JPH0724410B2 - Differential decoding device - Google Patents

Description

The present invention relates to a differential decoding device that enables application of a differential encoding method to a staggered QAM transmission system.

In general, the differential encoding system regards the transmission path code as a kind of state, determines the state at the next time by the current state and the current original information code, and sets the information sequence thus obtained as the transmission code sequence. It is a coding method and is widely used for the purpose of faithfully reproducing the original information code sequence by observing only the state transition on the receiving side even if the state is uncertain in the transmission system.

Typical uncertainties that occur in a transmission system are, for example, polar uncertainties for one-dimensional signals, quadrature uncertainties for two-dimensional signals, and differential codes effective for these uncertainties. The chemical method can be found in an intuitively clear way. However, in so-called staggered quadrature amplitude modulation (hereinafter abbreviated as staggered QAM) systems, since uncertainties that combine temporal uncertainties and phase uncertainties occur, differential encoding is conventionally considered difficult. It had been.

It has been pointed out that staggered QAM signals have many advantages such as strong resistance to phase jitter and small peak power. Furthermore, when multiple staggered QAM signals are orthogonally multiplexed using multiple carriers with different frequencies, they are strong against transmission distortion and impulse noise and have high frequency use efficiency.
It is also known that a so-called orthogonal QAM transmission system can be obtained. Despite these advantages, there have been few cases in which a transmission device using staggered QAM has been realized. One of the reasons is that the differential encoding in the staggered QAM transmission system is regarded as difficult as described above.

The present invention is a stagger QAM that has been considered almost impossible in the past.
The present invention provides a completely new differential decoding device that enables the application of differential encoding to a transmission system, the principle of which is based on the mathematical method described below.

Now, let I be a set of symbols that the original code can take and S be a set of N states. That is, I = {i | i = 1,2, ..., N} S = {si | i = 1,2, ..., N} Here, a certain symbol Cij for the transition from the state si to the state sj , The N-th order square matrix C is defined as follows.

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

On the other hand, if indeterminacy occurs in the transmission system, for example, the states s ₁ , s ₂ ,
…, S _N are converted to si ₁ , si ₂ ,…, si _N respectively. However, here, any ik is an integer satisfying 1 ≦ ik ≦ N. Therefore,
The uncertainty of the transmission system is the well-known permutation operator σ It is represented by. Now, let us say that there are L different types of uncertainties that occur in the transmission system, and the substitution operators corresponding to each are represented by σ ₁ , σ ₂ , ..., σ _L. Furthermore,
When an uncertainty of σk occurs at a certain time, the uncertainty that occurs at the next time is uniquely determined according to σk, Shall be Here, the symbol ~ represents an operation called a subsequent operation. With these preparations, the following matrix operator Tk (k = 1, 2, ..., L) is defined. That is, N-th square matrix
When B = Tk (A) for A and B, the i-th row and j-th column element aij of the matrix A is σk of the matrix B
(I) line Equal to the column element. Here, the notation σk (i) represents an integer resulting from replacing the integer i with the replacement operator σk.

Now, in order for the code C to be a differential code, it is necessary and sufficient that C be kept unchanged regardless of any uncertainties that occur in the transmission system. Expressing this using the matrix operator defined above, for any Tk, Tk (C) =
When it becomes C, it can be said that C is a differential code. Under such a formulation, the differential encoding theorem is then obtained. Theorem G _σ
Is a set of permutation operators.

(Theorem) For the existence of a differential code, G _σ is irreducible and forms an indivisible group, and for any _σ k, _σ l, ∈ G _σ Is necessary and sufficient. Also at this time,
The number of states N is an integer multiple of the indeterminate number L. Can be expressed as a product (where i ₁₁ = K), and the differential code C is constructed according to the following equation.

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

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 described with reference to 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 transmission device and (b) shows the configuration of a reception device. Reference numerals 102 and 111 are delay circuits that give a delay of half a clock cycle.
Reference numeral 104,105,107,108 is a multiplier for controlling modulation or demodulation, reference numeral 106 is an adder, and reference numeral 11 is a shaping filter for forming a baseband waveform.
3,114 is a sampler. As can be seen from FIG. 1, the first data sequence {ak} is formed into a baseband waveform by the forming filter 101, and is sent to the transmission line as an in-phase signal via the multiplier 104. On the other hand, the second data series {bk}
After being delayed by a half clock cycle in the delay circuit 102, is transmitted to the transmission line as a quadrature signal via the shaping filter 103 and the multiplier 105. Therefore, the signal s (t) sent to the transmission path is represented by the impulse response of the shaping filters 101 and 103 as g (t). Is expressed as However, ωc represents the carrier angular frequency.

On the receiving side, the transmission path signal s (t) is supplied to the multipliers 107 and 108. If the shaping filters 109 and 110 on the receiving side each pass only the stationary component of the corresponding multiplier output, the outputs of the shaping filters 109 and 110 are and Becomes Therefore, the output of the shaping filter 109 is delayed by the delay circuit 111.
Delayed by T / 2 seconds at sampler 112 at time kT +
If sampling is performed at T / 2, the first data sequence {ak} on the transmitting side is restored as an in-phase data sequence. On the other hand, the second data sequence on the transmission side is restored as an orthogonal data sequence by sampling the output of the shaping filter 110 through the sampler 113 at time kT + T / 2. However, here, g
It is assumed that (t) is a waveform response that satisfies the so-called Nyquist condition that the sample value g (kT) every T seconds is 1 when k = 0 and all the others are 0. Stagger like this
In the QAM transmission system, assuming that the demodulation carrier phase on the receiving side leads by Π / 2 on the transmitting side,
The in-phase carrier supplied to the multiplier 107 is −sinωct, and the quadrature carrier supplied to the multiplier 108 is cosωct. Therefore, the outputs of shaping filters 109 and 110 are, respectively, and Therefore, the input signals of samplers 113 and 114 are and Becomes Here, the sampling time is the above kT + T / 2
Then, by shifting from T / 2 to kT + T, the in-phase data and the quadrature data become −b ₁ , −b ₂ ,, ... and a ₂ , a ₃ , ..., respectively, and the phase twist between the in-phase and quadrature data. At the same time, it can be seen that a temporal twist occurs. In the staggered QAM transmission system, there are four kinds of uncertainties as such phase and time uncertainties. When expressed using the carrier phase shift θ and the sampling timing shift τ on the receiving side, these are (θ, τ ) = (0,0), (Π / 2, T / 2), (−Π / 2, T /
2), expressed as (Π, 0). FIG. 2 shows the in-phase data series and the quadrature data series obtained when these uncertainties occur in each case. That is, reference numerals 201 and 202 in FIG. 2 (a) respectively indicate an in-phase data series and a quadrature data series obtained when (θ, τ) = (0, 0), and reference numerals 203 and 204 in FIG. 2 (b). And reference numerals 205 and 206 in FIG. 2 (c) and reference numerals 207 and 208 in FIG. 2 (d) are (θ, τ) = (Π / 2, T / 2), and (θ, τ) =, respectively. (−Π / 2, T / 2), and (θ, τ) ＝
The in-phase data series and the quadrature data series at (Π, 0) are shown. As is clear from FIG. 2, in the staggered QAM transmission system, the in-phase data Xk at the k-th time is the same as in the phase modulation system.
If we consider a pair (Xk, Yk) of the and orthogonal data Yk as a state sequence (X ₁ , Y ₁ ), (X ₂ , Y ₂ ), ... It is not possible to define a stationary succeeding permutation operator that does not depend on the sampling time that is enabled, and differential encoding becomes impossible.

In the differential encoding system according to the present invention, as described above, the in-phase and quadrature data sequences are converted into the state sequence (X ₁ ,
Instead of considering them as Y ₁ ), (X ₂ , X ₂ ), state sequences (X ₁ , Y ₁ ), (Y ₁ , X ₂ ), (X ₂ , Y ₂ ), (Y ₂ , X ₃ ), ... As a result, a stationary subsequent replacement operator is defined, and differential encoding becomes possible according to the theorem.

As an example, s ₁ = (+, +), s ₂ = (+, −), s ₃ = (−,
Consider a 2 × 2 staggered QAM transmission system in which there are four states: +), s ₄ = (−, −). The substitution operators σ _{1 to} σ ₄ corresponding to the uncertainties described above are And each subsequent replacement operator Is It turns out that (However, E is an identity substitution operator.) At this time, the set Gσ of σ _{1 to} σ ₄ is clearly irreducible,
Since it forms an indivisible group and each of σ _{1 to} σ ₄ is an inverse element of itself, from the theorem, the differential code C To get Of these, for example, since the state transition from s ₁ to s ₃ and s ₄ cannot occur, symbols 3 and 4 are symbols that do not need to be allocated, and as a result, the differential code C is used. To get However, the part marked with ^* means that the code allocation is unnecessary. Consider differential encoding of the original information sequence 122111212 ... In accordance with the differential code C thus obtained. The initial state on the sending side
if s _1, the next state when the symbol 1 has occurred in a state s ₁ is found to be s ₁ than C. Next, since the symbol 2 has occurred in the current state s _{1, the} s _2nd state is as follows. Similarly, s ₁ s ₁ s ₂ s ₄ s ₄ s ₄ s ₄ s ₃ s ₂ s ₄ ... Are obtained as a transmission state sequence. Therefore, the transmission code sequence is Becomes On the other hand, in the transmission system, (θ, τ) = (Π /
If the uncertainty of (2, τ / 2) acts, the received code sequence becomes Becomes If this is expressed as a state sequence, it becomes s ₂ s ₃ s ₁ s ₂ s ₃ s ₂ s ₃ s ₁ s ₁ s ₂ ..., so when decoding according to the differential code C, 122111212 ... is obtained and the original information sequence is obtained. .

Generally, for N × N staggered QAM transmission system,
The differential code C can be defined. At this time, the in-phase data series X ₁ , X ₂ , ... and the quadrature data series Y ₁ , Y ₂ , ... are put together and the state transition series (X ₁ , Y ₁ ), (Y ₁ , X ₂ ), (X ₂ , Y ₂ ), (Y ₂ ,
It is basically a condition that can be regarded as X ₃ ), ...

Fig. 3 is based on the concept described above, especially 2m x 2m stagger QA
FIG. 4 is a block diagram showing a configuration of a differential encoder for the M transmission system, and FIG. 4 is a block diagram showing a configuration of a decoder corresponding thereto, that is, an embodiment of the present invention.
In FIG. 3, an m-bit original information sequence is input to the input terminal 301 every T / 2 seconds. Reference numeral 302 is a read-on memory (hereinafter abbreviated as ROM) that outputs an m-bit symbol whose address is determined by 3 m bits and whose output is R
While being fed back as a part of the address of the OM 302, it is input to the latch circuit 306 and the T / 2 second delay circuit 305. The output of the T / 2 second delay circuit 305 is input as a part of the address of the ROM 302 and the latch circuit 307. Thus, the address of the ROM 302 is determined by a total of 3 m bits of m bits of original information, m bits of symbols obtained at the point of reference number 303, and m bits of symbols obtained at the point of reference number 304. . Applying the example of the 2 × 2 staggered QAM transmission system, the address of the ROM 302 is determined by 3 bits,
The output will be represented by 1 bit. ROM 302 in this case
The relationship between the address and the stored data is as follows.

Address storage data 000 0 001 0 0 010 1 011 1 100 1 101 1 110 0 0 111 0 However, in the above table, the MSB of the address corresponds to the original information,
The above "1" is regarded as 0 and "2" is regarded as 1. Also, the MSB-2 of the address is the code obtained at the point 303, the MS of the address
B-1 is the code obtained at the point 304, and the "+" is regarded as 1 and the "-" is regarded as 0. So, for example,
Outputting at address 010 means that status s ₂
If the information is “1” in, it corresponds to the transition to the state s ₃ . The latch circuits 306 and 307 are the T thus obtained.
The transmission code sequence of every / 2 seconds is output to the output terminals 308 and 309 as an in-phase data sequence of every T seconds and a quadrature data sequence of every T seconds delayed by T / 2 seconds.

The decoder of the present invention shown in FIG. 4 provides an inverse transform to the encoder of FIG. 3, and in-phase data series and quadrature data series of T seconds are input to input terminals 401 and 402, respectively. . The multiplexer 403 multiplexes these two systems of data as a data sequence of every T / 2 seconds, and its output is delayed by the T / 2 second delay circuits 404 and 405. The address of the ROM 409 is determined by the signal of 3 m bits in total obtained at each point of reference numbers 406, 407, 408, and outputs m-bit data to the output terminal 401.

As described above, according to the present invention, it is possible to perform differential encoding on a staggered QAM transmission system, which has been regarded as impossible in the past. Therefore, it is possible to develop various communication devices utilizing the advantages of the staggered QAM system. Next, the practical significance is extremely great.

[Brief description of drawings]

FIG. 1 is a block diagram showing a general configuration of a staggered QAM transmission system, FIG. 2 is a timing chart for explaining uncertainties in the staggered QAM transmission system, and FIG. 3 is a differential code according to the concept of the present invention. FIG. 4 is a block diagram showing a configuration example of an encoder when the coding method is applied to a 2 m × 2 m staggered QAM transmission system, and FIG. 4 is a configuration example of a decoder corresponding to the encoder of FIG. It is a block diagram which shows one Example. In the figure, 101,103,109,110 ... Molding filter, 102,1
11 …… T / 2 second delay circuit, 104,105,107,108 …… Multiplier, 11
2,113 ... Sampler, 302 ... ROM, 305 ... T / 2 second delay circuit, 306,307 ... Latch circuit, 403 ... Multiplexer, 404,405 ... T / 2 second delay circuit, 409 ... ROM.

Claims (1)

[Claims] 1. A first m-bit codeword sequence and a second m-bit codeword sequence that occur every T seconds are input to obtain an m-bit original information codeword sequence that occurs every T / 2 seconds. In the differential decoder for conversion, the first and second m-bit codeword sequences are multiplexed according to a predetermined delay relationship of T / 2 seconds to form an m-bit codeword sequence occurring every T / 2 seconds. , T / 2
The m-bit codeword sequence occurring every second is the first input sequence,
The m-bit codeword sequence obtained by delaying the first input sequence by T / 2 seconds is the second input sequence, and the second input sequence is T / 2.
When the m-bit codeword sequence obtained by delaying by 2 seconds is used as the third input sequence, T / 2 is input in the first, second and third input sequences.
A differential decoding device comprising a state circuit that outputs an m-bit codeword every T / 2 seconds in accordance with a predetermined relationship with respect to an input bit pattern of 3 m bits determined every second.