JP2003163612A - Digital signal encoding method and decoding method - Google Patents

Abstract

(57) Abstract: In a multiple access communication system, error correction of a transmitted digital signal is performed even if there is channel noise. SOLUTION: An encoder 2- (i, j) performs Kronecker multiplication of a predetermined spread spectrum sequence by a Hadamard matrix of a predetermined order q to generate a resultant spread spectrum sequence, and receives an input digital signal. Is multiplied by the generated spread spectrum sequence, and the result of the multiplication is output as an encoded signal. The decoder 25 converts the received signal including the plurality of encoded signals into a matrix format, multiplies the transformed matrix by a Hadamard matrix, generates a matrix, and converts each component of the matrix. An error correction process is executed by changing the number to be the nearest multiple of the order q, and the error-corrected matrix is divided by the order q to calculate an intermediate signal vector for each encoded signal. A digital signal corresponding to each encoded signal is decoded from the signal vector.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to, for example, a synchronous CD.
MA (Code Division Multiple Access) system (hereinafter S-
It is called a CDMA system. The present invention relates to an encoding method and a decoding method of a digital signal, which are applicable to the above) and are capable of error correction.

[0002]

2. Description of the Related Art It is well known that spread spectrum sequences play an important role in recent wireless communication systems. The most famous spread spectrum sequence used in S-CDMA systems is the Walsh-Hadamard sequence. However, although these spread spectrum sequences can only support a limited number of potential users equal to the length of the spread spectrum sequence, recent developments in S-CDMA systems have increased their maximum allowed number of users. Are in need.

Coding methods for multi-users for multi-access adder channels have the potential to increase the maximum number of these allowed users, and in this attempt Khachatrian et al. And Wu. Et al. Have demonstrated that multi-user codes for multiple access adder channels can be used as a set of spread spectrum sequences for S-CDMA systems (see, eg, Prior Art Document 1 "GK Khachatria.
n et al., "A new approach to the design of codes f
or synchronous-CDMA systems ", IEEE Transaction on
Information Theory, Vol. IT-41, No. 5, pp.1503-150
6, September 1995 ”, Prior Art Document 2“ YW Wu et a
l. "Coding scheme for synchronous-CDMA systems", I
EEE Transaction on Information Theory, Vol. IT-43,
No. 3, pp.1065-1067, May 1997 ”. ). Their spread spectrum sequences have the unique effect of supporting a large number of users that far exceed their length.

[0004]

However, their work is limited to "noise-free" S-CDMA channels without taking into account noise in the transmission line, in other words, their spread spectrum sequence. The set has a problem that it has no error correction capability.

An object of the present invention is to solve the above-mentioned problems, and in a multiple access communication system, even if there is channel noise, an error correction of a transmitted digital signal can be carried out and a digital signal encoding method and decoding can be performed. It is to provide a method of computerization.

[0006]

A method for encoding a digital signal according to the present invention is designed such that a predetermined spread spectrum sequence is Kronecker-multiplied by a Hadamard matrix of a predetermined order q, and a Knecker multiplication result spread spectrum sequence is obtained. And a step of multiplying the input digital signal by the generated spread spectrum sequence and outputting the multiplication result as an encoded signal.

A digital signal decoding method according to the present invention is a digital signal decoding method for decoding a received signal including a plurality of coded signals coded by the above coding method. , A step of converting a received signal including a plurality of encoded signals so as to be expressed in a matrix format, multiplying the converted matrix by the Hadamard matrix, and generating a matrix of the multiplication result, and a matrix of the multiplication result. Error correction processing is performed by changing each of the components so that it is a multiple of the nearest order q, and the step of generating an error-corrected matrix, and dividing the error-corrected matrix by the order q By calculating the intermediate signal vector for each coded signal, and decoding the digital signal corresponding to each coded signal from the calculated intermediate signal vector Characterized in that it comprises a step.

[0008]

DETAILED DESCRIPTION OF THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

In the embodiment according to the present invention, for example, S-C
We propose a coding and decoding method for "error correction" spread spectrum sequences for S-CDMA systems, considering that the DMA channel is degraded by "noise". In the present embodiment, if the spread spectrum sequence having the specified length, the size of the user population, and the error correction capability are given in advance, the number of corrections per block is proportionally increased, and at the same time, a larger user population is generated. It is possible to construct a longer and larger set of spread spectrum sequences to support, the proposed spread spectrum sequences are able to correct errors induced by channel noise, and also to extend the length of spread spectrum sequences. It is possible to support a large number of users over

First, the basic configuration used in this embodiment will be described with reference to the S-CDMA radio communication system shown in FIG. In FIG. 1, a plurality of T user terminals 5
0-1 to 50-T, for example, T receiving terminals 25-1 to 25-through the multi-access channel transmission line 30 which is a wireless transmission line and the encoder 40 of the wireless base station.
The basic structure of the entire S-CDMA wireless communication system up to T is shown.

A plurality of T user terminals 50-1 to 50-
In the S-CDMA wireless communication system with T, the j-th user terminal 50-j (j = 1, 2, ..., T) has a spread spectrum sequence s _j ε having a value of ± 1 which is the length n. {-1, 1} ⁿ is assigned. S = {s
Let ₁ , s ₂ , ..., S _T } be a set of T spread spectrum sequences. Here, each user terminal 50
-J (j = 1, 2, ..., T) is a digital data signal generator 1 for generating a digital data signal b _j , respectively.
-J and encodes by multiplying the spread spectrum sequence s _j to digital data signals b _j, constituted by a coder 2-j to transmit the multiplied value as a transmission signal. The equivalent configuration of the multi-access channel transmission line 30 can be represented by T multipliers 31-1 to 31-T and an adder 32 provided in the subsequent stage. Further, the received signal via the multi-access channel transmission path 30 is spectrum despread with decoder 40, with the T number of receiving digital data signal b _'j, to the T receiver terminal 25-1, respectively 25- It is output to T.

In this embodiment, a multi-user code
From the viewpoint of optimization, the j-th user terminal 50-j has a component
Code {0ⁿ, S_j, -S_j} (J = 1, 2, ..., T) is
Assigned. Where 0ⁿIs the n-vector (length
A row vector of n; similarly described below. )so
And its n components are zero. jth user end
If the last 50-j is active, this is the digit
Tal data signal message b_j= 1 or b_jTo -1
Depending on the encoded transmission signal s_jOr -s_jTo send.
All user terminals 50-j in the idle state are coded and transmitted.
Signal 0ⁿAnd send them inactive
(Ie b_j= 0) is shown. Therefore, the j-th you
The encoded transmission signal transmitted by the terminal 50-j.
Ktor is b _js_jIs.

Next, the output vector (received signal) y from the above-mentioned equivalently constructed noisy S-CDMA multi-access channel transmission line 30 can be expressed algebraically as follows.

[0014]

[Equation 1]

Where e is the error vector induced by the channel noise and p _j is the received signal power from the j-th user terminal b _j . As in the case of the prior art document 2, all received signals are assumed to have equal power, and are expressed by the following equation without loss of generality.

## EQU00002 ## p ₁ = p ₂ = ... = p _T = 1

Full symbol and block synchronization are also assumed here. That is, all user terminals 50-
j generates and encodes a synchronized digital data signal based on the same clock signal. Then, based on the received signal y from the multi-access channel transmission line 30, the decoder 40 determines the state of each user terminal 50-j (ie active or not, even in the presence of noise e). Inactive) and the digital data signal from the user terminal 50-j is uniquely determined.

Before describing the specific encoding method and decoding method used in this embodiment, the notation and definition used here will be described. The weight of the integer n-vector y = (y ₁ , y ₂ , ..., Y _n ) of the received signal (so-called L-weight in this embodiment) is defined by the following equation.

[0018]

[Equation 3]

Here, the sum total on the right side of the above equation relates to a real number. The distance between the two vectors y and y '(so-called L-distance in this embodiment) is defined by the following equation.

## EQU00004 ## d _L (y, y ') = w _L (y-y') Here, the negative sign "-" indicates subtraction of the real number for each component.

<Definition 1> Two different arbitrary T-vectors, [b ₁ , b ₂ , ..., B _T ] and [b ′ ₁ , b ′ ₂ ,
, B ′ _T ] (where b _j , b ′ _j ε {−1,0,
1}),

[Equation 5] Then a spread spectrum sequence with length n
Set of S = {s₁, S _Two,…, S_T} Is "δ-decodeable
Noh ”, and the definition is as follows.

In the present embodiment, in T spread spectrum sequences of length n, the δ-decodable set S is called the (n, δ, T) set. If the set is δ-decodable, then this set is L of the error vector e.
The weight w _L (e) is

[Equation 6] Can be corrected (see, for example, prior art document 3 “SC Chang et al.,“ Cod
ing for T-user multiple-access channels ", IEEETran
sactions on Information Theory, Vol. IT-25, No. 6,
pp.684-691, November 1979 ". ). That is, “δ-decodable” means that it has the ability to correct and decode errors of the number equal to or less than the number represented by the right side of the above equation 6.

Here,

[Equation 7] Means the largest integer not exceeding p.

Alternatively, it is also used to detect δ-1 or less errors. (N, δ = 1,
The T) set is said to be "uniquely decodable". (N,
The decoder 40 using the δ = 1, T) set may independently and independently decompose any possible received vector into the codewords transmitted from each user terminal 50-j. it can.

In the coding method for the S-CDMA wireless communication system used in this embodiment, qδ-decodable set of qT spread spectrum sequences having a length qn is T having a length n. , Which is any well-defined, δ-decodable set of spread spectrum sequences. More specifically, given an arbitrary (n, δ, T) set S, the Hadamard matrix of order q gives (qn, qδ, q
T) Set S ^* is generated. In the following, (n, δ,
We demonstrate the main theory that we can generate (qn, qδ, qT) sets from T) sets.

Next, the encoding method according to this embodiment will be described in detail. Here, when (n, δ, T) set S is given in advance, from set S to (qn, qδ,
qT) indicates that the set S ^* can be generated. Here, q is the order of the Hadamard matrix. Below, Theorem 1 is shown and its proof is shown.

<Theorem 1> Set S = {s ₁ , s ₂ , ...,
s _T } has s _j ε {−1,1} ⁿ (n, δ, T)
Let h _{i be} the i th row vector of the Hadamard matrix H of degree q, and

[Equation 8] Let be the Kronecker product between h _i and s _j , then set S ^*

[Equation 9] Is the (qn, qδ, qT) set. Where s
_ij ^* is the ((i-1) T + j) th spread spectrum sequence in the set S ^* .

<Proof of Theorem 1> Clearly, the set S ^* has a sequence length qn, and according to the definition of the Kronecker product, the spread spectrum sequence {-1,1}.
belongs to ^qn . The number of spread spectrum sequences in the set S ^* is qT from the above equation 9. It is proved below that the set S ^* is “qδ-decodable”.

[0028]

[Equation 10]

The above inequality leads to two different qT-vectors:

[Equation 11] [b₁₁, ..., b_1T, ..., b_i1，
b_i2, ..., b_iT, ..., b_q1, ..., b _qT] ≠
[B '₁₁, ..., b '_1T, ..., b '_i1, B '_i2，
…, B ’_iT, ..., b '_q1, ..., b '_qT] Clarify that it holds for. Where i =
1,2, ..., q; j = 1,2, ..., T

[ _Mathematical formula-see original _document ] b _ij and _b'ij ε {-1,0,1}.

Here, for convenience, the intermediate signal vector θ _i is set as the following equation.

[0031]

[Equation 13]

Therefore, the following equation is obtained.

[0033]

[Equation 14]

Now, consider the q × n matrix of the following equation.

[0035]

[Equation 15]

Here, the superscript "T" means the transpose of the matrix. Multiplying Hadamard matrix H to both sides of the equation 15, the ^HH T = qI, the following equation is obtained.

[0037]

[Equation 16]

Where I is an identity matrix of order q. Since at least i ₀ exists,

[Expression 17] (b_i01, B_i02, ..., b_i0T) ≠
(B '_i01, B '_i02, ..., b ' _i0T) (See the above formula 11.), and the set S is δ-decodable.
Is. Therefore, the following equation holds.

[0039]

[Equation 18]

Therefore, the i ₀ -th row vector of the matrix HΦ needs to have the following weights.

[0041]

[Formula 19]

Here,

[Equation 20] as well as

[Equation 21] Are the components of the matrices H and Φ, respectively.

Since all the elements of the matrix H are from {-1,1}, the following equation is obtained.

[0044]

[Equation 22]

The weight of the vector of the above equation 14 is equal to the sum of the absolute values of all the components in the matrix Φ. That is, it is expressed by the following equation.

[0046]

[Equation 23]

Therefore, the set S ^* is qδ-decodable. This completes the proof of Theorem 1.

Next, the set S ^{* of} spread spectrum sequences of Theorem 1 will be considered from the viewpoint of the multiuser coding method. As mentioned above, the set S = {s ₁ , s ₂ ,
In the S-CDMA wireless communication system associated with ..., s _T , the component code {0
ⁿ , s _j , -s _j } are assigned. Since the codeword 0 ⁿ is shared by all users, the spread spectrum sequence set is the wireless transmission terminal device 10- (i, j) (i = 1) corresponding to the variable number of active user terminals in the S-CDMA wireless communication system. , 2, ...,
q; j = 1, 2, ..., T).

[0049]

[Equation 24]

Here, since the above equation holds, a common zero
B vector 0^nqAlso set S ^*Associated with
All users in S-CDMA wireless communication system
Shared with. Therefore, set S^*Is a variable number of
Active wireless transmission terminal device 10- (i, j)
It has such characteristics.

In the present embodiment, since a common zero codeword is assigned to each wireless transmission terminal device 10- (i, j) (see the above equation 24), the decoder 40 has each decoder 40-. It is possible to identify the state of (i, j) (zero codeword not active). Then, even in the presence of channel noise, it is possible to unambiguously determine the digital data signal from the active wireless transmission terminal 10- (i, j).

The present embodiment is limited to the case of the spread spectrum sequence s _j ε {−1,1} ⁿ , but for a positive integer k (≧ 2),

It is easy to develop s _j ε {± k, ± (k−1), ..., ± 1} ⁿ .

Δ in Theorem 1 is an arbitrary positive integer, but hereinafter, it will be considered as being limited to the case of δ = 1.

The following example shows that the well known Walsh-Hadamard sequence is a spread spectrum sequence for error correction in an S-CDMA wireless communication system.

<Example 1> Trivial set (n = 1, 1, T =
The set S which is 1) is set as S = {s ₁ = [1]}.
At this time, according to the above equation 9, a set of q spread spectrum sequences is obtained as shown in the following equation.

[0056]

[Equation 26]

According to Theorem 1, the set {s ₁ ^* , s ₂ ^* , ..., S _q ^* } obtained by the above equation 26 is “q-decodable” and is (q, q, q) set. . H _i in Equation 26 Walsh - It is well known that Hadamard sequences.

Next, the set {s ₁ ^* , s
Consider an example of ₂ ^* , ..., _Sq ^* } below. The Hadamard matrix H ₈ of order ₈ is expressed by the following equation.

[0059]

[Equation 27]

At this time, from the above equation 26, the following 8
A set of spread spectrum sequences is obtained.

[0061]

S ₁ ^* = [1,1,1,1,1,1,1,1,1]

S ₂ ^* = [1, -1,1, -1,1,1, -1,1, -1]

S ₃ ^* = [1,1, -1, -1, -1,1, -1, -1,]

S ₄ ^* = [1, -1, -1,1,1, -1, -1, -1,1]

S ₅ ^* = [1,1,1,1, -1, -1, -1, -1, -1]

S ₆ ^* = [1, -1,1, -1, -1, -1,1, -1,1]

S ₇ ^* = [1,1, -1, -1, -1, -1, -1,1,1]

S ₈ ^* = [1, -1, -1,1, -1, -1,1, -1, -1]

This is a (8,8,8) set according to Theorem 1.

In the prior art document 2, Wu et al. Constructed a uniquely decodable set by a spread spectrum sequence for an S-CDMA system. The spread spectrum sequence set of the prior art document 2 has the preceding S-CDMA for a long sequence length n (≧ 16).
It can support a number of users that far exceeds the system limits. Therefore, the set by Wu et al. Should be chosen for the set S in Theorem 1. Then the following conclusions are drawn.

<Example 2> (n, 1, T) of Prior Art Document 2
If the set S _WC is selected as S in Theorem 1, then
A (qn, q, qT) set S ^* is obtained. Set S ^*
Parameters are specified by the (n, 1, T) set S _WC . Here, n = 2 ^p (p is a positive integer), n ≧
The following equation holds for 16 (for example, in the related art document 2
reference. ).

[0065]

[Equation 36]

Next, an example when n = 4 is shown. Table 1
By using a Hadamard matrix H ₄ of degree q = 4 represented by the following equation, the set (4, 1,
3) shows a (4 × 4,4,4 × 3) set formed from FIG.

[0067]

[Equation 37]

[0068]

[Table 1] (4 × 4,4,4 × 3) set (4,1,3) set according to prior art document 2 ―――――――――――――――――――――――― ―――――――――――――― s ₁ = [-1, -1, -1, -1,1] s ₂ = [-1,1,1, -1] s ₃ = [-1, 1, -1,1] ――――――――――――――――――――――――――――――――――― (4 × 4,4,4 × 3) Set ―――――――――――――――――――――――――――――――――――― s ₁₁ ^* ＝ [-1, -1, -1,1, -1, -1, -1,1, -1, -1, -1,1, -1, -1, -1,1] s ₁₂ ^* = [-1,1,1, -1, -1,1,1, -1, -1,1,1, -1, -1,1,1, -1] s ₁₃ ^* = [-1,1, -1,1, -1 , 1, -1,1, -1,1, -1,1, -1,1, -1,1] s ₂₁ ^* = [-1, -1, -1,1,1,1,1, -1, -1, -1, -1,1,1,1,1, -1] s ₂₂ ^* = [-1,1,1, -1,1, -1, -1,1, -1 , 1,1, -1,1, -1, -1,1] s ₂₃ ^* = [-1,1, -1,1,1, -1,1, -1, -1,1, -1 , 1,1, -1, -1, -1] s ₃₁ ^* = [-1, -1, -1 , 1, -1, -1, -1,1,1,1,1, -1,1,1,1, -1] s ₃₂ ^* = [-1,1,1, -1, -1, 1,1, -1,1, -1, -1,1,1, -1, -1,1] s ₃₃ ^* = [-1,1, -1,1, -1,1, -1, 1,1, -1,1, -1,1, -1,1, -1] s ₄₁ ^* = [-1, -1, -1,1,1,1,1, -1,1,1 , 1, -1, -1, -1, -1,1] s ₄₂ ^* = [-1,1,1, -1,1, -1, -1,1,1, -1, -1, 1, -1,1,1, -1] s ₄₃ ^* = [-1,1, -1,1,1, -1,1, -1,1, -1,1, -1, -1, 1, -1,1] ―――――――――――――――――――――――――――――――――――

In this case, for example, the spread spectrum sequence s ₂₃ ^* is expressed by the following equation.

[0070]

[Equation 38]

In Example 2, it seems more appropriate to present an example of n ≧ 16, but in consideration of the encoding procedure and the display space in the specification, n is dared to simply indicate.
= 4 example is used. Set S constructed in Example 2
^* (Qn, q, qT) is

[Formula 39] It is possible to correct an error of less than or equal to n, and a large number qT of wireless transmission terminal devices 10- (i, i, which similarly exceed the length qn (n ≧ 16) of the spread spectrum sequence.
j) (i = 1, 2, ..., Q; j = 1, 2, ..., T) can be supported.

In the coding method, preferably, the following spread spectrum sequence set S = {s
_{1, s} 2, ···, a _{s T}} is used. Detection set {v ₁ ,
When v ₂ , ..., V _T }, v _j ε {0,1} ⁿ⁻¹ , the spread spectrum sequence set S = {s
₁ , s ₂ , ..., s _T }, s _j ε {−1,1} ⁿ are obtained from the detection set as follows:

S _j = [− 1,2 v _j −1] Here, the construction of this detection set can be performed based on the well-known Lindstrom algorithm (see prior art document 2), and the detection set is as follows. Can be defined as

<Definition of Detection Set> A non-zero binary (value of 0 or 1) vector {v ₁ , v ₂ , ..., V _T } is

[Formula 41] If all sums of are clearly identifiable (where a _j
Ε {0,1,2}) can be called a detection set having connectivity over {0,1,2} (Prior Art 2
reference). That is, the detection set v _j can uniquely detect the vector a _j from all the sums of the above equation 41.

Therefore, on the encoder side, a spread spectrum sequence set S ^* of the following equation is generated for the above spread spectrum sequence s _j (j = 1, 2, ..., T),

[Equation 42] This spread spectrum sequence set S ^* is multiplied by the digital data signal b _ij and then transmitted. Note that h _i is the i-th row vector of the Hadamard matrix B of order q.

Next, the error correction rule will be described. This embodiment proposes an error correction rule for the set S ^* in Theorem 1 when δ = 1. Here, the ((i-1) T + j) th wireless transmission terminal device 10
-(I, j) is the digital data signal b _ij (i = _1,1 )
2, ..., Q; j = 1, 2, ..., T). Correspondingly, the sum of the vectors of the transmitted coded transmission signals is expressed by the following equation.

[0076]

[Equation 43]

When noise e is present in the multi-access channel transmission line 30, the decoder 40 observes the following disturbed received signal y.

[0078]

[Equation 44]

Here, the noise e is, by assumption, an error vector having a weight w _L of the following equation.

[0080]

[Equation 45]

The task of the decoder 40 is to correct the errors in the received signal vector y and recover the digital data signals b _ij . The error correction and the determination of the digital data signal b _ij are carried out as follows. Intermediate signal vector θ slightly different from the above equation 13
_{i is given} by the following equation.

[0082]

[Equation 46]

Next, the received signal vector y is rewritten as the following equation.

[0084]

[Equation 47]

The error vector e can be divided into q n-vectors and is expressed by the following equation.

[Equation 48] e≡ [e ₁ , e ₂ , ..., E _q ] Here, consider Φ _y which is a q × n matrix.

[0086]

[Equation 49]

As in the case of the above equation 16, by multiplying the left side of the matrix Φ _{y by} the matrix H, the following equation is obtained.

[0088]

[Equation 50]

Here, if the error vector e is a zero vector, each element of the matrix HΦ _y is a multiple of q. If the error vector has weights w _L (e)

[Equation 51] Decoder 40 can correct these errors in matrix HΦ _y by changing the components that are not multiples of q to the nearest multiples of q. To be more precise,
let ζ _{ij be} a component of the matrix HΦ _y , and

Let r = ζ _ij mod q. Here, mod is a modulo operator modulo q. The error correction process is executed according to the following equation.

[0090]

[Equation 53]

Then, the corrected signal vector of the matrix HΦ _y is divided by q to obtain the following equation.

[0092]

[Equation 54]

Since the intermediate signal vector θ _i is the weighted sum of the vectors from the (n, 1, T) set S (see the above equation 46), the message b _ij (j = 1) of the transmitted digital data signal is obtained. , 2, ..., T) is
By decoding the (n, 1, T) set S, it is uniquely reproduced from the above equation (46) (for example, in the prior art document 2
According to the decoding procedure of (1), the set of the prior art document 2 serves as the spread spectrum sequence set S in Theorem 1).

Therefore, the error correction rule in the decoding method uses the following procedure. (A) Step SS1: The received signal vector y of the above-mentioned formula 47 is rearranged into the matrix Φ _y and converted (see the above-mentioned formula 49). (B) Step SS2: The matrix HΦ _y is calculated by multiplying the transformed matrix Φ _y by the Hadamard matrix H. (C) Step SS3: Matrix HΦ _y according to the above equation 53
The error correction process is executed by changing the order so that it is a multiple of the order q which is the closest to the component. (D) Step SS4: Intermediate signal vector θ is obtained by dividing the error-corrected matrix HΦ _y by the order q.
_i (i = 1, 2, ..., Q) is calculated. (E) Step SS5: Using the (n, 1, T) set S (for example, the set disclosed in the prior art document 2), from the intermediate signal vector θ _i of the above equation 46, the transmitted digital data signal Message b _ij (j = 1, 2,
..., T) is reproduced. This step SS5 is repeated from i = 1 to q.

FIG. 2 shows an S according to an embodiment of the present invention.
FIG. 3 is a block diagram showing a configuration of a CDMA wireless communication system. The same components as those in the basic configuration of FIG. 1 are designated by the same reference numerals. The configuration of FIG. 2 is characterized by being configured as follows in order to use the above-described encoding method and decoding method. In FIG. 2, i = 1, 2, ..., Q; j = 1, 2, ..., T, and the identification number of the wireless transmission terminal device 10- (i, j) is represented two-dimensionally. It has a total of qT devices. (A) A modified spread spectrum sequence signal set S ^* = {s ₁₁ connected to the encoder 2- (i, j)
Spread spectrum signal (hereinafter referred to as SS signal) s of each component of ^* , s ₁₂ ^* , ..., s _ij ^* , ..., s _qT ^* }.
An SS signal generator 3- (i, j) that generates _ij ^* is provided. (B) Hadamard matrix H and detection set vector v, which are stored in the data memory 26 and are necessary for decoding processing
_The decoder 24 that executes the decoding process including the error correction shown in FIG. 3 by using _j and the Hamming weight coefficient α (i).
Equipped with.

In FIG. 2, the wireless transmission terminal device 10- (i, j) (i = 1, 2,
, Q; j = 1, 2, ..., T), while a wireless receiver 20 is provided on the wireless base station side, and wireless communication is performed between them using free space. It should be noted that each wireless transmission terminal device 10- (i, j) is synchronized with each other to generate and encode a digital data signal based on the same clock signal, and the wireless transmission terminal devices 10- (i, j) are mutually synchronized. Configured similarly.

In each radio transmission terminal device 10- (i, j), the digital data signal generator 1- (i, j) is
The message b _ij of the digital data signal to be transmitted is generated and output to the encoder 2-j. On the other hand, the SS signal generator 3- (i, j) is generated by pre-calculating the SS signal set S ^* shown in the above equation 42, storing it in a table memory (not shown), and reading it. Then, each SS signal generator 3- (i, j) generates the SS signal s _ij ^* of the SS signal set S ^* and the encoder 2
-Output to (i, j). The encoder 2- (i, j) is
Message b of the input digital data signal
a _ij, by multiplying the sequence _{s ij} ^* of the SS signal, after calculating the encoded transmission signal _b ij _{s ij} ^*,
Up-converter 4-converts frequency to a predetermined radio signal
Transmit and radiate from the antenna 6- (i, j) via (i, j) and the power amplifier 5- (i, j).

On the other hand, the antenna 21 of the radio reception device 20 receives the encoded transmission signal transmitted from each radio transmission terminal device 10- (i, j), and then the low noise amplifier 22 and the band pass filter 23 are provided. The received signal y including the encoded signal is output to the decoder 24 via the down converter 23A that converts the signal into a predetermined intermediate frequency signal and the A / D converter 23b. Then, the decoder 24 uses the Hadamard matrix H in the data memory 26, the detection set vector v _j, and the Hamming weighting coefficient α (i) for the received signal y to perform the error correction shown in FIG. By executing the decoding process including the message b ′ _ij of each transmitted digital data signal, each receiving terminal 25- (i, j)
(I = 1, 2, ..., Q; j = 1, 2, ..., T).

FIG. 3 is a flow chart showing a decoding process including error correction, which is executed in the decoder 24 of FIG.

In FIG. 3, first, in step S1, the received signal vector y received is rearranged into a matrix Φ _y (in the matrix Φ _y , each row corresponds to j and each column corresponds to i). Then, in step S2, the matrix HΦ _y is calculated by multiplying the converted matrix Φ _y by the Hadamard matrix H in the data memory 26.
Then, in step S3, an error correction process is performed on the calculated matrix Φ _y using Equation 53,
In step S4, the error-corrected matrix HΦ _y is divided by the order q to obtain the intermediate signal vector θ.
_i (i = 1, 2, ..., Q) is calculated. Further, in step S5, the parameter i is initialized to 1, and in step S6, the intermediate signal vector θ _i is calculated using the matrix S of the (n, 1, T) set spread spectrum sequence.
From the digital data signal b _ij (j = 1, 2, ...,
T) is decoded, that is, the decoding process of FIG. 4 is executed. Then, in step S7, it is determined whether or not the parameter i is the order q or more. If NO, the parameter i is incremented by 1 in step S8, and then the process of step S8 is repeated. On the other hand, step S
If YES in step 7, in step S9, the decoded digital data signal b _ij (i = 1, 2, ...,
q; j = 1, 2, ..., T) respectively corresponding receiving terminals 25-
It is output to (i, j) and the decoding process is terminated.

FIG. 4 is a flow chart showing details of the decoding process (S6) which is the subroutine of FIG. This decryption process is

[Equation 55] _Is a process for decoding the message b _ij of the digital data signal transmitted from the intermediate signal vector θ _i represented by

Symbols and the like used in the description of the decoding process (S6) will be described below. First, each component of the intermediate signal vector θ _i is represented by the following equation.

[Equation 56] θ _i = [θ _{i, n} , θ _{i, n−1} , θ
_{i, n−2} , ..., θ _{i, 1} ] Further, the Hamming weight coefficient α (p) means the number of messages of the digital data signal in the binary representation of the order p, and h (p) is the following equation. Is an integer that satisfies.

[0103]

[Equation 57]

It is also defined that i ⊆ p only if i = i ∩ p, where the operator of i ∩ p is the bitwise AND of their binary representations. Further, the above-mentioned detection set v _j is {v ₁ , v ₂ , ..., V _T } or

[Equation 58] It can be expressed as. here,

[Equation 59] Is.

Furthermore, the following two vector description methods mean the same vector. {A ₁ , a ₂ , ..., a _T }

[Equation 60]

Next, the decoding process (S6) in FIG. 4 will be described in detail. In step S11 of FIG. 4, first, the intermediate signal vector θ _i and the detection set vector v _j
Based on and, the initial value of the decoded vector z and the order p are calculated by the following equation (see Prior Art Document 2).

[Equation 61]

P = 2 ^J-1 where:

[Equation 63] J = log ₂ n.

Then, in step S12, the following equation is used based on the Hamming weight coefficient α (i) and the order p,

[Mathematical formula-see original document] w _i ^(p) = 1; if i ⊆ ^p and α (i) is odd = -1; if i ⊆ p and α (i) is even = 0; other Then, a weight vector w ^(p) represented by the following equation is calculated.

[Mathematical formula-see original document] w ^(p) = [wn _- ^1p ,
w _n-2 ^p ,. ． ． , W ₁ ^p ]

Then, in step S13, the vector w ^(p) z ^T is decomposed into the vector z'by using the following equation.

[0109]

[Equation 66]

Further, in step S14, the vector z is updated based on the decomposed vector z'by using the following equation.

[0111]

[Equation 67]

Next, in step S15, the order parameter p is decremented by 1, and in step S16, it is determined whether p = 0 or z = 0 ^n-1 (n-1 zero vectors) is present, and NO is determined. If yes, return to step S12, while if YES, step S1
Proceed to 7. In step S17, the parameter j is initialized to 1, and in step S18 the message b _ij of the digital data signal is calculated using the following equation,

B _ij = a _j −1 In step S19, it is determined whether or not the parameter j has reached its maximum value T. If NO, the parameter j is incremented by 1 and then the process of step S18 is performed. repeat. On the other hand, YES in step S19
If so, in step S21, the calculated message vector b _ij is output and the process returns to the original main routine.

[0113]

EXAMPLE The following example shows a specific example of the error correction procedure for the set S ^* .

Example 3: Decode the (16,4,12) set S ^* in Table 1. Here, the spread spectrum sequence set S ^* is (n = 4, 1, T = 3) set S
Those generated by Hadamard matrix H ₄ of the order q = 4 (see Example 2).

Digital data signal message b _ij
Is the [(i−1) × 3 + j] th wireless transmission terminal device 1
0- (i, j) (i = 1, 2, 3, 4; j = 1, 2,
3), and the following equation is assumed.

[0116]

[Equation 69]

This is the wireless transmission terminal device 10- (1,
2), 10- (2,3), 10- (3,3) and 10-
It means that (4, 3) is active and that each of them is transmitting its binary information of 1, 1, 1 and -1. The other user terminal becomes idle. Here, the total vector of the coded transmission signals transmitted from the twelve wireless transmission terminal devices 10- (i, j) is expressed by the following equation.

B ₁₂ s ₁₂ ^* + b ₂₃ s ₂₃ ^* + b ₃₃ s ₃₃ ^* + b ₄₃ s ₄₃ ^* = s ₁₂ ^* + s ₂₃ ^* + s ₃₃ ^* -s ₄₃ ^* = [-2,2,0,0,- 2,2,0,0, -2,2,0,0,2, -2,4, -4]

Here, the error vector of the following equation

When disturbed by e = 0010000000000000, the received signal vector received is represented by the following equation.

Equation 72] ^{_{y = s 12 * + s 23}} * + s 33 * -s 43 * + e = [- 2,2, 1, 0, -2,2,0,0, -2,2,0,0,2 , -2,4, -4] In the above equation, the underlined portion is the error portion due to the error vector.

The decoder 24 first corrects this unique error in the received signal vector y and then determines which data is transmitted by each user terminal.
The error correction rule is divided into the following five steps as described above.

<Step SS1> The received signal vector y is rearranged into the matrix Φ _y and converted.

[0121]

[Equation 73]

<Step SS2> The matrix Φ _y is multiplied by the Hadamard matrix H _{4 of} 37 to obtain a matrix H ₄ Φ _y of the following formula.

[Equation 74]

<Step SS3> Looking at the right side of the above equation, it can be seen that the element in the third column of the matrix is not a multiple of 4. Therefore, the error correction is performed by changing the component of the third column to the nearest multiple of 4 (see the above formula 53).
That is, the following equation is changed.

[Expression 75] 5 → 4, −3 → −4, −3 → −4, 5 → 4 As a result, the error-corrected matrix H ₄ Φ _y is expressed by the following equation.

[0124]

[Equation 76]

<Step SS4> The following equation is obtained by dividing the error-corrected matrix H ₄ Φ _y by the order q = 4.

[0126]

[Equation 77]

<Step SS5> The intermediate signal vector θ ₁ expressed by the above equation 46 is expressed by the following equation.

Θ ₁ = b ₁₁ s ₁ + b ₁₂ s ₂ + b ₁₃ s ₃
= [-1, 1, 1, -1] message b _{11 of} the transmitted digital data signal,
b ₁₂ and b ₁₃ can be reproduced by decoding from the intermediate signal vector θ ₁ using the (4,1,3) set S according to the above-described decoding rule. That is, it is decoded as follows.

B ₁₁ = 0, b ₁₂ = 1, b ₁₃ = 0 Similarly, the following is obtained.

B ₂₁ = 0, b ₂₂ = 0, b ₂₃ = 1

B ₃₁ = 0, b ₃₂ = 0, b ₃₃ = 1

B ₄₁ = 0, b ₄₂ = 0, b ₄₃ = -1

As described above, according to this embodiment, in a multiple access radio communication system such as an S-CDMA system, a code capable of performing error correction on a transmitted digital signal even if there is channel noise. An encryption method and a decoding method can be provided. That is, in this embodiment, when a δ-decodable set of T spread spectrum sequences having a sequence length n is given in advance, the Hadamard matrix H _q of degree _q is used to obtain the sequence length. It has been shown that a qδ-decodable set of qT spread spectrum sequences with qn is obtained. The proposed spread spectrum sequence can correct errors and also support a large number of users far exceeding the length of the spread spectrum sequence. Further, if the proposed spread spectrum sequence is used, the decoder 24 that executes the proposed decoding process is
A digital data signal from the wireless transmitter terminal 10- (i, j) which is capable of identifying the state of (i, j) and is then unambiguously active even in the presence of channel noise. Can be uniquely determined and decoded.

[0129]

As described in detail above, according to the digital signal coding method of the present invention, a predetermined spread spectrum sequence is Kronecker-multiplied by a Hadamard matrix of a predetermined order q, and the Kronecker multiplication result is obtained. Of the spread spectrum sequence, the input digital signal is multiplied by the generated spread spectrum sequence, and the multiplication result is output as a coded signal. On the other hand, according to the decoding method of the digital signal according to the present invention, the received signal including the plurality of encoded signals is converted to be represented in the form of a matrix, the converted matrix is multiplied by the Hadamard matrix, The matrix of the multiplication result is generated, and the error correction processing is executed by changing each component of the matrix of the multiplication result to be the nearest multiple of the order q, and the error-corrected matrix is generated. An intermediate signal vector for each coded signal is calculated by dividing the error-corrected matrix by the order q, and a digital signal corresponding to each coded signal is decoded from the calculated intermediate signal vector. To do. Therefore, in a multiple access wireless communication system such as an S-CDMA system,
It is possible to provide an encoding method and a decoding method that can correct an error in a transmitted digital signal even if there is channel noise.

[Brief description of drawings]

FIG. 1 is an S-CDM used in an embodiment according to the present invention.
FIG. 3 is a block diagram showing a basic configuration of an A wireless communication system.

FIG. 2 is an S-CDMA according to an embodiment of the present invention.
It is a block diagram which shows the structure of a wireless communication system.

3 is a flowchart showing a decoding process including error correction, which is executed in the decoder 24 of FIG.

FIG. 4 is a decoding process (S
It is a flow chart which shows the details of 6).

[Explanation of symbols]

1- (1,1) to 1- (q, T) ... Digital data signal generator, 2- (1,1) to 2- (q, T) ... Encoder, 3- (1,1) to 3- (q, T) ... SS signal generator, 4- (1,1) to 4- (q, T) ... up converter, 5- (1,1) to 5- (q, T) ... power amplifier , 6- (1,1) to 6- (q, T) ... Antenna, 10- (1,1) to 10- (q, T) ... Radio transmitting terminal device, 20 ... Radio receiving device, 21 ... Antenna, 22 ... Low noise amplifier, 23 ... Band pass filter, 23A ... Down converter, 23B ... A / D converter, 24 ... Decoder, 25- (1, 1) to 25- (q, T) ... Receiving terminal, 26 ... Data memories 50-1 to 50-T ... User terminals.

Continued front page    (72) Inventor Yoichiro Watanabe             1-3 Tatara Totani, Kyotanabe, Kyoto Prefecture Doshisha             Faculty of Engineering, Department of Knowledge Engineering F term (reference) 5J065 AA01 AB01 AC02 AD07 AE02                       AF02 AF04 AH02 AH03 AH06                 5K014 AA01 HA10                 5K022 EE01 EE21 EE31

Claims (2)

[Claims] 1. A step of performing Kronecker multiplication of a predetermined spread spectrum sequence with a Hadamard matrix of a predetermined order q to generate a spread spectrum sequence as a result of the Kronecker multiplication, and the above generation for an input digital signal. And a step of multiplying the generated spread spectrum sequence and outputting a result of the multiplication as an encoded signal. 2. A decoding method of a digital signal for decoding a reception signal including a plurality of encoded signals encoded by the encoding method according to claim 1, comprising a plurality of encoded signals. The received signal is transformed to be represented in the form of a matrix, the transformed matrix is multiplied by the Hadamard matrix, and the matrix of the multiplication result is generated. a step of performing an error correction process by changing so as to be a multiple of q, and generating an error-corrected matrix; and dividing each of the error-corrected matrices by an order q Each step of calculating an intermediate signal vector for each, and decoding the digital signal corresponding to each of the encoded signals from the calculated intermediate signal vector. Decoding method Ijitaru signal.