WO2018168410A1 - Encoding device, encoding method, communication device, and communication system - Google Patents

Abstract

The encoding device is installed in a communication device for transmitting data in a predetermined signal space and is provided with an encoding processing unit. The encoding processing unit generates a plurality of subspaces which are mutually orthogonal from a plurality of subspaces which have been designated in the signal subspace and include subspaces which are not mutually orthogonal, the subspace generation being such that the number of mutually orthogonal subspaces obtained by encoding becomes greater than or equal to the number of mutually orthogonal subspaces among the designated plurality of subspaces.

Description

Encoding device, encoding method, communication device, and communication system

The present invention relates to an encoding device, an encoding method, a communication device, and a communication system.

Multiplexing technology is widely used to increase the capacity of communication systems. For example, different frequencies are assigned to a plurality of data signals. Alternatively, different time slots are assigned to a plurality of data signals. In addition, in wireless communication systems, MIMO (multi-input and multi-output) technology has been put into practical use. In the MIMO system, the transmitter includes a plurality of transmission antennas, and the receiver includes a plurality of reception antennas. The transmitter transmits a plurality of data signals using a plurality of transmission antennas, and the receiver receives a plurality of data signals transmitted via the plurality of transmission antennas using a plurality of reception antennas. .

In a communication system that multiplexes and transmits a plurality of data signals, the plurality of data signals are required not to interfere with each other. On the other hand, in order to increase the capacity of the communication system, it is required to multiplex more data signals. As the number of multiplexed data signals increases, the data signals easily interfere with each other.

An object according to one aspect of the present invention is to avoid or suppress interference between a plurality of multiplexed signals.

An encoding device according to one aspect of the present invention is implemented in a communication device that transmits data in a predetermined signal space, and includes a plurality of subspaces specified in the signal space, including subspaces that are not orthogonal to each other. Encoding that generates a plurality of subspaces that are orthogonal to each other such that the number of subspaces that are orthogonal to each other obtained by encoding is equal to or greater than the number of subspaces that are orthogonal to each other among the plurality of designated subspaces. A processing unit is provided.

According to the above aspect, interference between a plurality of multiplexed signals is avoided or suppressed.

It is a figure which shows an example of the division | segmentation of a time-frequency plane. It is a figure which shows an example of a Walsh wavelet packet. It is a figure explaining the outline | summary of a sub space encoding. It is a figure which shows an example of a sub space encoding. It is a figure which shows an example of the sub space encoding in an OFDM system. It is a figure which shows an example of the model of a subspace, a slice, and a transmission block. It is a figure which shows an example of the sub space transmission based on a wavelet packet. It is a figure which shows the model of the noise added to a received signal. It is a figure which shows an example of the sub space channel model for the wavelet packet modulation which uses three slices. It is a figure which shows an example of the subspace produced | generated by encoding in the wavelet packet modulation which uses three slices. It is a figure which shows an example of the sub space channel model for the wavelet packet modulation which uses four slices. It is a figure which shows an example of allocation of the data symbol to the sub space produced | generated by encoding. It is a figure which shows an example of the transmitter which transmits data using wavelet sub space coding. It is a figure which shows an example of the receiver which receives the signal produced | generated using wavelet sub space coding. It is a figure which shows an example of the hardware constitutions of a communication apparatus. It is a figure showing the channel capacity gain with respect to the number of slices and SNR in the communication system in which subspace coding is performed.

In the communication method according to one embodiment of the present invention, a data signal is transmitted using wavelet packet conversion. Therefore, first, the wavelet packet transform will be briefly described. Note that wavelet packet transformation is used in various fields (for example, compression of image data).

Discrete wavelet packet transformation is expressed by equation (1).

Note that h [n] and g [n] are a high-pass filter and a low-pass filter (one set of wavelet filters), and have a quadrature mirror filter characteristic.

Wavelet packet conversion has various characteristics. For example, when wavelet packet transformation is used in wavelet packet modulation, the spectral shape is improved and side lobes are suppressed compared to multicarrier modulation based on discrete Fourier transform. As a result, interference between carriers (ICI: inter carrier 帯 域 interference) and narrowband interference (NBI) are suppressed. In addition, the wavelet packet transform can divide the signal space almost arbitrarily. The signal space (or resource space) corresponds to a communication resource for transmitting a signal, and is configured by, for example, time and frequency.

Wavelet packet transform can derive multiple functions that are orthogonal to each other. “Orthogonal” corresponds to a state where they are independent of each other, and in communication, corresponds to a state where signals do not interfere with each other.

However, when the signal space is divided to obtain a plurality of subspaces, the areas of the subspaces in the time-frequency plane are required to be the same. For this reason, when the bandwidth is increased, the time slot length (symbol length) is reduced. Alternatively, increasing the time slot reduces the bandwidth.

FIG. 1 shows an example of time-frequency plane division. In this example, a binary Wellet packet tree is used. W _L ⁰ represents the wavelet space at the root when Ψ _L ⁰ (t) = φ _L (t). φ _L (t) represents a scale function.

The area of each subspace obtained by dividing the time-frequency plane is the same. For example, the areas of the two hatched areas shown in FIG. 1 are the same as shown in equation (2). The characteristics of wavelet packet modulation are described in Non-Patent Document 1 described above.

In communication systems, the features described above are useful to support multiple data streams with different requirements for transmission delay. That is, subcarriers with a wide bandwidth are allocated to channels that require a small transmission delay, and subcarriers with a narrow bandwidth are allocated to channels that allow a large transmission delay. This technique is described in Non-Patent Document 2 described above.

In order to specifically explain the wavelet packet conversion, consider a Walsh wavelet packet generated by a Haar conjugate mirror filter expressed by the equation (3).

In this case, the filter h [n] is localized in the time domain, but is not sufficiently localized in the frequency domain. The corresponding scale function is φ = 1 _[0,1] . The support size of the Walsh function Ψ _j ^p is 2 ^j . Then, the wavelet packet recursion relationship is expressed by equation (4).

FIG. 2 shows an example of a Walsh wavelet packet. These Walsh wavelet packets are calculated by giving Ψ ₀ ⁰ (t) to equation (4). The horizontal axis represents time, and the vertical axis represents signal power.

<Outline of sub-space coding>
The signal space includes one or more subspaces. In the following, it is assumed that the space S includes subspaces S ₁ to S _M. The following definitions are introduced.

Definition 1: Expressed by equation (5).

Definition 2: “Subspace S _k is orthogonal (or independent) to subspace S _i ” means that all vectors of S _k are orthogonal to all vectors of S _i , It is represented by

Definition 3: space S comprises only the subspace S _k and S _i, when the vector of the subspace S _k and S _i is denoted by V _k and V _i, respectively, of the subspace S _k and the sub-space S _i The orthogonality is calculated by a vector inner product expressed by the equation (7).

FIG. 3 is a diagram for explaining the outline of subspace coding. In this example, the space S includes five sub-space S _{k (k} = 1,2,3,4,5). The space S is expressed by the equation (8).

In the communication system, the subspace S _k corresponds to a channel resource that propagates a data signal. The subspace S _k may be a subcarrier in an OFDM (orthogonal frequency division multiplexing) system, a transmission antenna in a MIMO system, or a pseudo noise sequence in a code division multiple access (CDMA) system. May be.

In FIG. 3, the subspaces that do not overlap each other are orthogonal to each other. For example, the subspaces S ₃ , S ₄ , and S ₅ are orthogonal to the subspace S ₁ . On the other hand, the subspaces that overlap each other in FIG. 3 are not orthogonal to each other. For example, the subspace S ₂ are not orthogonal with respect to the sub-space S _1. In the communication system, signals transmitted through subspaces overlapping each other can interfere with each other.

In the subspace coding, one or a plurality of new subspaces are generated from a plurality of given subspaces by the function f _c shown in the equation (9). S _{k, i} represents a new subspace generated by subspace coding. C _{k, i} represents a codeword matrix for generating a new subspace from a given subspace.

Equation (10) represents an operation for generating two new subspaces by performing subspace coding on the subspace S ₁ and the subspace S ₂ . Further, (11) executes a subspace coding shows the operation of generating one new sub-space relative subspace S ₃ and the sub-space S _5.

In the example shown in FIG. 3, four subspaces are obtained from five subspaces by subspace coding. At this time, the sub-space encoding is executed so that all the generated sub-spaces are orthogonal to each other, as represented by Expression (12). That is, four subspaces orthogonal to each other are obtained. In order to make the subspaces obtained by subspace coding orthogonal to each other _, it is required to appropriately determine the codeword matrix C _{k, i} .

In the example shown in FIG. 3, among the given subspaces (that is, the subspace before encoding), the subspaces S ₁ and S ₂ are not orthogonal to each other, and the subspaces S ₃ and S ₂ are not orthogonal to each other. ₅ are not orthogonal to each other. That is, the number of subspaces orthogonal to each other is 3 before encoding. On the other hand, after encoding, the number of subspaces orthogonal to each other is four. Thus, the number of subspaces orthogonal to each other is increased by subspace coding.

In the communication system, when not performing subspace coding, may interfere with the signal transmitted by the signal and the sub-space S ₂ transmitted by the sub-space S ₁ is generated, the sub-space S ₃ Interference may occur between the signal transmitted by the sub-space S ₅ and the signal transmitted by the subspace S ₅ . On the other hand, the four subspaces obtained by the subspace coding are orthogonal to each other, so that interference is removed. Therefore, by performing sub-space coding, the number of signals transmitted without interference increases and the transmission capacity of the communication system increases.

Thus, the sub-space coding has the following two features.

Features 1: space S includes a sub-space _{S k (k = 1 ~ M} ) , when at least a portion of the subspace of the subspace _{S k (k = 1 ~ M} ) are not orthogonal to each other, the subspace By performing subspace coding on S _k (k = 1 to M), subspaces that are orthogonal to each other can be generated. At this time, the number of subspaces orthogonal to each other obtained by subspace encoding is the number of subspaces orthogonal to each other included in the subspace S _k (k = 1 to M) before subspace encoding. That's it. However, the number of subspaces orthogonal to each other obtained by subspace coding may be less than or equal to the number of subspaces S _k (k = 1 to M).

Feature 1 relates to the problem of how to collect sufficient subspaces in a communication system to increase the number of subspaces orthogonal to each other. For example, each transmit antenna of a MIMO system can be considered as a subspace, but usually a MIMO system does not guarantee orthogonality between antenna subspaces. Therefore, for example, if processing based on singular value decomposition (SVD) is introduced, a MIMO channel is converted into a plurality of single-input single-output channels that are parallel and free of interference, and complete orthogonal transmission is performed. Can be realized. In this case, the processing based on the singular value decomposition has the same concept as the subspace coding according to the embodiment of the present invention. In this case, the subspace coding will transform the MIMO antenna into n MIMO orthogonal subspaces. When the number of transmitting antennas is M and the number of receiving antennas is N, n corresponds to the smaller value of M and N (n = min (M, N)).

Feature 2: In order to ensure the degree of freedom of subspace coding, the dimensions of the subspace are required to be kept sufficiently high. The higher the subspace dimensions in subspace coding, the higher the efficiency in generating subspaces that are orthogonal to each other.

Feature 2 represents that in order to obtain a large number of mutually orthogonal subspaces, the dimensions of the subspaces must be high. For example, a MIMO system is required to have a sufficiently large number of antennas. The maximum MIMO rank corresponds to the smaller value of the number of transmission antennas and the number of reception antennas. In addition, feature 2 is that subspace coding operates in a system that combines a plurality of different communication schemes (for example, a subspace related to OFDM, a subspace based on CDMA, and a subspace based on MIMO). Represents that it is preferable.

The above features can be proved mathematically. However, in the following, it will be explained that the above-described features are correct with reference to some examples.

<Example of sub-space coding>
FIG. 4 shows an example of subspace coding. In this example, the space S is a time-frequency space. The space S includes four subspaces S ₁ , S ₂ , S ₃ and S ₄ as shown in FIG. Different frequencies are assigned to the subspaces S ₁ and S ₂ . That is, the sub-space S _1, S ₂ are orthogonal to each other. Also, different time slots are allocated to the subspaces S ₃ and S ₄ . That is, the subspaces S ₃ and S ₄ are also orthogonal to each other. This state is expressed by equation (13).

The space S can be realized by OFDM, for example. However, the space S can be divided into different forms. For example, the frequency bandwidths assigned to the subspaces S ₁ and S ₂ are the same, and the time widths assigned to the subspaces S ₁ and S ₂ are also the same. Here, compared with the subspaces S ₃ and S ₄ , the frequency bandwidth allocated to the subspaces S ₁ and S ₂ is ½, and the frequency bandwidths allocated to the subspaces S ₁ and S ₂ are allocated. The time span is twice.

Therefore, in the following, it is assumed that each subspace S _k (k = 1 to 4) is represented by a two-dimensional vector. Here, the two-dimensional vector V _k is expressed by equation (14). Note that a _k is a vector element.

In the example shown in FIG. 4 (a), the sub-space orthogonal to the subspace S ₁ is only S _2, subspace orthogonal to the subspace S ₂ is only S _1. Similarly, the sub-space orthogonal to the subspace S ₃ is only S _4, subspace orthogonal to the subspace S ₄ is only S _3. Therefore, the maximum value of the number of subspaces orthogonal to each other is 2. In this case, the maximum number of data signals that can be transmitted simultaneously without interference is two.

In order to increase the capacity of the transmission system, it is required to increase the maximum value of the number of subspaces orthogonal to each other. Therefore, in order to increase the number of subspaces orthogonal to each other, subspace coding is performed on the space S (that is, designated subspaces S ₁ to S ₄ ).

As an example, new subspaces S _{3 and 4} are generated by performing subspace coding on the subspaces S ₃ and S ₄ . At this time, a new sub-space S _{3, 4} is orthogonal to the subspace S _1, and is generated to be perpendicular to the sub-space S _2. As a result, three subspaces S ₁ , S ₂ , S _{3 and 4} orthogonal to each other are obtained. That is, the number of subspaces orthogonal to each other is increased from 2 to 3 by subspace coding.

Next, a method for generating a sub-space S _{3, 4} running subspace coding on the sub-space S _3, S _4. The subspaces S ₃ and S ₄ are represented by two-dimensional vectors V ₃ and V ₄ , respectively. The component of the vector V ₃ is (a ₃ , a ₃ ), and the component of the vector V ₄ is (a ₄ , a ₄ ). The subspace _S3,4 is represented by a vector _V3,4 .

In this case, the sub-space encoding is expressed by equation (15). Incidentally, C _{3, 4} is a codeword matrix for realizing a subspace coding.

A process for generating the vectors V ₃ and ₄ representing the subspaces S ₃ and ₄ is expressed by, for example, Expression (16).

The 4 × 4 matrix in the equation (16) represents the codeword matrix _C3,4 . Then, the vector V _3,4 is generated by multiplying the sum of the vector representing the subspace S ₃ and the vector representing the subspace S ₄ by the codeword matrix C ₃ , ₄ . That is, one encoded four-dimensional vector V _3,4 is obtained from two two-dimensional vectors (V ₃ and V ₄ ).

FIG. 4B shows a new subspace obtained by the subspace coding of the equations (15) and (16). Subspaces S _{3 and 4} have the same time-frequency domain as the sum of subspace S ₁ and subspace S ₂ . Of the components of the vectors V _{3 and 4} representing the sub space S ₃ and ₄ , the component corresponding to the same region as the sub space S ₁ is (a ₃ , −a ₃ ). In addition, among the components of the vectors V _{3 and 4} representing the sub space S ₃ and ₄ , the components corresponding to the same region as the sub space S ₂ are also (a ₃ , −a ₃ ).

Here, the orthogonality of the _three subspaces S ₁ , S ₂ , S _{3 and 4} will be examined. The orthogonality between subspaces is calculated by the inner product of vectors.

For example, the inner product of the subspace S ₁ and when calculating orthogonality between the "subspace S ₁ except subspace" is a vector representing the subspace S ₁ "vector representing the subspace S ₁ except subspace" Is calculated. Therefore, first, “a subspace other than the subspace S ₁ ” is calculated. The “subspace other than the subspace S ₁ ” is expressed by Expression (17). In the equation (17), since the subspaces S ₁ and S ₂ are orthogonal to each other, the overlap between them is zero.

Here, as shown in FIG. 4B, among the components of the vectors V _{3 and 4} representing the subspace S ₃ and ₄ , the components corresponding to the same region as the subspace S ₁ are (a ₃ , −a ₃ ). Therefore, a vector representing “a subspace other than the subspace S ₁ ” is expressed by Expression (18a). Similarly, “a vector representing a subspace other than subspace S ₂ ” is represented by equation (18b), and “a vector representing a subspace other than subspace S _{3 and 4} ” is represented by equation (18c).

When the inner product of the vector representing each subspace and the “vector representing the other subspace” is calculated, all become zero as shown in the equations (19a) to (19c).

In this way, if the subspace coding of the equations (15) and (16) is performed on the subspaces S ₁ , S ₂ , S ₃ and S ₄ shown in FIG. Spaces S ₁ , S ₂ , S _3,4 are obtained. In other words, if the codeword matrix C ₃ , ₄ represented by the equation (20) is found, sub-spaces S ₁ , S ₂ , S ₃ , ₄ that are orthogonal to each other can be obtained.

<Realization of sub-space coding>
A case where the subspace coding shown in FIG. 4 is realized in the OFDM system will be described. That is, by performing subspace coding on the subspaces S ₁ , S ₂ , S ₃ , S ₄ using the codeword matrix C ₃ , ₄ , the subspaces S ₁ , S ₂ , S ₃ that are orthogonal to each other. _{, 4} is generated.

FIG. 5 shows an example of sub-space coding in a communication system that transmits data signals using OFDM. In this example, the communication system transmits data signals using two subspace slices. Each slice is realized by a transmission antenna of a MIMO system, for example.

As shown in FIG. 5, each slice transmits a data signal using frequencies f ₁ and f ₂ and time slots t ₁ and t ₂ . That is, slices S1 and S2 use the same time-frequency domain. Therefore, even if the data signal of slice S1 and the data signal of slice S2 are transmitted via different transmission antennas, these data signals may interfere with each other.

Therefore, the communication system generates subspaces orthogonal to each other by the subspace coding shown in FIG. By this subspace encoding, three subspaces S ₁ , S ₂ , S _{3 and 4} shown in FIG. 5 are generated. Specifically, the slice S1 is includes a sub-space S _1, S _2, slice S2 are including subspace S _{3, 4.}

In slice S1, data is transmitted using subcarriers of Δ _t × 2Δ _f. Specifically, subspace S ₁ transmits data symbol d ₁ using time slot t ₁ × frequency band f ₁ to f ₂ . Subspace S ₂ transmits data symbol d ₂ using time slot t ₂ × frequency bands f ₁ to f ₂ .

On the other hand, the slice S2, data is transmitted using subcarriers 2Δ _t × Δ _f. However, the subspaces S _{3 and 4} transmit one data symbol in one symbol time. Specifically, subspaces S _{3 and 4} transmit data symbol d ₃ using time slots t ₁ to t ₂ × frequency band f ₁ , and time slots t ₁ to t ₂ × frequency band f ₂ . The inverted data symbol d ₃ (−d ₃ ) is transmitted. “Inversion” is realized, for example, by inverting the phase of a symbol. As an example, when the phase of d ₃ is π / 2, the phase of −d ₃ is 3π / 2.

Therefore, the subspace coding may include a mapping process for assigning data symbols to corresponding subspaces. In the embodiment shown in FIG. 5, the mapping process assigns data symbol d ₁ to subspace S ₁ (t ₁ × f ₁ to f ₂ ) and assigns data symbol d ₂ to subspace S ₂ (t ₂ × f ₁ to assigned to f _2), assign the data symbol d ₃ into the sub-space _{S 3,4 (t 1 ~ t 2} × f 1), inverted data symbols d ₃ subspace _{S 3,4 (t 1 ~ t 2} × assigned to f ₂ ).

The codeword matrix used in the above subspace coding can be obtained by modifying the above equation (20) in consideration of the subspace based on the subcarrier in the OFDM system. However, each data symbol is required to have the same transmission quality. Therefore, the codeword matrix is determined so that each data symbol is transmitted with the same power. In this case, the codeword matrix is expressed by equation (21).

Thus, the three data symbols d ₁ , d ₂ , d ₃ are represented by four subcarriers d ₁ ^(t) to d ₄ ^{(t) in} the three subspaces S ₁ , S ₂ , S ₃ , 4. Is transmitted. Incidentally, the sub-space S ₁ is composed of a sub-carrier d ₁ ^(t), the sub-space S ₂ is comprised of subcarriers d ₂ ^(t), the sub-space S _{3, 4} subcarrier d ₃ ^(t) and d ₄ ^(t) . Each subcarrier is expressed by equation (22).

When the communication system transmits data by MIMO, for example, subcarriers d ₁ ^(t) to d ₂ ^(t) belonging to slice S1 are transmitted via transmission antenna TX1, and subcarrier d belonging to slice S2 is transmitted. ₃ ^(t) to d ₄ ^(t) may be transmitted via the transmission antenna TX2. Each subcarrier is received by the receiver 20.

The receiver 20 receives the subcarriers d ₁ ^(t) to d ₄ ^(t) using one or a plurality of reception antennas. Here, since the subcarriers d ₁ ^(t) and d ₂ ^(t) are transmitted in different time slots, they are orthogonal to each other. Further, since the subcarriers d ₃ ^(t) and d ₄ ^(t) are transmitted at different frequencies, they are orthogonal to each other. Therefore, the received signals r ₁ to r ₄ obtained by the receiver 20 are expressed by the equation (23). δ ² represents the noise energy received at each subcarrier.

Here, when Expression (23) is transformed using Expression (22), Expression (24) is obtained. Therefore, the receiver 20 can reproduce the data symbols d ₁ and d ₂ from the received signals r ₁ and r ₂ , respectively.

Further, when r ₄ is subtracted from r _{3 in} equation (24), equation (25) is obtained. Therefore, the receiver 20 can reproduce the data symbol d ₃ from the received signals r ₃ and r ₄ .

Finally, the signal-to-noise ratio of each data symbol is expressed by equation (26). P represents signal transmission power.

Thus, if sub-space coding is used in an OFDM system, the number of orthogonal channels can be increased. In this embodiment, the number of channels orthogonal to each other is increased from 2 to 3 due to sub-space coding. Therefore, the capacity of the communication system is increased by 50%.

<Subspace model>
In the following description, in order not to lose generality, the subspace represents the minimum transmission unit. The subspaces can have differently shaped rectangles, for example in the time-frequency plane, but are required to have the same area. In this case, the data transmission capability of each subspace is substantially the same.

In the following description, it is assumed that the communication system transmits data signals using M subspace slices. Each slice has 2 ^M-1 subspaces. Here, the subspaces in the slice are set to be orthogonal to each other. In the signal space, M slices are combined to form a transmission block. Each slice may be realized by a transmission antenna in a MIMO system, for example.

FIG. 6 shows an example of a model of subspace, subspace slice, and transmission block. In OFDM, a subspace as a minimum transmission unit corresponds to a subcarrier that transmits a data symbol. Further, each sub-space slice, in order to transmit the 2 ^M-1 data symbols, having 2 ^M-1 sub-space (i.e., 2 ^M-1 sub-carriers). Each data symbol is generated by a desired modulation scheme (for example, QPSK, 16QAM, 64QAM).

However, the shape of the subspace differs for each slice as shown in FIG. Specifically, the sub-space that is used in the slice 1 (i.e., subcarriers) duration and frequency bandwidth is Δt and 2 ^M-1 × Δf. The time width and frequency bandwidth of the subspace used in slice 2 are 2 × Δt and 2 ^M−2 × Δf. Similarly, the time width and frequency bandwidth of the subspace used in slice n are 2 ^n-1 × Δt and 2 ^Mn × Δf. Therefore, the time width and frequency bandwidth of the subspace used in the slice M are 2 ^M−1 × Δt and Δf.

Thus, the communication system transmits data signals using M subspace slices. Each slice has 2 ^M-1 subspaces. Therefore, the communication system can transmit a maximum of M × 2 ^M−1 data symbols. However, interference may occur between subspaces that are not orthogonal to each other. That is, in the communication system, it is actually difficult to transmit M × 2 ^M−1 data symbols using the model shown in FIG.

<Wavelet sub-space transmission>
In the following description, it is assumed that a signal is transmitted through a channel with low fading and flat frequency characteristics. That is, it is assumed that the channel response is constant in the 1st to ^2M- 1th time regions and the channel response is constant in the 1st to ^2M- 1th frequency regions. In order to simplify the description, the channel response at time t _k and frequency f _i is assumed to be “1” below.

In the OFDM system of LTE (long term evolution) 5G NR (new radio), the above-mentioned channels are, for example, 7.5 kHz, 15 kHz, 30 kHz, 60 kHz, 120 kHz subcarrier frequency intervals, and 16 Tc, 8 Tc, 4 Tc, 2 Tc, This can be realized by generating a Tc subcarrier time interval (see Non-Patent Document 3 described above).

FIG. 7 shows an example of sub-space transmission based on wavelet packets. In this example, transmitter 10 transmits data signals in parallel using M subspace slices. At this time, for each subspace, a data signal is generated from the data symbols using inverse wavelet packet transformation. That is, the waveform of the transmission signal is formed using inverse wavelet packet transformation. In the MIMO system, data signals of M slices are transmitted via different transmission antennas. Also, slices 1 to M follow the model shown in FIG.

The receiver 20 receives a signal via one or a plurality of reception antennas. At this time, the received signal includes data signals of M slices. In addition, noise is added to the received signal. Then, the receiver 20 reproduces a symbol from the received signal using wavelet packet conversion.

FIG. 8 shows a model of noise added to the received signal. η _{k, i} represents reception noise. The energy (or power) of this reception noise is expressed by equation (27). Note that δ ² represents noise energy received in each subcarrier.

<Wavelet subspace coding with 3 slices>
If three subspace slices are used in the model shown in FIG. 6 or FIGS. 7 to 8, the communication system has a maximum of 12 (= 2 ^M−1 × M = 2 ^{3− per} transmission block). can be assigned to ¹ × 3) data symbols. However, in this case, not all subspaces are orthogonal to each other. That is, if 12 data symbols are transmitted in parallel, interference may occur. In other words, in order to remove interference, it is required to find a codeword matrix that guarantees the orthogonality of all subspaces in the signal space S. In the following, the codeword matrix that guarantees the orthogonality of the subspace will be examined mathematically.

FIG. 9 shows an example of a sub-spatial channel model for wavelet packet modulation using three sub-spatial slices. In this example, the transmitter 10 transmits data symbols using three slices 1-3. Slices 1 to 3 correspond to MIMO transmission antennas, for example.

Slice 1 includes the following four subspaces.
S _1,1 : time t ₁ × frequency f ₁ to f ₄
S _1,2 : time t ₂ × frequency f ₁ to f ₄
S _1,3 : time t ₃ × frequency f ₁ to f ₄
S _1,3 : time t ₄ × frequency f ₁ to f ₄
Slice 2 includes the following four subspaces.
S _2,1 : time t ₁ to t ₂ × frequency f ₁ to f ₂
S _2,2 : Time t ₃ to t ₄ × frequency f ₁ to f ₂
S _2,3 : time t ₁ to t ₂ × frequency f ₃ to f ₄
S _2,4 : time t ₃ to t ₄ × frequency f ₃ to f ₄
Slice 3 includes the following four subspaces.
S _3,1 : Time t ₁ to t ₄ × frequency f ₁
S _3,2 : Time t ₁ to t ₄ × frequency f ₂
S _3,3 : time t ₁ to t ₄ × frequency f ₃
S _3,4 : Time t ₁ to t ₄ × frequency f ₄
The receiver 20 receives signals transmitted via the slices 1 to 3 with one or a plurality of antennas. In this case, the received signal R obtained by the receiver 20 is expressed by the following equations (28) and (28a) to (28d).

H represents a codeword matrix. D represents a data symbol transmitted by the transmitter 10. The data symbol d _{k, i} is assigned to the subspace S _{k, i} . N represents a noise component. Z ^T represents the transpose of the matrix Z.

Here, in order to simplify mathematical analysis, equation (28) is transformed to obtain equation (29).

Specifically, the received signal R is represented by _three 1 × 4 matrices R ₁ to R ₃ . The data symbol D is represented by _three 1 × 4 matrices D ₁ to D ₃ . The noise component N is represented by _three 1 × 4 matrices N ₁ to N ₃ . The codeword matrix H is represented by a 4 × 4 matrix A, B, C, I. I represents a unit matrix.

Furthermore, in order to convert the codeword matrix of equation (29) into an upper triangular matrix, matrices X, Y, and E are introduced as shown in equation (30).

By the way, according to the equation (29), the rank of the codeword matrix is 8 instead of 12. Therefore, in the communication system shown in FIG. 9, it is considered preferable to perform sub-space encoding to realize rank = 8 complete orthogonal transmission.

Considering the characteristics of the matrices A, B, C, X, and Y, if data symbols are transmitted in the pattern shown in equation (31), interference between received signals can be completely removed in each subspace. .

The pattern of equation (31) corresponds to the codeword matrix shown in equations (32a) to (32c). That is, codeword matrices C ₁ to C ₃ used for each subspace are obtained.

According to the equation (31), the communication system has eight data symbols (d ₁ ) for each transmission block by twelve subcarriers configured in time slots t ₁ to t ₄ and frequencies f ₁ to f ₄ . _{, 1} , d _1,2 , d _1,3 , d _1,4 , d _2,1 , d _2,2 , d _3,1 , d _3,3 ). Specifically, as shown in FIG. 10, eight data symbols are transmitted.

In slice 1, four data symbols (d _1,1 to d _1,4 ) are allocated to four subcarriers as described below. That is, four data symbols are transmitted by slice 1.
Subcarrier S _1,1 (t ₁ × f ₁ to f ₄ ): d _1,1
Subcarrier S _1,2 (t ₂ × f ₁ to f ₄ ): d _1,2
Subcarrier S _1,3 (t ₃ × f ₁ to f ₄ ): d _1,3
Subcarrier S _1,4 (t ₄ × f ₁ to f ₄ ): d _1,4
In slice 2, two data symbols (d _2,1 , d _2,2 ) are allocated to four subcarriers as described below. That is, two data symbols are transmitted by slice 2. At this time, the same data symbols are assigned to the subcarriers S _2,1 and S _2,3 . However, the phase of the data symbol assigned to subcarrier S _2,3 is inverted with respect to the phase of the data symbol assigned to subcarrier S _2,1 . Similarly, the same data symbol is allocated to the sub-carrier S _{2, 2} and S _{2, 4.} However, the phase of the data symbol assigned to subcarrier S _2,4 is inverted with respect to the phase of the data symbol assigned to subcarrier S _2,2 .
Subcarrier S _2,1 (t ₁ to t ₂ × f ₁ to f ₂ ): d _2,1
Subcarrier S _2,2 (t ₃ to t ₄ × f ₁ to f ₂ ): d _2,2
Subcarrier S _2,3 (t ₁ to t ₂ × f ₃ to f ₄ ): -d _2,1
Subcarrier S _2,4 (t ₃ to t ₄ × f ₃ to f ₄ ): -d _2,2
In slice 3, two data symbols (d _3,1 , d _3,3 ) are allocated to four subcarriers as described below. That is, two data symbols are transmitted by slice 3. At this time, the same data symbols are assigned to the subcarriers S _3,1 and S _3,2 . However, the phase of the data symbol assigned to subcarrier S _3,2 is inverted with respect to the phase of the data symbol assigned to subcarrier S _3,1 . Similarly, the same data symbols are allocated to subcarriers S _3,3 and S _3,4 . However, the data symbols allocated to the subcarriers S _{3, 4} phase is inverted with respect to the data symbols allocated to the subcarriers S _3,3 phases.
Subcarrier S _3,1 (t ₁ to t ₄ × f ₁ ): d _3,1
Subcarrier S _3,2 (t ₁ to t ₄ × f ₂ ): -d _3,1
Subcarrier S _3,3 (t ₁ to t ₄ × f ₃ ): d _3,3
Subcarrier S _3,4 (t ₁ to t ₄ × f ₄ ): -d _3,3
Here, in the equation (30), since B · D ₂ = 0, A · D ₃ = 0, and E · D ₃ = 0, the following equation (33) is obtained.

Therefore, the receiver 20 can reproduce the data symbol D ₁ (d _1,1 to d _1,4 ) from the received signal R ₁ . In addition, since the matrix X is known, the receiver 20 can reproduce the data symbol D ₂ (d _2,1 , d _2,2 ) from the received signal R ₂ . Furthermore, since the matrix Y is known, the receiver 20 can reproduce the data symbol D ₃ (d _3,1 , d _3,3 ) from the received signal R ₃ . At this time, since the subspaces are orthogonal to each other, no interference occurs between the eight data symbols.

Note that the SNR of each received symbol is expressed by equation (34). P represents each data symbol transmission power.

<Generalization of wavelet subspace coding>
Consider the transmission capacity of wavelet subspace coding using M subspace slices. Here, as described with reference to FIG. 6, the maximum number of resources that can be used as a subspace in each slice is 2 ^M−1 . Therefore, in the communication system using the M slices, 2 ^M-1 × M symbols are allocated at the maximum with respect to one transmission block.

However, if subspace coding is performed so that the subspaces are orthogonal to each other, the number of symbols assigned to one transmission block is less than 2 ^M−1 × M. Specifically, in a communication system using three slices, eight data symbols are allocated to one transmission block as shown in FIG. In the communication system using four slices, as shown in FIG. 11, eight data symbols are assigned to slice 1, and four data symbols are assigned to slices 2 to 4, respectively. Therefore, 20 data symbols are assigned to one transmission block.

Generally, as shown in FIG. 12, 2 ^M-1 data symbols are allocated to slice 1, and 2 ^M-2 (= 2 ^M-1 / 2) are assigned to slices 2 to M, respectively. 2) Data symbols are assigned. Therefore, in a communication system using M slices, the number of data symbols transmitted simultaneously in one transmission block is expressed by equation (35).

The number of data symbols represented by the equation (35) is transmitted in mutually orthogonal subspaces. On the other hand, when subspace coding is not performed, the number of subspaces orthogonal to each other is, for example, the same as the number of subspaces in one slice, which is 2 ^M−1 . Therefore, compared to the case where sub-space coding is not performed, the number of symbols that can be transmitted without interference (ie, transmission capacity) is (M + 1) / 2 times by performing sub-space coding. However, in order to obtain the same communication quality, (M + 1) / 2 times the transmission power is required in the case where subspace coding is performed, compared to the case where subspace coding is not performed.

In wavelet subspace coding, subspaces orthogonal to each other are generated from a plurality of given subspaces according to the following rules. In the following description, a plurality of subspaces allocated to the nth slice among M slices are subspace matrices each composed of 2 ^n-1 frequency regions and 2 ^Mn time slots. Shall be represented.

(1) In slice 1, each subspace is encoded with “1”. “1” indicates that the output of the encoding device is the same as the input of the encoding device. That is, in the slice 1, substantially no encoding is performed on a given subspace.

(2) In slice n (n = 2 to M), each subspace arranged in the odd-numbered row is encoded with “1”, and each subspace arranged in the even-numbered row is “−”. 1 ”. “−1” represents a state in which the output of the encoding device is inverted with respect to the input of the encoding device.

In wavelet subspace coding, input symbols are assigned to corresponding subspaces according to the following rules.

(1) In slice 1, 2 ^M-1 data symbols are allocated to the corresponding subspaces.

(2) In slice n (n = 2 to M), the same as the first subspace corresponding to x rows and y columns of the subspace matrix and the second subspace corresponding to x + 1 rows and y columns of the subspace matrix Assign data symbols. This mapping process is executed for all combinations of odd numbers of x = 1 to 2 ⁿ⁻¹ and y = 1 to 2 ^Mn . If x is an odd number, the first subspace is encoded with “1”, and the second subspace is encoded with “−1”.

The mapping rule in slice n (n = 2 to M) is decomposed as follows.
(2a) Assign symbol 1 to the subspace corresponding to the first row and first column of the subspace matrix.
(2b) When the first row and the second column exist, the symbol 2 is assigned to the subspace corresponding to the first row and the second column.
(2c) The processes 2a to 2b are repeated until the last column of the first row. That is, by 2a to 2c, corresponding data symbols are assigned to the respective subspaces in the first row.
(2d) In 2a to 2c, the same symbols as those assigned to the subspaces in the first row are assigned to the corresponding subspaces in the second row, respectively. That is, symbol 1 is assigned to the subspace corresponding to the second row and first column of the subspace matrix. When the second row and the second column exist, the symbol 2 is assigned to the subspace corresponding to the second row and the second column. Similarly, corresponding symbols are assigned up to the last column of the second row. However, the sign of the symbol assigned to each subspace in the second row is inverted with respect to the sign of the corresponding symbol assigned to each subspace in the first row. That is, the inverted symbols obtained by inverting the signs of the data symbols assigned to the subspaces in the first row are assigned to the corresponding subspaces in the second row.
(2e) The processes 2a to 2d are repeated until the last row of the subspace matrix. That is, a data symbol is assigned to each subspace of each odd-numbered row of the subspace matrix, and the corresponding data symbol whose code is inverted is assigned to each subspace of the next row of each odd-numbered row (ie, adjacent even-numbered row) Are assigned to each.

In the above-described embodiment, encoding is performed on slices 2 to M, and encoding is not performed on slice 1. However, the present invention is not limited to this method. That is, the encoding apparatus may perform encoding on slices 1 to M−1 and not perform encoding on slice M. Further, the encoding apparatus may encode each subspace of the odd-numbered row with “−1” and encode each subspace of the even-numbered row with “1”. Further, the encoding apparatus may execute encoding for the other M−1 slices without performing encoding for any one of the slices 1 to M.

In the subspace pair to which the same data symbol is assigned, it may be arbitrarily determined for each subspace pair which subspace is assigned the inverted symbol. That is, the encoding apparatus may assign inverted symbols to subspaces belonging to even rows in a certain subspace pair, and assign inverted symbols to subspaces belonging to odd rows in another subspace pair. However, even in this case, all subspaces are required to be orthogonal to each other.

<Transmitter and receiver>
FIG. 13 shows an example of a transmitter that transmits data using wavelet subspace coding. As shown in FIG. 13, the transmitter 10 includes a serial / parallel converter 11, a subspace encoder 12, and an inverse wavelet packet converter (IWPT) 13. The transmitter 10 may further include other elements not shown in FIG.

In this example, transmitter 10 transmits data using M subspace slices. M is an integer and is not particularly limited, and is, for example, 3, 4 or 5. Then, slice number information indicating the number of slices used by the transmitter 10 (that is, the value of M) is given to the transmitter 10. The slice number information is given from, for example, a user or a network administrator. Here, when a transmission signal is generated using wavelet packet transformation, as shown in FIG. 6, the arrangement of subspaces in each slice is determined according to the number of slices. Therefore, the slice information given to the transmitter 10 specifies the arrangement of subspaces in each slice. The arrangement of subspaces is specified in this example by frequency and time slot. When transmitter 10 transmits data using ^M slices, each slice includes 2 ^M−1 subspaces in a state before encoding. That is, the transmitter 10 uses 2 ^M−1 subcarriers for each slice.

When transmitting data using M slices, the transmitter 10 has 2 ^M−1 +2 ^M−2 (M−1) pieces per transmission block as described with reference to FIG. Subspace coding is performed to transmit data symbols. Therefore, in this case, the serial / parallel converter 11 distributes the ^{2 M-1 +2 M-2} (M-1) data symbols in the slice 1 ~ M. Specifically, it distributes 2 ^M-1 data symbols on the slice 1, distributes the 2 ^M-2 data symbols respectively slices 2 ~ M.

Note that the number of bits transmitted by each data symbol depends on the modulation method. For example, when QPSK is used, each data symbol transmits 2 bits of data, and when 16 QAM is used, each data symbol transmits 4 bits of data.

The sub-space encoder 12 includes encoders 12-1 to 12-M. Encoders 12-1 to 12-M are implemented for slices 1 to M, respectively. In addition, the encoders 12-1 to 12-M each perform sub-space encoding. Each of encoders 12-1 to 12-M assigns data symbols provided from serial / parallel converter 11 to a plurality of subspaces generated by subspace encoding. Here, the operations of the encoders 12-1 to 12-M will be described with reference to FIG. 6 and FIG.

Also, the sub space encoder 12 (or encoders 12-1 to 12-M) has a mapping function. That is, the subspace encoder 12 can convert each input data symbol into electric field information representing the phase / amplitude corresponding to the value according to the designated modulation scheme. The electric field information may represent the phase / amplitude of the symbol as a complex number (in-phase component and quadrature component).

In slice 1, encoder 12-1 encodes all subspaces with “1”. That is, the encoder 12-1 does not substantially perform sub-space encoding. Therefore, the encoder 12-1 assigns the first data symbol (d _1,1 ) to the first subspace and assigns the second data symbol (d _1,2 ) to the second subspace. Similarly, each data symbol is assigned to a corresponding subspace.

In slice 2, encoder 12-2 encodes each subspace belonging to the first row of the subspace matrix with “1”, and each subspace belonging to the second row with “−1”. . Therefore, the encoder 12-2 assigns the first data symbol (d _2,1 ) to the first subspace of the first row, inverts the sign of the same data symbol (d _2,1 ), and outputs 2 Assign to the first subspace of the row. Similarly, the same data symbol is assigned to the same time slot in the first row and the second row. However, the signs of the data symbols assigned to the same time slot in the first row and the second row are reversed from each other.

Inversion of the sign of the data symbol is realized, for example, by inverting the phase of the transmission signal. In this case, the inversion of the code of the data symbol is realized by the mapping function of the encoder 12-2. For example, when the phase of the data symbol d _2,1 assigned to the first subspace in the first row is π / 2, the data symbol d _2,1 assigned to the first subspace in the second row The phase is 3π / 2.

In slice 3, the encoder encodes the subspaces belonging to the first and third rows with “1”, respectively, and encodes the subspaces belonging to the second and fourth rows with “−1”, respectively. To do. Therefore, the encoder assigns the first data symbol (d _3,1 ) to the first subspace of the first row, inverts the sign of the same data symbol (d _3,1 ), and Assign to the first subspace. Similarly, the same data symbol is assigned to the same time slot in the first row and the second row. However, the signs of the data symbols assigned to the same time slot in the first row and the second row are reversed from each other. Further, data symbols are assigned to the subspaces belonging to the third and fourth rows in the same manner.

In slice M, encoder 12 -M encodes subspaces belonging to odd rows with “1”, and encodes subspaces belonging to even rows with “−1”. Therefore, the encoder 12-M assigns the _first data symbol (d _{M, 1} ) to the subspace of the first row, inverts the sign of the same data symbol (d _{M, 1} ), and Assign to subspace. Similarly, data symbols are assigned to the remaining subspaces.

The IWPT 13 includes converters 13-1 to 13-M. Converters 13-1 to 13-M are implemented for slices 1 to M, respectively. Then, converters 13-1 to 13-M generate transmission signals by inverse wavelet packet conversion based on the data symbols assigned to the subspaces by corresponding encoders 12-1 to 12-M, respectively. .

Specifically, when a data symbol d _{k, i} is given, the IWPT 13 is a resource to which the data symbol d _{k, i} is allocated using inverse wavelet packet transformation, and the data symbol d _{k, i} Generate a signal representing the phase / amplitude of. For example, when the electric field information indicating the phase / amplitude of the data symbol is given, the IWPT 13 performs inverse wavelet packet conversion on the electric field information to generate a transmission signal. Wavelet packet conversion is as described with reference to equations (1) to (4).

The transmitter 10 outputs a signal generated for each slice by the IWPT 13 (converters 13-1 to 13-M). At this time, the transmitter 10 may combine and output a plurality of signals generated by the converters 13-1 to 13-M. In the MIMO system, the transmitter 10 may output the signals generated by the converters 13-1 to 13-M via the corresponding transmission antennas.

FIG. 14 shows an example of a receiver that receives a signal generated using wavelet subspace coding. As shown in FIG. 14, the receiver 20 includes a wavelet packet converter (WPT) 21 and a sub-spatial decoder (SS decoder) 22. Note that the receiver 20 may further include other elements not shown in FIG.

The receiver 20 receives a signal transmitted from the transmitter 10 shown in FIG. At this time, noise n (t) is added to the signal transmitted from the transmitter 10 in the transmission path. This noise n (t) is added at each frequency and in each time slot, for example, as shown in FIG.

The WPT 21 includes converters 21-1 to 21-M. Converters 21-1 to 21-M are implemented for slices 1 to M, respectively. Then, the converters 21-1 to 21-M regenerate the received signals by executing the inverse processing of the converters 13-1 to 13-M, respectively. That is, the converters 21-1 to 21-M reproduce the received signals by executing wavelet packet conversion corresponding to the converters 13-1 to 13-M, respectively. For example, in the case of M = 3, the received signal r shown in Equation (28) is obtained.

The sub spatial decoder 22 reproduces data symbols based on the received signals reproduced by the converters 21-1 to 21-M. For example, in the case of M = 3, the sub-spatial decoder 22 performs the operations shown in the equations (28) to (33) and reproduces the data D from the received signal R. The codeword matrix H is assumed to be known.

<Hardware configuration>
FIG. 15 shows an example of the hardware configuration of the communication apparatus. The communication device 30 includes a transmitter and a receiver. The transmitter corresponds to, for example, the transmitter 10 illustrated in FIG. The receiver corresponds to, for example, the receiver 20 illustrated in FIG. When the communication device 30 is used in a wireless communication system, the communication device 30 includes an antenna. In the MIMO system, the communication device 30 includes a plurality of transmission antennas and a plurality of reception antennas.

The communication device 30 includes a processor 31 and a memory 32 as shown in FIG. The memory 32 stores a program describing a function for generating a transmission signal based on transmission data and a function for reproducing data from the reception signal. The memory 32 can also temporarily store data.

The processor 31 implements a function of generating a transmission signal based on an input data symbol and a function of reproducing a data symbol from a reception signal by executing a program stored in the memory 32. Note that the serial / parallel converter 11, the sub-space encoder 12, and the inverse wavelet packet converter 13 shown in FIG. In addition, the wavelet packet converter 21 and the sub-spatial decoder 22 shown in FIG. However, some of the functions of the serial / parallel converter 11, the sub space encoder 12, the inverse wavelet packet converter 13, the wavelet packet converter 21, and the sub space decoder 22 may be realized by a hardware circuit. .

<Performance>
In a channel with only AWGN (additive white gaussian noise), Shannon capacity and wavelet subspace code are compared in consideration of band efficiency modulation and power efficiency modulation. The Shannon channel capacity C _s is expressed by equation (36). The average received power (watts) is indicated. W represents a bandwidth (Hz). N ₀ represents the noise power spectral density (watts / Hz).

Here, when the transmission power P in Expression (36) is multiplied by (M + 1) / 2 times, the Shannon channel capacity C _s is expressed by Expression (37).

On the other hand, if the signal is transmitted at the same power as the expression (37), channel capacity C _Wssc based on wavelet subspace coding is expressed by equation (38).

Then, the gain ρ resulting from the wavelet subspace coding (that is, the gain of the channel capacity based on the wavelet subspace coding with respect to the Shannon channel capacity) is calculated by the equation (39). M represents the maximum number of slices. Γ represents the SNR of the symbol. Specifically, Γ corresponds to P / (N ₀ W).

FIG. 16 represents channel capacity gain with respect to the number of slices and SNR in a communication system in which subspace coding is performed. Each characteristic shown in FIG. 16 represents a case where the SNR of the symbol is 0, 5, 10, 15, 20 dB. According to this embodiment, the following characteristics can be obtained.
(1) The channel capacity gain increases linearly with the number of slices. That is, sub-space coding provides a linear relationship between transmission power and channel capacity.
(2) According to sub-space coding, the higher the SNR of a data symbol, the greater the channel capacity gain.
(3) Theoretically, if the number of slices becomes infinite, the channel capacity gain also becomes infinite.

Thus, in the subspace coding according to the embodiment of the present invention, new subspaces orthogonal to each other are generated from the given subspace. At this time, the number of newly generated subspaces orthogonal to each other is equal to or greater than the number of subspaces orthogonal to each other included in the given subspace. Therefore, the number of data symbols transmitted without interference increases and the transmission capacity increases. In addition, in sub-space coding, a codeword matrix is used so that a linear relationship is obtained between transmission power and channel capacity. Further, sub-space coding can be applied to wired communication, wireless communication, and optical fiber communication.

10 Transmitter 11 Serial / Parallel Converter 12 Sub-Space Encoder 12-1 to 12-M Encoder 13 Inverse Wavelet Packet Converter (IWPT)
13-1 to 13-M Converter 20 Receiver 21 Wavelet packet converter (WPT)
21-1 to 21-M Converter 22 Sub-spatial decoder 30 Communication device 31 Processor 32 Memory

Claims (10)

1. An encoding device mounted on a communication device that transmits data in a predetermined signal space,
   The number of mutually orthogonal subspaces obtained by encoding from a plurality of subspaces specified in the signal space including subspaces that are not orthogonal to each other is orthogonal to each other among the specified subspaces. An encoding apparatus comprising: an encoding processing unit that generates a plurality of subspaces orthogonal to each other so as to be equal to or greater than the number of subspaces.
2. The encoding apparatus according to claim 1, wherein each subspace represents a combination of a frequency band and a time slot.
3. The communication device is configured to transmit data using M slices in the signal space;
   The signal space is composed of frequency and time;
   Each slice is assigned 2 ^M-1 subspaces,
   The 2 ^M-1 subspaces allocated to the n (n = 1 to M) th slice of the M slices divide the signal space into 2 ^n-1 in the frequency domain, and the time domain in is represented by a matrix obtained by dividing the 2 ^Mn pieces,
   The encoding processing unit includes:
   In the first slice, each transmission symbol is assigned to a corresponding subspace,
   In each of the second to Mth slices, a transmission symbol is assigned to a first subspace corresponding to x rows and y columns of the matrix, and a code is assigned to a second subspace corresponding to x + 1 rows and y columns of the matrix. By assigning the inverted transmission symbols, a process of generating a new subspace from the first subspace and the second subspace is performed by using an odd number of x = 1 to 2 ⁿ⁻¹ and y = The encoding apparatus according to claim 1, wherein the encoding apparatus is executed for all combinations with 1 to 2 ^Mn .
4. The first slice is given 2 ^M-1 transmitted symbols,
   The encoding apparatus according to claim 3, wherein 2 ^M-2 transmission symbols are given to each of the second to Mth slices.
5. An encoding method used in a communication device that transmits data in a predetermined signal space,
   The number of mutually orthogonal subspaces obtained by encoding from a plurality of subspaces specified in the signal space including subspaces that are not orthogonal to each other is orthogonal to each other among the specified subspaces. A plurality of subspaces orthogonal to each other are generated so that the number of subspaces is equal to or greater than the number of subspaces.
6. The communication device is configured to transmit data using M slices in the signal space;
   The signal space is composed of frequency and time;
   Each slice is assigned 2 ^M-1 subspaces,
   The 2 ^M-1 subspaces allocated to the n (n = 1 to M) th slice of the M slices divide the signal space into 2 ^n-1 in the frequency domain, and the time domain It is represented by a matrix obtained by dividing into 2 ^Mn by
   In the first slice, each transmission symbol is assigned to a corresponding subspace,
   In each of the second to Mth slices, a transmission symbol is assigned to a first subspace corresponding to x rows and y columns of the matrix, and a code is assigned to a second subspace corresponding to x + 1 rows and y columns of the matrix. By assigning the inverted transmission symbols, a process of generating a new subspace from the first subspace and the second subspace is performed by using an odd number of x = 1 to 2 ⁿ⁻¹ and y = ^6. The encoding method according to claim 5, wherein the encoding method is executed for all combinations with 1 to 2 ^Mn .
7. A communication device for transmitting data in a predetermined signal space,
   The number of mutually orthogonal subspaces obtained by encoding from a plurality of subspaces specified in the signal space including subspaces that are not orthogonal to each other is orthogonal to each other among the specified subspaces. An encoding processing unit that generates a plurality of subspaces orthogonal to each other so that the number of subspaces is equal to or greater than
   A signal generation unit that generates a transmission signal based on a plurality of subspaces generated by the encoding processing unit;
   A communication device comprising:
8. The communication device is configured to transmit data using M slices in the signal space;
   The signal space is composed of frequency and time;
   Each slice is assigned 2 ^M-1 subspaces,
   The 2 ^M-1 subspaces allocated to the n (n = 1 to M) th slice of the M slices divide the signal space into 2 ^n-1 in the frequency domain, and the time domain It is represented by a matrix obtained by dividing into 2 ^Mn by
   The encoding processing unit includes:
   In the first slice, each transmission symbol is assigned to a corresponding subspace,
   In each of the second to Mth slices, a transmission symbol is assigned to a first subspace corresponding to x rows and y columns of the matrix, and a code is assigned to a second subspace corresponding to x + 1 rows and y columns of the matrix. By assigning the inverted transmission symbols, a process of generating a new subspace from the first subspace and the second subspace is performed by using an odd number of x = 1 to 2 ⁿ⁻¹ and y = Run for all combinations with 1-2 ^Mn ,
   The communication according to claim 7, wherein the signal generation unit generates a transmission signal using wavelet packet transform based on a plurality of subspaces generated by the encoding processing unit for each slice. apparatus.
9. When transmitting data symbols in a predetermined signal space, the number of mutually orthogonal subspaces obtained by encoding from a plurality of subspaces specified in the signal space, including subspaces that are not orthogonal to each other, An encoding processing unit that generates a plurality of subspaces that are orthogonal to each other so that the number of subspaces that are orthogonal to each other is equal to or greater than the number of subspaces that are specified, and a plurality of generated by the encoding processing unit A communication device that communicates with a transmitter comprising: a signal generation unit that generates a data signal that transmits the data symbols based on a subspace of
   A receiving unit for receiving the data signal;
   A decoder that reproduces the data symbols from the data signal received by the receiver;
   A communication device comprising:
10. A communication system for transmitting data symbols from a first communication device to a second communication device in a predetermined signal space,
    The first communication device is:
    The number of mutually orthogonal subspaces obtained by encoding from a plurality of subspaces specified in the signal space including subspaces that are not orthogonal to each other is orthogonal to each other among the specified subspaces. An encoding processing unit that generates a plurality of subspaces orthogonal to each other so as to be equal to or greater than the number of subspaces to be
    A signal generation unit that generates a data signal for transmitting the data symbols based on a plurality of subspaces generated by the encoding processing unit,
    The second communication device is:
    A receiving unit for receiving the data signal;
    And a decoder that reproduces the data symbol from the data signal received by the receiving unit.

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