JPH03113937A - Differential decoding device - Google Patents

Abstract

PURPOSE:To reproduce an original information code series with fidelity by making differential coding possible for a stagger QAM transmission system. CONSTITUTION:An m-bit original information series is inputted to an input terminal 301 for T/2 sec each. An output of a T/2sec delay circuit 305 is inputted as part of an address for a ROM 302 and inputted to a latch circuit 307. The address of the ROM 302 is 3 bits and its output is expressed in 1 bit. In- phase data series and orthogonal data series for each T sec are inputted respectively to input terminals 401, 402. The address of a ROM 409 is decided by a signal in total 3m-bit obtained at each point of reference numbers 406, 407, 408 and an m-bit data is outputted to an output terminal 410. Thus, the differential coding to the stagger QAM transmission system having been impossible in a conventional device is realized.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a differential decoding device that makes it possible to apply a differential encoding method to a staggered QAM transmission system.

Generally, the differential encoding method considers the transmission path code to be a type of state, determines the state at the next time based on the current state and the current original information code, and uses the information sequence obtained in this way as the transmission code sequence. This is a coding method that is widely used for the purpose of faithfully reproducing the original information code sequence by observing only state transitions on the receiving side even if the state is uncertain in the transmission system.

Typical uncertainties that occur in the transmission system include polarity uncertainty for one-dimensional signals, element uncertainty for two-dimensional signals, etc., and differential codes that are effective against these uncertainties are The conversion method can be found in an intuitively obvious way. However, in the so-called staggered quadrature amplitude modulation (hereinafter abbreviated as staggered QAM) system, it is difficult to conventionally perform differential encoding because it produces an uncertainty that is a combination of temporal uncertainty and phase uncertainty. was being watched.

Staggered QAM signals are more resistant to phase jitter than before.
It was pointed out that it has many advantages such as low peak power. Furthermore, it is also known that by orthogonally multiplexing a plurality of staggered QAM signals using a plurality of carriers with different frequencies, a so-called orthogonal QAM transmission system that is resistant to transmission distortion and impulse noise and has high frequency usage efficiency can be obtained. Despite these advantages, conventional staggered QAM
There were only a few examples of transmission devices using . One of the reasons for this is that differential encoding in a staggered QAM transmission system has been considered difficult as described above.

The present invention enables staggered QA, which was considered impossible in the past.
This invention provides a completely new differential encoding method that enables differential encoding for M transmission systems, and its principle is based on the mathematical method described below.

Now, let I be the set of symbols that the original code can take, and let S be the set of N states. That is, I=(i I i=1
．． 2. ..., N) 3 = (su = 1.2..., N) Here, if we assign the symbol C1, consisting of the transition from state s9 to state S, then the following An 8th order square matrix C is defined.

Using matrix C, if the current state is S and the original information symbol is C1, then the next time state S can be determined.
can. Therefore, matrix C can be regarded as a coding matrix that defines a transmission code, and in this sense, it will be simply referred to as code C hereinafter.

On the other hand, if uncertainty occurs in the transmission system, for example, the state s1.
s2.・, sN are each sil'si2' ””
It will be converted to siN. However, here any li,
is an integer satisfying 1≦tkSN. Therefore, the uncertainty in the transmission system is expressed by the well-known permutation operator σ. Assume that there are L different types of uncertainties that occur in the transmission system, and that the permutation operators corresponding to each type are represented by 011'21...IOL. Furthermore, when an uncertainty of σ□ occurs at a certain time, the uncertainty that occurs at the next time is 0. is uniquely determined according to 6
．． shall be. Here, the symbol ~ represents an operation called a subsequent operation. With these preparations, the following matrix operator T, (k==1.2...,L) is defined.

That is, when B=T, (A) for N-dimensional square matrices A and B, element a of row i and column j of matrix A is σk(
i) Row CIk(j) is equal to column element. However, here, the notation σk(i) represents an integer resulting from replacing an integer i with a permutation operator σ.

Now, in order for the code C to be a differential code, it is necessary and sufficient for the code C to remain unchanged regardless of any uncertainties occurring in the transmission system. Expressing this using the matrix operator defined earlier, for any T, Tk(C
):C, it can be said that C is a differential code. Under this formulation, we then obtain the differential encoding theorem. In the theorem, G represents a set of permutation operators.

(Theorem) For a differential sign to exist, G forms an irreducible, indivisible group, and any σ2. σ, , (σk for Go
It is necessary and sufficient that Oe)=decIk holds true. Also, at this time,
The number of states N is an integer multiple of an uncertain number, and can be expressed as a product by appropriately rearranging the states (where 11□=K), and a differential code C is constructed according to the following equation.

However, N symbols may be independently assigned to the first row vector of each matrix.

Using the above theorem, a differential encoding scheme for the staggered QAM transmission system can be found.

Hereinafter, the principle of the present invention will be explained using the drawings.

FIG. 1 is a block diagram showing a general configuration of a staggered QAM transmission system, in which (a) shows the configuration of a transmitting device and (b) shows the configuration of a receiving device. Reference numbers 102 and 111 are delay circuits that provide a delay of half a clock cycle;
01.103.109.110 is a shaping filter that forms a baseband waveform, and reference number 104.105.
107° 108 are multipliers in charge of modulation or demodulation, reference number 106 is an adder, reference numbers 113 and 114
is a sampler. As can be seen from FIG. 1, the first data series (ak) is formed into a baseband waveform by the forming filter 101, and sent to the transmission path as an in-phase signal via the multiplier 104. On the other hand, the second data series (b,)
is delayed by half a clock cycle in a delay circuit 102, and then sent out to a transmission line as an orthogonal signal via a shaping filter 103 and a multiplier 105. Therefore, the signal 5(t) sent to the transmission path is transmitted to the shaping filter 101.
, 103 is expressed as g(t). However, ωC represents the carrier angular frequency.

On the receiving side, the transmission line signal 5(t) is multiplied by a multiplier 107.10.
Supply to 8. Assuming that each of the shaping filters 109 and 110 on the receiving side passes only the stationary component of the multiplier output corresponding to the month, the outputs of the shaping filters 09 and 110 are expressed as mo kg (t-kT) and Σbkg (t- kT −/2). Therefore, if the output of the shaping filter 09 is delayed for 12 seconds by the delay circuit 111 and sampled by the sampler 112 at time kT+ 72, the first data sequence (a,) on the transmitting side is restored as an in-phase data sequence. be done. On the other hand, for the second data series on the transmitting side, the output of the shaping filter 10 is processed by the sampler 113 at time kT+ /2.
By sampling at , it is restored as an orthogonal data series. However, here, g(t) is a waveform response that satisfies the so-called Nyquist condition, such that the sample value g(kT) every T seconds is 1 when = 0 and 0 otherwise. . In such a staggered QAM transmission system,
The demodulated carrier phase on the receiving side is n compared to that on the transmitting side.
Assuming that the in-phase carrier is advanced by 12, the in-phase carrier supplied to multiplier 107 becomes -5 inωt, and multiplier 1
The orthogonal carrier supplied to 08 becomes COSωt. Therefore, the outputs of the shaping filters 109 and 110 are -Eb, g(t-kT -/2) and the valley ahg(t kT), respectively, so the input signals of the samplers 113 and 114 are respectively -Σbkg(t-kT - T) and Σahg(t kT). Here, the sampling time is set to the above kT+T
If we shift 12 from /2 to kT+T, the in-phase data and quadrature data will be -bl, -b2 .・・・
・And a2+ a3 block.

It can be seen that not only topological distortion but also temporal distortion occurs between in-phase and orthogonal data. In a staggered QAM transmission system, there are four types of phase and time uncertainties, and when expressed using a carrier phase shift of 0 and a sampling timing shift of 1 on the receiving side, these are (θ, )= (0,0), (“/2゜T/
2), (-n/2./2), (n, 0) FIG. 2 shows the in-phase data series and the orthogonal data series obtained when these uncertainties occur in each case. That is, reference number 2 in FIG. 2(a)
01.202 shows the in-phase data series and orthogonal data series obtained when (θ,'c)=(0,0), respectively.
Reference numbers 203 and 204 in Figure 2(b) and Figure 2(b)
C) reference number 205.206 and FIG. 2(d) (
7) 4 lights No. 207, 208! ;t,, respectively, (e,
t) = (”/2. T/2).

and (e, I)=(-72,/2), and (θ, r
, :): (n, 0) The in-phase data series and orthogonal data series at (7) are shown, respectively. As is clear from FIG. 2, in the staggered QAM transmission system, a set of in-phase data xk and quadrature data Yk& (xk, Y
k) and convert it into a state series (X1+
Yl)+(X2+Y2''..., it is impossible to define a steady subsequent permutation operator independent of sampling time that makes differential encoding possible, making differential encoding impossible.

In the differential encoding method according to the present invention, as described above, in-phase and quadrature data sequences are converted into state sequences every T seconds (Xp Y
x) t (X2+ Y2), instead of considering it as TI2 seconds state series (XIs Yl), (Yls x2)) (
It is assumed that X2+Y2)p (Y21 x3)t "'. This defines a stationary subsequent permutation operator, and according to the above theorem, differential encoding becomes possible.

As an example, S□”(+, 10)+62==(+, −
), $3==(-,+).

2×2 staggered QA with 4 states of s=(+,-)
Consider the M transmission system. The permutation operators 01 to σ4 corresponding to the aforementioned uncertain elements are as follows, and the subsequent permutation operators 151 to 64 corresponding to each are 6 to E
・+52=03・Cl5=02・+54=04. (However, E is an identity permutation operator.) At this time, the set Go of 01 to o4 clearly forms an irreducible and indivisible group, and since each of 01 to σ4 is its own inverse element, , from the theorem, we obtain the differential sign C. Of these, symbols 3 and 4 do not need to be allocated because a state transition from sl to 83184, for example, cannot occur, and the differential code C is obtained as a result. However, the locations marked with * indicate that code assignment is not necessary. Consider differentially encoding the original information series 122111212, . . . according to the differential code C obtained in this way. Assuming that the initial state on the transmitting side is 51, it can be seen that the next state when symbol 1 occurs in state S1 is as follows from C. Next, since symbol 2 occurs in the current state S0, S2
The next state is. Similarly, the transmission state series is 5ISISzS4S4S4S4S3S2S4°°°°.

get. Therefore, the transmission code sequence is as follows. On the other hand, in the transmission system (θy T,)=
If the uncertainty of ("2F '2)" is applied, the received code sequence becomes.

If this is expressed as a state series, 52S3SIS2S3S2S3S1S1S2...
Therefore, when decoding according to the differential code C, 1221
11212... The original information sequence is obtained.

Generally, a differential code C can be determined for the NXN staggered QAM transmission system in the same way as described above. At this time, the in-phase data series X1. X2. ...and orthogonal data series Y1゜Y2. −..., state transition series (xp Yl
)+ (Yp x2)+(X2>Y2)> (Y2+
X3) It is a condition in which it is basically free to regard it as t...

Figure 3 is based on the above-mentioned idea, especially the 2×2 staggered Q
This is a block diagram showing the configuration of a differential encoder for an AM transmission system, and FIG. 4 is a block diagram showing the configuration of a corresponding decoder, that is, one embodiment of the present invention. In FIG. 3, an m-bit original information sequence is input to an input terminal 301 every TI 2 seconds. Reference number 302 is 3
This is a read-on memory (hereinafter referred to as ROM) that has an address determined by m bits and outputs an m-bit symbol, and its output is fed back as part of the address of ROM 302, while a latch circuit 306 and a 12 second delay are used. It is input to circuit 305. The output of the T7272 second delay 305 is input as part of the address of the ROM 302 and is also input to the latch circuit 307. In this way the ROM
For 302, the address is determined using m bits of original information, m bits of the symbol obtained at the point with reference number 303, and m bits of the symbol obtained at the point with reference number 304, a total of 3 m bits. Applying the above example of the 2×2 staggered QAM transmission system, the address of the ROM 302 is determined by 3 bits, and the output is expressed by 1 bit. The relationship between the address of the ROM 302 and its stored data in this case is as follows.

Address storage data ooooo.

ooi,.

101 111 001 011 100 110 However, in the above table, the MSB of the address corresponds to the original information, and the above "1" and 0.2" are considered to be 1. Also,
The MSB-1 of the address is the code obtained at point 303, where the above "10" is replaced by 1. "'-" is regarded as 0. Therefore, for example, outputting 1 at address 010 corresponds to transitioning to state s3 if the information is "1" in state s2 in the above example. The latch circuits 306 and 307 convert the thus obtained transmission code sequence every T12 seconds into an in-phase data sequence every T seconds and an orthogonal data sequence every T seconds delayed by TI2 seconds from the output terminal 3.
Output on 08,309.

The decoder of the invention shown in FIG. 4 provides an inverse transform to the encoder of FIG.
2 receives an in-phase data sequence and an orthogonal data sequence every T seconds. The multiplexer 403 multiplexes these two systems of data as a data sequence every 12 seconds, and its output is sent to 12 second delay circuits 404 and 405.
subject to delays.

The address of the ROM 409 is determined by a total of 3m bits of signals obtained at each point with reference numbers 406, 407, and 408, and outputs m-bit data to the output terminal 410.

As described above, by using the present invention, differential encoding for a staggered QAM transmission system, which was considered impossible in the past, becomes possible, so it is possible to develop various communication devices that take advantage of the advantages of the staggered QAM system. Therefore, the practical significance is extremely large.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing the general configuration of a staggered QAM transmission system, Fig. 2 is a timing chart for explaining uncertain elements in the staggered QAM transmission system, and Fig. 3 is a differential code according to the concept of the present invention. In particular, the conversion method is 2×2 staggered Q.
FIG. 4 is a block diagram showing an example of the configuration of an encoder when applied to an AM transmission system, and FIG. 4 is a block diagram showing an example of the configuration of a decoder corresponding to the encoder of FIG. be. In the figure, 101.103.109.110... Shaping filter, 102, 111... TI 2 second delay circuit,
104.105.107.108... Multiplier, 112
．． 113... Sampler, 302... ROM, 30
5...12 second delay circuit, 306.307...Latch circuit, 403...Multiplayer■ Figure 10 Figure 2 Figure Figure Figure

Claims (1)

[Claims] A first m-bit codeword sequence and a second m-bit codeword sequence occurring every T seconds.
m that occurs every T/2 seconds.
In a differential decoder that converts the original information codeword sequence of bits, the first and second m-bit codeword sequences are multiplexed according to a predetermined delay relationship of T/2 seconds, and
Let the m-bit codeword sequence occur every second, and the m-bit codeword sequence that occurs every T/2 seconds is the first input sequence, and m obtained by delaying the first input sequence by T/2 seconds. The bit codeword sequence is a second input sequence, and the second input sequence is T/2.
When the m-bit codeword sequence obtained by delaying by seconds is used as the third input sequence, the first, second, and third input sequences are T
The m-bit code word is converted to T according to a predetermined relationship for the 3-m-bit input bit pattern determined every /2 seconds.
A differential decoding device comprising a state circuit that outputs an output every /2 seconds.