruption in the receiver can be detected. also a correction can be made with great certainty by the received block or the received signal the next probable block or the next probable signal sequence with high security is assigned. The effectiveness of a correction is the same bigger, the bigger the smallest difference between the im Code space adjacent valid blocks or between the im Signal space adjacent permissible signal sequences.  

The parity principle and the signal coding have several Disadvantages in common. The two most significant disadvantages are:

• 1) The procedures for the blockwise summary of the Character or the exclusive sequence must be explicitly agreed in advance so that the from the transmitter coded blocks or signal sequences the receiver can be evaluated.
• 2) The channel capacity must be for systematic enforcement a recognizable distance between the error-free Blocks or the error-free signal sequences be what a reduction of the effective Transmission rate has the consequence.

In order to detect and eliminate errors of the received signal even without additional information, non-redundant transmission methods have been developed. In the transmitter, characters of the message to be transmitted are modulated onto a carrier signal by a defined phase shift of the carrier signal within the character period, depending on the character to be displayed. The data are random characters without systematic relationship to each other. In the receiver, the phase shift between the character boundaries is determined and deduced therefrom to the sent character. In a disturbed channel transmission errors may occur, but due to the periodicity of the vibrations can be detected and eliminated. For this purpose, various methods are known, which are presented below:
U.S. Patent 3,529,290 discloses non-redundant error detection and error correction. As characters, two successive bits from the message are combined into one pair. In a table, the zugeord neten phase shifts of the carrier phase in the drawing period to each of the four possible characters are set, such. As shown in the following table. An essential prerequisite is that always progresses starting from the phase at the end of the previous drawing section, the carrier phase continu- ously. Thus, no abrupt phase jumps may occur.

character phase shift 00 | -45 ° 01 + 45 ° 10 -135 ° 11 + 135 °.

To detect transmission errors, the phase position at Edge and the phase change within a character ab with the completion phase of the immediately preceding the or with the terminal phase of the immediately following Character section compared to conformity. On the one hand must the phase change within the character portion of the dif between the closure phase and the follow-up phase of the correspond to adjacent character sections and on the other hand must also the phase itself correspond to the boundary conditions chen. If that is not true, then by the recipient the most appropriate phase change to be adopted Correcting.

In the article "Differential PSK System with Nonredundant Error Correction "by S. Samejima et al., IEEE Journal on Selected Areas in Communications, Vol. SAC 1, no. 1, Jan. 1983, a method is described in which the bit pairs a be assigned defined phase shift. In one Phase detector becomes the difference of a first Character section with that of another sign section educated. Due to the periodicity of the modulated Carrier signal are independent of the distance between the two compared character sections so determined Phase differences between 0 and 2π, which is a modulo-2π Operation over the sum of all phase shifts between corresponds to the two compared character sections. to Error determination will be for the immediately adjacent ones Values of the received signal up to the order of k values disparate values determines the phase differences.  

To detect transmission errors are in the receiver the Phase differences between several not just immediately determined adjacent character sections. There are syndromes by comparing between the decoded characters sections are formed with a table containing the cumulative phase shifts from unadulterated Contain strings. These give information about possible Distortions and, where appropriate, how the sent characters can probably be corrected.

Conventionally, for every received character, that can take one of m values, a series of Determined phase differences with adjacent characters. From the measured phase differences are syndrome values Comparison with the sum of the phase differences modulo-2π the the character decoded between the character portions to be assigned are determined. From a prepared table can probably think about the syndrome values as pointers valid strings.

The disadvantage of the conventional, non-redundant methods lies in the fact that in advance one possibly very create and implement extensive table or Complex calculations are required. In addition, you can only single errors and only in exceptional cases double errors Getting corrected.

Object of the invention

The object of the invention was therefore to provide a method for correcting a non-redundant transmitted phase-coded signal, wherein characters of a string are transmitted such that a defined phase shift dφt at the signal time t with respect to the phase at an adjacent time t-1 or t + 1 corresponds to a defined character value, wherein the time of occurrence of a phase shift is the character limit, and the character values d _{t of} a character string are recovered by determining the phase shifts between the respective character boundaries. The phase coding takes place with a continuous phase.

The procedure should have a low implementation requirement have and not just single characters, but also Error sequences, so-called error bursts, can correct. In addition, an estimate of the probable Residual error density may be possible to the correction result to be able to judge.

invention

The object is achieved by the method according to claim 1.

To correct a current character d _t , first a sequence of parity values c _{t, v of} the actual phase shifts from the received signal between the signal time t of the current character and signal time points of corresponding adjacent character boundaries are determined. The parity values correspond to the 2n + 1 checksums of the transmitted character states modulo 2π. In addition, a sequence of correction values p _{t, v of} the theoretical phase shifts is calculated from the character value d _t and corresponding adjacent character values d _tv . The correction values p _{t, v} are the checksums which correspond to the received character states modulo 2 π. According to the invention, syndrome signs s _{t, v are formed} by comparing the corresponding parity values c _{t, v} with the correction values p _{t, v} , a syndrome character s _{t, v} indicating whether the respective parity value c _{t, v is} equal to or different from the corresponding correction value p _{t , v} is. The syndrome signs s _{t, v of} the current character d _t are then summed up. The essential step of the invention is that the current sign d _t is recognized as defective if more than half of the syndrome signs s _{t, v} indicates an inequality between the respective parity value c _{t, v} and the corre sponding correction value p _{t, v} . After each correction of a supposed transmission error, the syndrome signs are to be determined in the following error treatments with the previously corrected signs d _t .

By the inventive definition that the majority of Syndrome sign decides if a character is corrected or not, it is possible to provide signals with sufficient certainty to recognize and correct.

In addition, the evaluation of syndromes can be independent of an error correction for estimating the occurred Error rate can be used.

drawings

The invention is based on the following figures explained. Show it:

Fig. 1 shows the relationship between the corrected mark d _t, the parity values c _{t, v,} the correction values p _{t, v,} and the syndrome symbol s _{t, v;}

Fig. 2 is a string of 32 random and independent bits;

Fig. 3 shows two components I and Q of the modulated signal without the phase components of the constant carrier;

Fig. 4 shows the I and Q components of the signal at the receiver superimposed with a strong perturbation;

Figure 5 shows the parity values c _{t, v} for a defined character spacing.

Fig. 5 signals of the method; and

Fig. 6 shows the residual error rate BERR on the causative error rate p for various n.

embodiment

The method is not redundant in receivers transmitted received signals suitable. The calculation methods The correction should be beneficial in specifically for this adapted arithmetic units are executed to the necessary To achieve processing speed.

The received carrier signal represents the freely selectable characters a string through differential phase changes between each two immediately consecutive  Character state limits. The term "freely selectable" stands here for the fact that the characters are not statistical Must have relationship to each other, but random characters are, as they occur in usual messages. At a continuous phase modulation is the phase difference between two arbitrary character boundaries the checksum, modulo 2π, the sign of the characters lying between these character boundaries String.

For demodulation, as sketched in FIG. 1, the phase difference between the corresponding character boundaries is first formed for the time t of each character d _t , and the result is deduced from the character value d _t . Then the parity values c _{t, 2. , , v} determined by determining the phase differences between three and more consecutive character boundaries. The index L denotes the length of the string considered, the index v is the number of characters that lie between the considered character boundaries.

Through the relationship

b ' _t = [s _{t, 1} -b _t-1,1 -. , , - b _{t- (L-1), 1} ] mod 2

between the parity values c _{t, 1} and the previously determined characters d _{t-1. , , (L-1)} , a correction value p _{t, v} , ie, a theoretical current sign d ' _t , is retrieved.

These correction values are calculated according to the following equation certainly:

p ' _{t, v} = [s _{t, v} - p _{t-1, v} -. , , p _{t- (L-1), v} ] mod 2.

For each character d _{t of} the character string, so-called syndrome symbols s _{t, v are} determined, which allow a statement about the state of the characters controlled by them. The freedom from syndromes are zero if the corresponding sign d _t is free of errors. The syndrome signs are determined from the parity values c _{t, v} and the correction values p _{t, v} according to the following equation:

S _{t, v} = [p _{t, v} + b _t +. , , + b _{t- (v-1)} ] mod 2.

A current sign d _t is error-free if the majority of associated syndrome signs indicate no error.

The method according to the invention is presented by way of example on an MSK signal with 32 random independent bits in the following FIGS. 2 to 6. The values of the signal are represented by whole π / 2 steps for the assigned, character-wise impressed phase difference.

Fig. 2 shows the 32 random and independent bits of a string of the MSK signal. The signal is divided into two quadrature components I and Q, which are shifted by 90 ° to each other.

The phase change of the MSK carrier signal to the nominal phase of the carrier is represented by its quadrature components I and Q with 8 steps per character portion in the following FIG . It can be seen that the phase changes continuously. This means that no abrupt phase jumps occur. This is an essential prerequisite of the proceedings, since only then can the checksum, modulo 2π, be determined.

The same quadrature components I and Q of the signal sampled at L = 8 steps per character segment are shown in Figure 4, after being superimposed with band-limited Gaussian noise, as is usually present at the input of a receiver. The signal is so disturbed that it is no longer recognizable.

From the received signal, the following rule gradually calculates the current character values d _t from the phase differences between every two consecutive samples between t and t-1, the amplitudes being corrected by the following equation:

From this above signal Δ, the most probable phase position τ of the character boundary is determined for the sampling phase, in order then to determine the received characters by the following "integrated-dump" rule with the data signal DC _t over 1 sampling steps from δ = 0 to L-1 make:

The methods for determining the phase position are sufficient known, so that will not be discussed further.

Furthermore, the binary parity values c _{t, v are derived} for different character intervals 2 _v for the respective character d _t . This is done separately from the individual signal components I and Q in this example. The results are summarized below. The factors τ _i and τ _q are the sampling factors which control the evaluation of the sign, the sign, the phase difference alternately between I and Q.

Parity values for the I component:

Parity values for the Q component:

Summary of parity values for the I and Q comm  component:

C _{t, v} = (CI _{t, v} + CQ _{t, v} ) mod 2.

FIG. 4 shows the parity values c _{t, v} determined with the above provisions for a character spacing λ = 3 for 2v = 6.

The following rule forms the checksums over the received strings d _t :

From the next equation, the binary syndrome signs s _{t, v are formed} by comparing the parity values c _{t, v} with the corresponding correction values p _{t, v} :

S _{t, v} = | C _{t, v} - P _{t, v} |.

The procedure concludes with the error correction, which after the following rule continuously with time character by character progresses. The index n stands for the number of received characters that are coherent in each rating be included retroactively. The variable e denotes the corrected characters:

For the computational procedure, post and preambles, - these are the unavailable characters of a received signal at the beginning or end of a correction phase - if required as zeros.

FIG. 6 shows the effects of the method according to the invention step by step. The following signals are shown from top to bottom:

• a) The signal D _t in the first line is the transmitted, random and independent bit string;
• b) This is followed by d _t , the string recovered in the receiver from the disturbed signal by character-wise determination of the phase difference between two adjacent character boundaries, with an error component BER of 18.8%;
• c) The signal e _t is the corrected after the application of the method string with only 6.3% character errors;
• d) The following five signals are five of the syndrome signs s _{t, 1. , , 5} , which have been calculated according to the invention from the left of it, uncorrected characters.

Finding the character boundaries is not part of this Invention and is well known. It's about it here also not described further.

FIG. 6 shows the residual error rate BER over the causative error rate p for different n. It can be seen that the residual error rate BER decreases as the number of received characters n that are retroactively included in each evaluation increases.

On the relatively large correction probability at low computational complexity, the described method has the Advantage that limits the effectiveness of the process well can be predetermined. For this purpose, as follows three Assumptions assumed:

• 1. There is the possibility for each transmitted character of a set of 2n + 1 independent parity values c _{t, v} and control values p _{t, v} , where v = 2. , , 2n + 1, to be determined.
• 2. The errors in the received characters and the Control marks occur randomly and independently from each other.
• 3. The majority of the 2n + 1 syndrome signs s _{t, v} , with v = 1. , , 2n + 1, decide whether a received character is corrected or not.

For the residual error rate BER of the corrected string in Dependency of random errors probably The speed p of the received signal applies when 2n + 1 is included Parity and control values:

BERr (p, n) = p- [p * e (p, n)] + [1-p] * [1-e (p, n)];

BER _r (p, n) = 1 - e (p, n).

Here, e (p, n) is the probability that a decision a correct one due to the majority of the syndrome values Decision is, so a falsified sign to right Character is converted. Thus, 1-e (p, n) is the equivalent probability that a correct sign will not is corrupted by the correction process.

The probability of a decision being based on the Majority of syndrome values is a correct decision if 2n + 1 syndrome values can be determined beforehand and the Error probability p is, is calculated as follows:

The correction is thus not accidental, but can be predict.

Claims (6)

A method for correcting errors in non-redundantly transmitted received signals, wherein characters of a character string are transmitted such that a defined phase shift dφ _t at the signal time t with respect to the phase at an adjacent time t-1 or t + 1 corresponds to a defined character value wherein the time of occurrence of a phase shift is the character limit, and the character values d _{t of} a character string are recovered by determining the phase shifts between the respective character boundaries, and the correction of a current character d _{t is performed} with the steps of:

• 1) determining a sequence of parity values c _{t, v of} the actual phase shifts from the received signal between the signal instant t of the current character and signal timings of corresponding adjacent character boundaries;
• 2) calculating a sequence of correction values p _{t, v of} the theoretical phase shifts from the character value d _t and corresponding adjacent character values d _tv ;

marked by

• 3) formation of syndrome signs s _{t, v} by comparing the corresponding parity values with the correction values, a syndrome character s _{t, v} indicating whether the respective parity value c _{t, v is} equal to the corresponding correction value p _{t, v} ,
• 4) summing the syndrome characters s _{t, v of} the current character d _t ;
• 5) recognizing that the current sign d _{t is} erroneous if more than half of the syndrome signs s _{t, v} indicate an inequality between the respective parity value c _{t, v} and the corresponding correction value p _{t, v} ;
• 6) Correction of a faulty character d _t .

2. The method according to claim 1, characterized in that the Input signal in two mutually phase-shifted by 90 ° Signals I and Q is divided, the signals I and Q alternately sampled and the correction for each of both signals I and Q is carried out separately. 3. The method according to claim 1 or 2, characterized that the characters represent binary values and an error correct character by giving it exactly that is assigned to other binary characters. 4. The method according to claim 3, characterized in that the Phase difference for the one value of the binary sign -90 ° and for the other value of the binary sign 90 ° is. 5. The method according to any one of the preceding claims, characterized characterized in that after a correction of a Significantly, the correction values and the syndrome signs for the subsequent characters taking into account the corr gated character.