WO2008147138A1

WO2008147138A1 - Method of transmitting and receiving a signal and apparatus for transmitting and receiv0ing a signal

Info

Publication number: WO2008147138A1
Application number: PCT/KR2008/003054
Authority: WO
Inventors: Woo Suk Ko; Sang Chul Moon
Original assignee: Lg Electronics Inc.
Priority date: 2007-05-30
Filing date: 2008-05-30
Publication date: 2008-12-04
Also published as: KR20080105355A

Abstract

A method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal are disclosed. More particularly, a method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal, which are capable of increasing a data transfer rate, are disclosed. It is possible to arrange symbols according to an optimal symbol mapping method such that gaps between neighboring symbols are equalized, modulate the symbols, and transmit the modulated symbols. Accordingly, it is possible to improve the data transfer rate on the basis of a SNR gain and improve signal transmission/reception performance of a transmitting/receiving system.

Description

METHOD OF TRANSMITTING AND RECEIVING A SIGNAL AND APPARATUS FOR TRANSMITTING AND RECEIVOING A

SIGNAL

Technical Field

[1] The present invention relates to a method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal, and more particularly toa method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal, which are capable of increasing a data transfer rate. Background Art

[2] As a digital broadcasting technology has been developed, a broadcasting signal including a high definition (HD) moving image and high-quality digital sound can be transmitted/received. With continuous development of a compression algorithm and high performance of hardware, a digital broadcasting system has been rapidly developed. A digital television (DTV) system can receive a digital broadcasting signal and provide a variety of supplementary services to users as well as a video signal and an audio signal.

[3] As a digital broadcast has come into wide use, a demand for a service such as a more excellent video and audio signal has been increased and the size of data or the number of broadcasting channels, which are desired by users, has been gradually increased. Disclosure of Invention Technical Problem

[4] However, in the existing method of transmitting/receiving a signal, the quantity of transmitted/received data or the number of broadcasting channels cannot be increased. Accordingly, there is a need for a new method of transmitting/receiving a signal, which is capable of improving channel bandwidth efficiency and reducing cost consumed for constructing a network for transmitting/receiving the signal, compared with the existing method of transmitting/receiving the signal.

[5] An object of the present invention is to provide a method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal, which are capable of increasing a data transfer rate and using the existing network for transmitting/receiving the signal. Technical Solution

[6] The object of the present invention can be achieved by providing an apparatus for transmitting a signal, the apparatus including, a forward error correction (FEC) encoder which FEC-encodes input data, an interleaver which interleaves the FEC- encoded data, a symbol mapper which maps the interleaved data to symbol data according to a symbol mapping method for arranging symbols such that gaps between neighboring symbols in a constellation are equalized; and a transmitter which modulates and transmits the mapped symbol data, and a method of transmitting a signal.

[7] The symbol mapper may enable three neighboring symbols in the constellation to be arranged in a regular triangle shape.

[8] In another aspect of the present invention, provided herein is an apparatus for receiving a signal, the apparatus including, a demodulator which demodulates the received signal, a frame parser which outputs data obtained by parsing a frame of the demodulated signal, a symbol demapper which demaps symbols and outputs the demapped symbols if symbol data included in the data output from the frame parser is symbol data having the same gap between neighboring symbols, a deinterleaver which deinterleaves the data output from the symbol demapper, and a forward error corre ction (FEC) decoder which FEC-decodes the deinterleaved data, and a method of receiving a signal.

[9] The symbol mapper may enable three neighboring symbols in the constellation to be arranged in a regular triangle shape.

[10] In another aspect of the present invention, provided herein is an apparatus for receiving a signal, the apparatus including, a demodulator which demodulates the received signal, a frame parser which outputs data obtained by parsing a frame of the demodulated signal, a symbol demapper which demaps symbols and outputs the demapped symbols if symbol data included in the data output from the frame parser is symbol data having the same gap between neighboring symbols, a deinterleaver which deinterleaves the data output from the symbol demapper, and a forward error correction (FEC) decoder which FEC-decodes the deinterleaved data, and a method of receiving a signal.

[11] The symbol demapper may include a plurality of decision units which decide whether the symbol data is positioned in a specific region of decision boundaries, and a plurality of rotation units which rotate the decision boundaries decided by the decision units.

[12] Any one of the plurality of decision units may include a first decision unit which decides whether or not the symbol data is positioned in a rectangular region formed by two sides of a hexagonal region included in decision boundary regions.

[13] Any one of the plurality of decision units may include a second decision unit which decides whether or not the symbol data is included in a region excluding the rectangular region formed by the two sides of the hexagonal region included in the decision boundary regions from the hexagonal region.

Advantageous Effects

[14] According to a method of transmitting/receiving a signal and an apparatus for transmitting/receiving a signal of the present invention, it is possible to facilitate the switching of a signal transmitting/receiving system using the existing signal transmitting/receiving network and reduce cost.

[15] In addition, it is possible to improve a data transfer rate such that a SNR gain can be obtained and estimate a channel with respect to a transmission channel having a long delay spread property so as to increase a signal transmission distance by. Accordingly, it is possible to improve the signal transmission/reception performance of the transmitting/receiving system.

Brief Description of the Drawings

[16] FIG. 1 is a schematic block diagram showing an apparatus for transmitting a signal according to an embodiment of the present invention.

[17] FIG. 2 is a schematic view showing the positions of points of an optimal constellation according to an embodiment of the present invention.

[18] FIG. 3 is a flowchart illustrating a method of deciding points of an optimal constellation according to an embodiment of the present invention.

[19] FIG. 4 is a schematic view showing an optimal constellation having 16 points according to an embodiment of the present invention.

[20] FIG. 5 is a schematic view showing an optimal constellation having 64 points according to an embodiment of the present invention.

[21] FIG. 6 is a schematic view showing an optimal constellation having 256 points according to an embodiment of the present invention.

[22] FIG. 7 is a schematic view showing another optimal constellation having 256 points according to an embodiment of the present invention.

[23] FIG. 8 is a block diagram showing an apparatus for receiving a signal according to an embodiment of the present invention.

[24] FIG. 9 is a schematic block diagram showing decision boundaries of the optimal constellation having 64 points.

[25] FIG. 10 is a schematic block diagram showing a symbol demapper for demapping a received optimal constellation symbol according to an embodiment of the present invention.

[26] FIG. 11 is a schematic block diagram showing another symbol demapper for demapping a received optimal constellation symbol according to an embodiment of the present invention.

[27] FIG. 12 is a schematic view showing a process of demapping a received optimal con- stellation symbol according to an embodiment of the present invention.

[28] FIG. 13 is a schematic view showing a process of demapping a received optimal constellation symbol of an edge region according to an embodiment of the present invention. [29] FIG. 14 is a schematic block diagram showing another example of an apparatus for transmitting a signal according to an embodiment of the present invention. [30] FIG. 15 is a schematic block showing a forward error correction encoder according to an embodiment of the present invention. [31] FIG. 16 is a view showing an interleaver for interleaving input data according to an embodiment of the present invention. [32] FIG. 17 is a schematic block diagram showing a linear pre-coder according to an embodiment of the present invention. [33] FIGs. 18 to 20 are views showing a code matrix for dispersing input data according to an embodiment of the present invention. [34] FIG. 21 is a view showing the structure of a transmission frame according to an embodiment of the present invention. [35] FIG. 22 is a schematic block diagram showing an apparatus for transmitting a signal using a plurality of transmission paths according to an embodiment of the present invention. [36] FIGs. 23 to 27 are views showing examples of a 2x2 code matrix for dispersing input symbols according to an embodiment of the present invention. [37] FIG. 28 is a view showing an example of an interleaver according to an embodiment of the present invention. [38] FIG. 29 is a view showing a detailed example of the interleaver of FIG. 28 according to an embodiment of the present invention. [39] FIG. 30 is a view showing an example of a multi-input/output method according to an embodiment of the present invention. [40] FIG. 31 is a view showing the structure of a pilot symbol interval according to an embodiment of the present invention. [41] FIG. 32 is a view showing another structure of the pilot symbol interval according to an embodiment of the present invention. [42] FIG. 33 is a schematic block diagram showing another example of an apparatus for receiving a signal according to an embodiment of the present invention. [43] FIG. 34 is a schematic block diagram showing an example of a linear pre-coding decoder according to an embodiment of the present invention.

[44] FIG. 35 is a schematic block diagram showing another example of the linear pre- coding decoder according to an embodiment of the present invention. [45] FIGs. 36 to 38 are views showing examples of a 2x2 code matrix for restoring dispersed symbols according to an embodiment of the present invention. [46] FIG. 39 is a schematic block diagram showing a forward error correction decoder according to an embodiment of the present invention. [47] FIG. 40 is a schematic block diagram showing an apparatus for receiving a signal using a plurality of reception paths according to an embodiment of the present invention. [48] FIG. 41 is a view showing an example of a multi-input/output decoding method according to an embodiment of the present invention. [49] FIG. 42 is a view showing a detailed example of FIG. 40 according to an embodiment of the present invention. [50] FIG. 43 is a flowchart illustrating a method of transmitting a signal according to an embodiment of the present invention. [51] FIG. 44 is a flowchart illustrating a method of receiving a signal according to an embodiment of the present invention.

Best Mode for Carrying Out the Invention [52] A method of transmitting/receiving a signal and an apparatus for transmitting/ receiving a signal according to the present invention will be described in detail with reference to the accompanying drawings. [53] FIG. 1 is a schematic block diagram showing an apparatus for transmitting a signal according to an embodiment of the present invention. The signal transmitting apparatus of FIG. 1 may be a signal transmitting system for transmitting video data such as a broadcasting signal, for example, a signal transmitting system according to a digital video broadcasting (DVB) system. The signal transmitting system according to the embodiment of the present invention now will be described with reference to FIG. 1. [54] The embodiment of FIG. 1 includes an outer encoder 100, an inner encoder 110, a first interleaver 120, a symbol mapper 130, a linear pre-coder 140, a second interleaver

150, a frame builder 160, a modulator 170 and a transmitter 180. [55] The outer coder 100 and the inner coder 110 code respective input signals and output the encoded signals such that an error generated in transmitted data is detected and corrected in the receiving apparatus. That is, the outer coder 100 and the inner coder

110 configure a forward error correcting (FEC) encoder. [56] The outer coder 100 codes the input data in order to improve transmission performance of the input signal, and the inner coder 110 codes the signal to be transmitted again in order to prevent an error from occurring in the transmitted signal.

The types of the encoders vary according to coding methods used in the signal transmission system. [57] The first interleaver 120 shuffles the data output from the inner encoder 110 to random positions so as to become robust against a burst error which occurs in the data when the signal output from the inner coder 110 is transmitted. For example, the first interleaver 120 can use a convolution interleaver or a block interleaver. The interleaving method of the first interleaver 120 may be changed according to the method used in the signal transmitting system.

[58] The symbol mapper 130 maps the data interleaved by the first interleaver 120 to a symbol according to the transmitting method. For example, as the mapping method of the symbol mapper 130, a quadrature amplitude modulation (QAM), a quadrature phase shift keying (QPSK), an amplitude phase shift keying (APSK) or a pulse amplitude modulation (PAM) may be used. In the present embodiment, an optimal constellation mapping method is used as the symbol mapping method of the symbol mapper 130.

[59] The symbol mapper 130 maps the input data to symbols according to the optimal constellation mapping method having a predetermined number of points and outputs the symbols. A detailed example thereof will be described with reference to FIGs. 2 to 7.

[60] The linear pre-coder 140 disperses input symbol data into several pieces of output symbol data so as to decrease a probability that all information is lost due to fading when experiencing frequency- selective fading of a channel.

[61] The second interleaver 150 interleaves the symbol data output from the linear pre- coder 140 again such that the symbol data does not experience the same frequency- selective fading. The second interleaver 150 may use a convolution interleaver or a block interleaver.

[62] The frame builder 160 inserts a pilot signal into a data interval to build a frame such that the interleaved signal is modulated by an orthogonal frequency division multiplex (OFDM).

[63] The modulator 170 inserts a guard interval into the data output from the frame builder 160 and modulates the inserted data such that the data is transmitted in a state of being carried in OFDM sub carriers. The transmitter 180 converts the digital signal having the guard interval and the data interval, which is output from the modulator 170, into an analog signal and transmits the converted analog signal.

[64] FIG. 2 is a schematic view showing the positions of points of an optimal constellation according to an embodiment of the present invention. For optimal constellation mapping, constellation points shown in FIG. 2 may be used. The constellation points indicate the positions of the symbols mapped in the constellation. The numerals of the constellation points indicate powers of the points.

[65] The x-axis (horizontal axis of y=0) values of the optimal constellation points may be odd numbers (1, 3, 5, ...) or even numbers (2, 4, 6, ...) and the y-axis (vertical axis of x=0) values thereof may be an integral multiple of "3

[66] For example, the points positioned on the x axis have the odd values of 1, 3, 5, ... and the powers thereof are 1, 9, 25. The points positioned on the y axis have the values of

^

3 V 3

5V^

... and the powers thereof are 3, 27, 75, .... In the point having a power of 13, the x- axis value is 1 and the y-axis value is

2V 3

. In the point having a power of 7, the x-axis value is 2 and the y-axis value is "3

[67] As shown, the transmission power of the symbols can be efficiently used by arranging points close to a circle form and arranging possible points far from a DC position. If the symbols are arranged according to the shown constellation, gaps between neighboring symbols are equalized and thus a SNR gain can be obtained. Accordingly, it is possible to minimize the transmission power of the symbols by arranging the symbols in a circle form centered on a DC (an original point of the constellation) according to the shown constellation. Hereinafter, a constellation in which the symbols are arranged such that the gaps between neighboring symbols are equalized is called an optimal constellation. In the example of FIG. 2, three neighboring symbols are arranged in a regular triangle form in the constellation.

[68] Instead of the positions of the points shown in FIG. 2, the positions obtained by symmetrically arranging the points with respect to the x axis, the y axis or the original point may be used. Alternatively, the positions obtained by rotating the points about the original point by any angle may be used. This may vary according to implementation examples.

[69] FIG. 3 is a flowchart illustrating a method of deciding points of an optimal con- stellation according to an embodiment of the present invention. A necessary number of optimal constellation points are obtained from the constellation points shown in FIG. 2.

[70] First, constellation points having a smallest power are selected from the constellation points shown in FIG. 2 (S300). The number of constellation points selected is compared with the number of necessary constellation points (S310). If the number of constellation points selected is smaller than the number of necessary constellation points, the step S300 is performed again such that constellation points having a smallest power are selected from the points which are not previously selected. If the number of constellation points selected is larger than the number of necessary constellation points, the constellation points are removed in descending order of the power by the excessive number of points (S320). A desired number of constellation points can be obtained by the above-described process, and the input data can be mapped to symbol data using the obtained constellation points.

[71] FIGs. 4 to 7 are schematic views showing optimal constellations having points selected by the above-described process, according to the embodiments of the present invention. That is, FIGs. 4 to 7 are schematic views showing the positions of optimal constellations having 16 points, 64 points, 256 points and 256 points, respectively. Accordingly, FIG. 4 shows 16QAM, FIG. 5 shows 64QAM and FIGs. 6 and 7 show 256QAM. The gain of the transmission power can be obtained.

[72] FIG. 6 shows another embodiment having positions different from the constellation point positions shown in FIG. 2, in which a symbol is arranged on the DC or symbols are arranged very close to the DC. In contrast, FIG. 7 shows an example in which 256 symbols are arranged such that a symbol is not arranged on the DC.

[73] As described above, instead of the point positions of FIGs. 4 to 7, the positions obtained by symmetrically arranging points positioned according to the method described with reference to FIG. 3 with respect to the x axis, the y axis or the original point may be used. Alternatively, the positions obtained by rotating the points about the original point by any angle may be used. This may vary according to implementation examples.

[74] FIG. 8 is a schematic block diagram showing an apparatus for receiving a signal according to an embodiment of the present invention. The embodiment of FIG. 8 is an apparatus for receiving a broadcasting signal according to a DVB system.

[75] The embodiment of FIG. 8 includes a receiver 800, a synchronizer 810, a demodulator 820, a frame parser 830, a first deinterleaver 840, a linear pre-coding decoder 850, a symbol demapper 860, a second deinterleaver 870, an inner decoder 880 and an outer decoder 890.

[76] The receiver 800 down-converts the frequency band of a received RF signal, converts the signal into a digital signal, and outputs the digital signal. The synchronizer 810 acquires synchronization of the received signal output from the receiver 800 in a frequency domain and a time domain and outputs the synchronization. The synchronizer 810 may use an offset result of the data output from the demodulator 820 in the frequency domain, for acquiring the synchronization of the signal in the frequency domain.

[77] The demodulator 820 demodulates the received data output from the synchronizer

810 and removes the guard interval. The demodulator 820 may convert the received data into the frequency domain and decode data values dispersed into the subcarriers to the values allocated to subcarriers. The frame parser 830 may output symbol data of the data symbol interval excluding the pilot symbol according the frame structure of the signal demodulated by the demodulator 820.

[78] The first deinterleaver 840 deinterleaves the data stream output from the frame parser

830 and restores the data into the sequence of the data before interleaving. The first deinterleaver 840 deinterleaves the data stream according to a method corresponding to the interleaving method of the second interleaver 150 shown in FIG. 1 and restores the sequence of the data stream.

[79] The linear pre-coding decoder 850 performs an inverse process of the linear pre- coding process of dispersing the data in the apparatus for transmitting the signal and restores original data dispersed in the data input to the linear pre-coding decoder 850.

[80] The symbol demapper 860 may restore the symbol data restored by the linear pre- coding decoder 850 into a bit stream. As the symbol demapping method, a method corresponding to the mapping method used by the symbol mapper 130 included in the apparatus for transmitting the signal is used. Hereinafter, for convenience of description, for example, it is assumed that symbol data is mapped by the symbol mapper 130 of FIG. 1 according to the optimal constellation mapping method having 64 points. The number of points is only exemplary, for convenience of description.

[81] FIG. 9 is a schematic block diagram showing decision boundaries of the optimal constellation having 64 points. The symbol demapper 860 demaps the received symbol data using the decision boundaries shown in FIG. 9. In the optimal constellation mapping method, the constellation has a honeycomb shape in order to efficiently use the transmission power, and, in the symbol demapper 860, each symbol has a hexagonal decision boundary as shown in FIG. 9. Each of symbols corresponding to points positioned at outermost sides has a decision boundary of which one side is opened, instead of the hexagonal decision boundary.

[82] If it is recognized that the input symbol data is positioned in a specific hexagon of the decision boundary shown in FIG. 9, the symbol demapper 860 demaps the input symbol data to a symbol of the point corresponding to the specific hexagon.

[83] FIG. 10 is a schematic block diagram showing the symbol demapper for demapping a received optimal constellation symbol according to an embodiment of the present invention.

[84] The symbol demapper 860 may demap the symbol using all the decision boundaries of the optimal constellation shown in FIG. 9 at a time or may demap the symbol using a rectangular decision boundary like the symbol demapper of FIG. 10 or 11.

[85] The symbol demapper of FIG. 10 includes a decision unit 1000, a second decision unit 1002, a first rotation unit 1004, a third decision unit 1006, a fourth decision unit 1008, a second rotation unit 1010, a fifth decision unit 1012, a sixth decision unit 1014, and a bit converter 1016.

[86] When the symbol data is input to the symbol demapper 860, the first decision unit

1000 decides whether the input symbol data is positioned in a rectangular decision boundary region using the rectangular decision boundary region formed by two opposite sides of each of hexagonal decision boundary regions.

[87] The second decision unit 1002 decides whether the input symbol data is positioned in a constellation edge region, that is, in an edge region, of which one side is opened, in all the decision boundaries shown in FIG. 9. The second decision unit 1002 decides whether the symbol is positioned in a decision boundary region denoted by a solid line among the edge regions of the constellation, which will be described in detail with reference to FIG. 13. The first decision unit 1000 and the second decision unit 1002 decide the position of the input symbol data using the decision boundaries which are not rotated.

[88] The first rotation unit 1004 rotates the decision boundaries used in the first decision unit 1000 and the second decision unit 1002. For example, the first rotation unit 1004 rotates the decision boundaries by 60 degrees in order to decide the symbol like the decision boundaries of Fig. 9.

[89] The data output from the first rotation unit 1004 is input to the third decision unit

1006. The third decision unit 1006 decides whether the input symbol data is positioned in the rectangular decision boundary region using the rectangular decision boundary region formed by two opposite sides of the hexagonal decision boundary region among all the decision boundary regions rotated by 60 degrees. The fourth decision unit 1008 decides whether the input symbol data is positioned in the constellation edge region. Referring to FIG. 13, the fourth decision unit 1008 decides whether the symbol is positioned in a decision boundary region denoted by a dashed dotted line, among the constellation edge regions, which will be described in detail with reference to FIG. 13.

[90] The third decision unit 1006 and the fourth decision unit 1008 decide the position of the input symbol data using the decision boundaries rotated one time (decision boundaries rotated by 60 degrees).

[91] The second rotation unit 1010 rotates all the decision boundaries used in the third decision unit 1006 and the fourth decision unit 1008. The second rotation unit 1010 rotates the decision boundaries by a predetermined angle (for example, the same angle as the first rotation unit 1004) in the same rotation direction as the first rotation unit 1004. The data output from the second rotation unit 101 is input to the fifth decision unit 1012. The fifth decision unit 1012 decides whether the input symbol data is positioned in the rectangular decision boundary using the rectangular decision boundaries formed by two opposite sides in each of the hexagonal decision boundary regions among all the decision boundary regions rotated by 60 degrees again.

[92] The sixth decision unit 1014 decides whether the input symbol data is positioned in the constellation edge region. Referring to FIG. 13, the sixth decision unit 1014 decides whether the symbol is positioned in a decision boundary region denoted by a dotted line, among the constellation edge regions, which will be described in detail w ith reference to FIG. 13. The fifth decision unit 1012 and the sixth decision unit 1014 may decide the position of the input symbol data using the decision boundaries rotated two times, that is, using the decision boundaries rotated from the original decision boundaries by 120 degrees.

[93] If the constellation edge regions are decided by the second decision unit 1002, the fourth decision unit 1008 and the sixth decision unit 1014, the decision of the position parallel to the x axis and the y axis is performed using a saturation method and the decision of the position of an oblique line is performed using a linear equation corresponding to the oblique line.

[94] The bit converter 1016 converts the information decided by the determination units, that is, the value decided to the symbol of the point corresponding to the input symbol data, to bit data corresponding to the decided symbol value.

[95] All the two times of rotation processes and the six times of decision processes may be performed. Alternatively, if the symbol of the point corresponding to the received symbol data is decided by a specific decision of six times of decision processes, the decision information may be output to the bit converter 1016 and may be converted to the bit data without further performing the rotation or decision process. This may vary according to implementation examples.

[96] The concept that the symbol is decided by the first decision unit 1000, the third decision unit 1006 and the fifth decision unit 1012 in FIG. 10 is shown in FIG. 12 and the concept that the symbol is decided by the second decision unit 1002, the fourth decision unit 1004 and the sixth decision unit 1006 is shown in FIG. 13.

[97]

[98] FIG. 11 is a schematic block diagram showing another symbol demapper for demapping a received optimal constellation symbol according to an embodiment of the present invention. The symbol demapper of FIG. 11 uses a recursive decoding method using a feedback.

[99] The symbol demapper of FIG. 11 includes a buffer 1020, a selector 1022, a first decision unit 1024, a second decision unit 1026, a rotation unit 1028, and a bit converter 1030.

[100] The buffer 1020 temporarily stores and outputs the input symbol data. The selector 1022 receives the symbol data output from the buffer 1020 and the symbol data output from the rotation unit 1028 and outputs one piece of symbol data. The selector 1022 outputs the symbol data fed back from the rotation unit 1028 when the recursive decoding method is performed and outputs the symbol data received from the buffer 1020 when a decision process is performed with respect to new symbol data.

[101] The first decision unit 1024 decides whether the input symbol data is positioned in the rectangular decision boundary region using the rectangular decision boundary region formed by two opposite sides in each of the hexagonal decision boundary regions. The second decision unit 1026 decides whether the input symbol data is positioned in a constellation edge region, that is, an edge region, of which one side is opened, in the decision boundaries shown in FIG. 9. The second decision unit 1026 decides whether the input symbol data is positioned in a decision boundary region den oted by a solid line (non-rotation), a dashed dotted line (one time of rotation), or a dotted line (two times of rotation) according to the number of times of rotation. The description of the decision of the symbol positioned in the edge region of which one side is opened will be described in detail with reference to FIG. 13. The rotation unit 1028 may rotate the decision boundaries used in the first decision unit 1024 and the second decision 1026 by a predetermined angle. For example, the decision boundaries are rotated by 60 degrees according to the symbol mapping method.

[102] The bit converter 1030 converts the information decided by the decision units, that is, the value decided to the symbol of the point corresponding to the input symbol data, to bit data corresponding to the decided symbol value.

[103] The symbol demapper of FIG. 11 may perform all the two times of rotation processes and the six times of decision processes. Alternatively, if the symbol of the point corresponding to the received symbol data is decided by the first decision unit 1024 and the second decision unit 1026 during the recursive decoding process, the decision information may be output to the bit converter 1030 and may be converted into the bit data. This may vary according to implementation examples. The concepts that the symbol is decided by the first decision unit 1024 and the second decision unit 1026 are shown in FIGs. 12 and 13.

[104] FIG. 12 is a schematic view showing a process of demapping a received symbol according to an embodiment of the present invention. FIG. 12 shows four hexagonal decision boundary regions in all the decision boundaries. [105] FIG. 12 shows a deciding process of a decision unit which decides whether the symbol data is positioned in the rectangular decision boundary region using the rectangular decision boundary region formed by two opposite sides in the hexagonal boundary region, among the decision units of FIG. 10 or 11.

[106] First, in a first decision boundary form which is not rotated, it is decided whether the input symbol data is positioned in the rectangular decision boundary region, using the rectangular decision boundary region formed by two opposite sides of each of the hexagonal decision boundary regions. If the decision is completed, all the decision boundaries are rotated by 60 degrees and it is decided whether the input symbol data is included in the rectangular decision boundary region, using the rectangular decision boundary region formed by two opposite sides of each of the hexagonal decision boundary regions. Then, all the decision boundaries are rotated by 60 degrees again and it is decided whether the input symbol data is included in the rectangular decision boundary region, using the rectangular decision boundary region formed by two opposite sides of each of the hexagonal decision boundary regions. In FIG. 12, a second decision boundary form and a third decision boundary form represent regions which are subjected to the decision process while performing the rotation process.

[107] By two times of rotation processes, the rectangular decision boundary regions cover the whole hexagonal region. Accordingly, each of the hexagonal decision boundary regions can be demapped to the symbols corresponding to the points having the hexagonal decision boundary region.

[108] According to the implementation example, if it is determined that the input symbol data is positioned in the rectangular decision boundary region, the decision process may be completed without further performing the rotation and the decision. Although the rectangular decision boundary region formed by two opposite right and left sides of the hexagon is used in the example of FIG. 12, a region using two opposite sides other than the right and left sides, for example, a parallelogram decision boundary region may be first used or a rectangular decision boundary region formed by two upper and lower sides may be first used.

[109] FIG. 13 is a schematic view showing a process of demapping a received optimal constellation symbol in an edge region according to an embodiment of the present invention.

[110] FIG. 13 is a view showing all the decision boundaries of a 64-point optimal constellation mapping method. FIG. 13 shows a deciding process of the decision unit which decides whether input symbol data is positioned in the constellation edge region, that is, the edge region of which one side is opened, by the decision units of FIGs. 11 and 12.

[I l l] First, in a first decision boundary form which is not rotated, it is decided whether the input symbol data is positioned in a region denoted by a solid line among the constellation boundary regions. If the decision is completed, all the decision boundaries are rotated by 60 degrees and it is decided whether the input symbol data is included in a region denoted by a dashed dotted line among the constellation boundary regions. Then, all the decision boundaries are rotated by 60 degrees again and it is decided whether the input symbol data is included in a region denoted by a dotted line among the constellation boundary regions.

[112] According to the implementation example, the sequence of the region denoted by the solid line, the region denoted by the dashed dotted line and the region denoted by the dotted line may be changed. For example, after the region denoted by the dotted line is decided in the first decision boundary form of FIG. 12, the region denoted by the solid line (one time of rotation) and the region denoted by the dashed dotted line (two times of rotation) may be decided.

[113] The second deinterleaver 870 performs the inverse process of the interleaving process with respect to a bit data stream demapped by the symbol demapper 860. The second deinterleaver 870 performs the deinterleaving process corresponding to the first interleaver 120 of FIG. 1. The inner decoder 880 may decode the deinterleaved data and correct an error included in the data. The outer decoder 890 performs an error correction decoding process with respect to the bit data decoded by the inner decoder 880. The inner decoder 880 and the outer decoder 890 decode the data according to the decoding methods corresponding to the inner encoder 110 and the outer decoder 110 of FIG. 1.

[114] FIG. 14 is a schematic block diagram showing another example of an apparatus for transmitting a signal according to an embodiment of the present invention. The transmitting/receiving system may use a multi-input multi-output (MIMO) method. The transmitting apparatus of FIG. 14 corresponds to the case where the MIMO method is applied to the transmitting apparatus shown in FIG. 1. Hereinafter, the embodiment of the signal transmitting system according to the present invention will be described with reference to FIG. 14.

[115] The embodiment of FIG. 14 includes a forward error correction (FEC) encoder 1300, a first interleaver 1310, a symbol mapper 1320, a linear pre-coder 1330, a second interleaver 1340, a multi- input/output encoder 1350, a frame builder 1360, a modulator 1370 and a transmitter 1380.

[116] The FEC encoder 1300 encodes an input signal and outputs the encoded signal such that an error generated in transmitted data is detected and corrected by a receiving apparatus. The data encoded by the FEC encoder 1300 is input to the first interleaver 110. The detailed example of the FEC encoder 1300 will be described in detail with reference to FIG. 15. [117] The first interleaver 1310 mixes a data stream output from the FEC encoder 1300 and disperses the data stream at random locations so as to be robust against a burst error generated in data at the time of transmission of data. As the first interleaver 1310, a convolution interleaver or a block interleaver may be used, which may be changed according to a transmission system. The detailed example of the first interleaver 1310 will be described in detail with reference to FIG. 15.

[118] The data interleaved by the first interleaver 1310 is input to the symbol mapper 120. The symbol mapper 1320 may map the transmitted signal to symbols according to a quadrature amplitude modulation (QAM) or quadrature phase-shift keying (QPSK) scheme, in consideration of a pilot signal and a transmission parameter signal according to a transmission mode.

[119] The symbol mapper 1320 may use the above-described optimal constellation symbol mapping method.

[120] The linear pre-coder 1330 disperses input symbol data into several pieces of output symbol data such that a probability that all information is lost by fading when experiencing a frequency- selective fading channel is reduced. The detailed example of the linear pre-coder 1330 will be described with reference to FIGs. 17 to 20.

[121] The second interleaver 1340 interleaves the symbol data output from the linear pre- coder 1330 again. That is, if the second interleaver 1340 performs interleaving, it is possible to correct an error generated when the symbol data experiences the same frequency- selective fading at a specific location. As the second interleaver 1340, a convolution interleaver or a block interleaver may be used.

[122] The linear pre-coder 1330 and the second interleaver 1340 process data to be transmitted so as to be robust against the frequency-selective fading of the channel, and may be collectively called a frequency-selective fading coder.

[123] The multi-input/output encoder 1350 encodes the data interleaved by the second interleaver 1340 so as to be transmitted via a plurality of transmission antennas. The apparatus for transmitting/receiving the signal can process the signal according to the multi-input/output method. Hereinafter, the multi-input/output method includes a multi-input multi-output (MIMO) method, a single-input multi-output (SIMO) and a multi-input single-output (MISO) method.

[124] The multi- input/output encoding method may include a spatial multiplexing method and a spatial diversity method. In the spatial multiplexing method, different data is simultaneously transmitted using multiple antennas of a transmitter and a receiver such that the data can be rapidly transmitted without increasing the bandwidth of the system. In the spatial diversity method, data having the same information is transmitted via multiple transmission antennas such that the diversity effect can be obtained.

[125] At this time, as the multi-input/output encoder 150 of the spatial diversity method, a space-time block code (STBC), a space-frequency block code (SFBC) or a space-time trellis code (STTC) may be used. As the multi-input/output encoder 1350 of the spatial multiplexing method, a method of dividing the data stream by the number of transmission antennas and transmitting the data stream, a full-diversity full-rate (FDFR) code, a linear dispersion code (LDC), a vertical-bell lab layered space-time (V-BLAST), or a diagonal-BLAST (D-BLAST) may be used.

[126] The frame builder 1360 inserts the precoded pilot signal into a predetermined location of a frame and builds the frame defined in the transmission/reception system. The frame builder 1360 may arrange a data symbol interval and a pilot symbol interval, which is a preamble of the data symbol interval, in the frame.

[127] For example, the frame builder may arrange dispersed pilot carriers, of which the locations are temporally shifted, in a data carrier interval. In addition, the frame builder may arrange consecutive pilot carriers, of which the locations are temporally fixed, in the data carrier interval.

[128] The modulator 1370 carries the data output from the frame builder 1360 in orthogonal frequency division multiplex (OFDM) subcarriers so as to perform the OFDM modulation and inserts a guard interval between the modulated symbols.

[129] The transmitter 1380 converts a digital signal having the guard interval and the data interval, which is output from the modulator 1370, into an analog signal and transmits the analog signal.

[130] FIG. 15 is a schematic block showing a forward error correction (FEC) encoder according to an embodiment of the present invention. The FEC encoder of FIG. 15 includes a Bose-Chaudhuri-Hocquenghem (BCH) encoder 1302 and a low density parity check (LDPC) encoder 1304 as an outer encoder and an inner encoder, respectively.

[131] A LDPC code is an error correction code which can reduce a probability that data information is lost. The LDPC encoder 1304 encodes the signal in a state in which the length of an encoding block is large such that the transmitted data is robust against a transmission error. In order to prevent hardware complexity from being increased due to the increase of the block size, the density of the parity bit is decreased so as to decrease the complexity of the encoder.

[132] In order to prevent an error floor from occurring in the output data of the receiver, the BCH encoder 1302 is concatenated in front of the LDPC encoder 1304 as the additional outer encoder. If an ignorable error floor occurs even when only the LDPC encoder 1304 is used, the BCH encoder 1302 may not be used. Alternatively, other encoders may be used as the outer encoder, instead of the BCH encoder.

[133] In the case that the two error correction encoders are used, parity check bits (BCH parity check bits) for the BCH encoding are added to the input data frame and parity check bits (LDPC parity check bits) for the LDPC encoding is added to the BCH parity check bits. The length of the BCH parity check bits added to the encoded data frame may vary according to the length of a LDPC codeword and a LDPC code rate.

[134] The data which is FEC-encoded by the BCH encoder 1302 and the LDPC encoder 1304 is output to the first interleaver 1310.

[135] FIG. 16 is a view showing an interleaver for interleaving input data according to an embodiment of the present invention. The interleaver of FIG. 16 is a block interleaver, which is an example of the interleaver which can be used in the first interleaver 1310.

[136] The interleaver of FIG. 16 stores input data in a matrix-shaped memory space in a predetermined pattern and reads and outputs the data in a pattern different from the pattern used for storing the data. For example, the interleaver of FIG. 16 has an NrxNc memory space composed of Nr rows and Nc columns and the data input to the interleaver is filled from a position corresponding to a first row and a first column of the memory space. The data is stored from the first row and the first column to an Nr row and the first column and, if the first column is filled up, is then stored from the first th row to the Nr row of a next column (second column). The data may be stored up to th e Nr row of an Nc column in this sequence (i.e. the data are stored column-wise).

[137] In the case that the data stored as shown in FIG. 16 is read, the data is read and output from the first row and the first column to the first row and the Ncthcolumn. If all the data of the first row is read, the data is read and output from the first column of a next row (second row) in the column direction. The data may be read and output up to the Nc' column of the Nr row in this sequence (i.e. the data are read out row- wise). At this time, the position of a most significant bit (MSB) of the data block is a left uppermost side and the position of a least significant bit (LSB) thereof is a right lowermost side.

[138] The size of the memory block, the storage pattern and the read pattern of the interleaver are only exemplary and may be changed according to implementation embodiments. For example, the size of the memory block of the first interleaver may vary according to the size of the FEC-encoding block.

[139] According to the example of FIG. 15, the number of rows NR and the number of columns Nc of the block which decide the size of the block interleaved by the first interleaver may vary according to the length of the LDPC code block. If the length of the LDPC code block is increased, the length of the block (for example, the number of the rows of the block) can be increased.

[140] FIG. 17 is a schematic block diagram showing a linear pre-coder according to an embodiment of the present invention.

[141] The linear pre-coder 130 may include a serial/parallel converter 132, an encoder 134 and a parallel/serial converter 136. [142] The serial/parallel converter 132 converts the input data into parallel data. The encoder 134 disperses the values of the converted parallel data into several pieces of data via the operation of anencoding matrix. [143] An encoding matrix is designed by comparing an transmission symbol with an reception symbol such that a pairwise error probability (PEP) that the two symbols are different from each other is minimized. If the encoding matrix is designed such that the

PEP is minimized, a diversity gain and a coding gain obtained via the linear pre-coding are maximized. [144] In addition, if a minimum Euclidean distance of the linearly pre-coded symbol is maximized by the encoding matrix, it is possible to minimize an error probability when the receiver uses a maximum likelihood (ML) decoder. [145] The parallel/serial converter 1336 converts the data received from the encoder 1334 into a serial data and outputs the serial data. [146] FIG. 18 is a view showing an example of the encoding matrix, that is, a code matrix for dispersing input data. FIG. 18 shows an example of the encoding matrix for dispersing the input data into several pieces of output data, which is also called a vanderMonde matrix. [147] The input data may be arranged in parallel by the length of the number (L) of output data. [148] Θ of the matrix may be expressed by the following equation and may be defined by other methods. If the vanderMonde matrix is used as the encoding matrix, a matrix element may be determined according to Math Figure 1. [149] The encoding matrix of Math Figure 1 rotates the input data by the phase of Math

Figure 1 corresponding to input dataand generates the output data. Accordingly, the values input according to the characteristics of the matrix of the linear pre-coder may be dispersed in at least two output values. [150] MathFigure 1

[Math.l]

[151] In Math Figure 1, L denotes the number of the output data. If an input data group input to the encoder is x and a data group which is encoded and output by the encoder using the matrix of Math Figure 1 is y, y is expressed by Math Figure 2.

[152] MathFigure 2 [Math.2]

[153] FIG. 19 shows another example of the encoding matrix. FIG. 19 shows another example of the encoding matrix for dispersing the input data into several pieces of output data, which is also called a Hadamard matrix. The matrix of FIG. 19 is a matrix having a general form, in which L is expanded by 2 . Here, L denotes the number of output symbols into which the input symbols will be dispersed.

[154] The output symbols of the matrix can be obtained by a sum and a difference among L input symbols. In other words, the input symbols may be dispersed into the L output symbols, respectively.

[155] Even in the matrixof FIG. 19, if an input data group input to the encoder 1334 of FIG.17 is x and a data group which is encoded and output by the encoder 1334 using the above-described matrix is y, y is a product of the above-described matrix and x.

[156]

[157] FIG. 20 shows another example of the encoding matrix for dispersing the input data. FIG. 20 shows another example of the encoding matrix for dispersing the input data into several pieces of output data, which is also called a Golden code. The Golden code is a 4x4 matrix having a special form. Alternatively, two different 2x2 matrixes may be alternately used.

[158] C of FIG. 20 denotes a code matrix of the Golden code and xl, x2, x3 and x4 in the code matrix denote symbol data which can be input to the encoder 1334. Constants in the code matrix may decide the characteristics of the code matrix, and the values of the rows and the columns computed by the constants of the code matrix and the input symbol data may be expressed by the output symbol data. The output sequence of the symbol data may vary according to the implementation embodiments.

[159]

[160] FIG. 21 is a view showing a structure of a transfer frame of the data channel-coded by the above-described embodiment. The transfer frame formed according to the present embodiment may include a pilot symbol including pilot carrier information and a data symbol including data information.

[161] In the example of FIG. 21, a frame includes M (M is a natural number) intervals and is divided into M- 1 data symbol intervals and a pilot symbol interval which is used as a preamble. The frame having the above-described structure is repeated.

[162] Each symbol interval includes carrier information by the number of OFDM subcarriers. The pilot carrier information of the pilot symbol interval is composed of random data in order to decrease a peak- to- average power ratio (PAPR). An auto- correlation value of the pilot carrier information has an impulse shape in a frequency domain. The correlation value between file carrier symbols may be close to 0.

[163] Accordingly, the pilot symbol interval used as the preamble allows the receiver to quickly recognize the signal frame of FIG. 21 and may be used for correcting and synchronizing a frequency offset. Since the pilot symbol interval represents the start of the signal frame, a system transmission parameter for allowing the received signal to be quickly synchronized may be set. The frame builder builds the data symbol intervals and inserts the pilot symbol interval in front of the data symbol intervals, thereby building a transfer frame.

[164] If a separate interval including the pilot carrier information is present in the transfer frame as shown in FIG. 21, the pilot carrier information may not be included in the data symbol intervals. Accordingly, it is possible to increase a data capacity. In the DVB, for example, since a percentage of pilot carriers in all the valid carriers is about 10%, the increasing rate of the data capacity is expressed by Math Figure 3.

[165] MathFigure 3 [Math.3]

[166] In Math Figure 3, denotes the increasing rate and M denotes the number of intervals included in a frame.

[167]

[168] FIG. 22 is a schematic block diagram showing another example of the apparatus for transmitting the signal in the case where the apparatus for transmitting the signal has a plurality of transmission paths according to the embodiment of the present invention. Hereinafter, for convenience of description, it is assumed that the number of transmission paths is two.

[169] The example of FIG. 19 includes a FEC encoder 1900, a first interleaver 1910, a symbol mapper 1920, a linear pre-coder 1930, a second interleaver 1940, a multi- input/output encoder 1950, a first frame builder 1960, a second frame builder 1965, a first modulator 1970, a second modulator 1975, a first transmitter 1980 and a second transmitter 1985.

[170] The signal processing from the FEC encoder 1900, the first interleaver 1910, the symbol mapper 1920, the linear pre-coder 1930, the second interleaver 1940 and the multi-input/output encoder 1950 is equal to that of the corresponding components shown in FIG. 1.

[171] The FEC encoder 1900 includes a BCH encoder and an LDPC encoder, FEC- encodes input data, and outputs the encoded data. The output data is interleaved by the first interleaver 810 such that the data stream are mixed. As the first interleaver 1910, a convolution interleaver or a block interleaver may be used.

[172] The symbol mapper 1920 maps the transmitted signal to symbols according to the

QAM or QPSK scheme, in consideration of a pilot signal and a transmission parameter signal according to a transmission mode. For example, 7-bit data may be included in one symbol in the case where the signal is mapped to the symbols by 128QAM and 8-bit data may be included in one symbol in the case where the signal is mapped to the symbols by 256QAM.

[173] The linear pre-coder 1930 includes a serial/parallel converter, an encoder and a parallel/serial converter. An example of a coding matrix used by the encoder of the linear pre-coder 1930 is shown in FIGs. 23 to 27.

[174] The second interleaver 1940 interleaves the symbol data output from the linear pre- coder 1930 again. As the second interleaver 1940, a convolution interleaver or a block interleaver may be used. The second interleaver 1940 mixes the symbol data such that the symbol data dispersed in the data output from the linear pre-coder 1930 does not experience the frequency- selective fading at a specific location of a frame. The interleaving method may vary according to the implementation examples of the transmission/reception system.

[175] In the case where the block interleaver is used, the length of the interleaver may vary according to the implementation examples. If the length of the interleaver is equal to or smaller than the length of an OFDM symbol, interleaving is performed only with respect to one OFDM symbol and, if the length of the interleaver is larger than the length of the OFDM symbol, interleaving may be performed with respect to several symbols. FIGs. 15 and 16 show the interleaving method in detail.

[176] The interleaved data is output to the multi-input/output encoder 1950. The multi- input/output encoder 1950 encodes the input symbol data so as to be transmitted via the plurality of transmission antennas and outputs the encoded data. For example, if two transmission paths are included, the multi-input/output encoder 1950 outputs the pre-coded data to the first frame builder 860 or the second frame builder 1965.

[177] In the spatial diversity method, the data having the same information is output to the first frame builder 1960 and the second frame builder 1965. If encoding is performed by the spatial multiplexing method, different data is output to the first frame builder 1960 and the second frame builder 1965.

[178] The first frame builder 1960 and the second frame builder 1965 build frames, into which a pilot signal is inserted, such that the received signals are modulated by the OFDM method.

[179] The frame includes one pilot symbol interval and M-I data symbol intervals. In the case where the transmission system of FIG. 22 performs multi-input/output encoding method using the plurality of antennas, the structure of the pilot symbol may be decided such that the transmission paths are distinguished by the receiving apparatus. [180] [181] The example of the multi-input/output encoder 1950 of FIG. 22 is shown in FIGs. 31 and 32. [182] The first modulator 1970 and the second modulator 1975 modulate the data output from the first frame builder 1960 and the second frame builder 1965 so as to be transmitted by the OFDM subcarriers. [183] The first transmitter 1980 and the second transmitter 1985 respectively convert the digital signals having the guard interval and the data interval, which are output from the first modulator 1970 and the second modulator 1975, into analog signals and transmit the converted analog signals. [184] [185] FIGs. 23 to 27 are views showing an example of a 2x2 code matrix for dispersing input symbols as an example of the encoding matrix of the linear pre-coder. The code matrixes of FIGs. 23 to 27 disperse two pieces of data input to the encoding unit of the linear pre-decoder 1930 to two pieces of output data. [186] The matrix of FIG. 23 is an example of the vanderMonde matrix described with reference to FIG. 18, in which L is 2. In the matrix of FIG. 23, first input data and second input data, of which phase is rotated by 45 degrees (

TC

), of the two pieces of input data are added and first output data is output. Then, first input data and second input data, of which phase is rotated by 225 degrees (

5π

4

), are added and second output data is output. The output data is divided by

so as to be scaled.

[187]

[188] The code matrix of FIG. 24 is an example of the Hadamard matrix.

[189] In the matrix of FIG. 24, first input data and second input data of the two pieces of input data are added and first output data is output. Then, second input data are subtracted from first input data and second output data is output. The output data is divided by so as to be scaled. [190] [191] FIG. 25 shows another example of the code matrix for dispersing the input symbols.

The matrix of FIG. 25 is an example of a code matrix different from the matrix described with reference to FIGs. 18 to 20. [192] In the matrix of FIG. 25, first input data, of which phase is rotated by 45 degrees ( π 4

), and second input data, of which phase is rotated by -45 degrees (- π ~4

), of the two pieces of input data are added and first output data is output. Then, second input data, of which phase is rotated by -45 degrees, is subtracted from first input data, of which phase is rotated by 45 degrees, and second output data is output. The output data is divided by

so as to be scaled. [193] [194] FIG. 26 shows another example of the code matrix for dispersing the input symbols.

The matrix of FIG. 26 is an example of a code matrix different from the matrix described with reference to FIGs. 18 to 20. [195] In the matrix of FIG. 26, first input data which is multiplied by 0.5 and second input data are added and first output data is output. Then, second input data which is mul- tipliedby 0.5 is subtracted from first input data and second output data is output. The output data is divided by

so as to be scaled.

[196]

[197] FIG. 27 shows another example of the code matrix for dispersing the input symbols. The matrix of FIG. 27 is an example of a code matrix different from the matrix described with reference to FIGs. 7 to 9. "*" of FIG. 27 denotes a complex conjugate of the input data. [198] In the matrix of FIG. 27, first input data, of which phase is rotated by 90 degrees ( π 2

), and second input data of the two pieces of input data are added and first output datais output. Then, the complex conjugate of first input data and the complex conjugate of second input data, of which phase is rotated by -90 degrees ( π

1

), are added, and second output data is output. The output data is divided by

so as to be scaled.

[199]

[200] FIG. 28 is a view showing an example of an interleaving method of the interleaver. The interleaving method of FIG. 28 is an example of the interleaver of the OFDM system having a symbol length N, which can be used in the second interleaver 1940 of the transmitting apparatus shown in FIG. 22.

[201] N denotes the length of the interleaver and i has a value corresponding to the length of the interleaver, that is, an integer from 0 to N-I. n denotes the number of valid transmission carriers in a transmitting system. FI(i) denotes a permutation obtained by a modulo-N operation, and dn has a FI(i) value which is located in a valid transmission carrier area excluding a value N/2 in sequence, k denotes an index value of an actual transmission carrier. N/2 is subtracted from dnsuch that the center of the transmission bandwidth becomes DC. P denotes a permutation constant which may vary according to implementation embodiments.

[202] FIG. 29 is a view showing a variable which varies according to the interleaving method of FIG. 28. In the example of FIG. 29, the length of the OFDM symbol and the length N of the interleaver are set to 2048 and the number of valid transmission carriers are set to 1536 (1792-256).

[203] Accordingly, i is an integer from 0 to 2047 and n is an integer from 0 to 1535. FI(i) denotes a permutation obtained by a modulo-2048 operation, dn has a FI(i) value with respect to a value 256<FI(i)<1792 excluding a value 1024(N/2) in sequence, k denotes a value obtained by subtracting 1024 from dn. P has a value of 13.

[204] Using the interleaver according to the above-described method, data corresponding to the sequence i of the input data may be changed to the sequence k of the interleaved data with respect to the length N of the interleaver. [205] FIG. 30 is a view showing an example of the encoding method of the multi- input/output encoder. The embodiment of FIG. 30 is the STBC which is one of the multi-input/output encoding methods and may be used in the transmitting apparatus shown in FIG. 22.

[206] In the example of the STBC encoder, T denotes a symbol transmission period, s denotes an input symbol to be transmitted, and y denotes an output symbol. * denotes a complex conjugate, and a first antenna (Tx #1) and a second antenna (Tx #2) denote a first transmission antenna and a second transmission antenna 2, respectively.

[207] In the example of FIG. 30, at a time t, the first antenna Tx #1 transmits s0 and the second antenna Tx #2 transmits si. At a time t+T, the first antenna Tx #1 transmits - si* and the second antenna Tx #2 transmits sθ*. The transmission antennas transmit data having the same information of s0 and si in the transmission period. Accordingly, the receiver can obtain spatial diversity effect using the signals output from the multi- input/output encoder according to the shown method.

[208] The signals transmitted by the first antenna and the second antenna shown in FIG. 30 are examples of the multi-input/output encoded signals. When FIG. 19 is described from a different viewpoint, the signals transmitted by the first antenna and the second antenna may be transmitted by a multi-input single-output method.

[209] In the example of FIG. 30, it may be considered that two temporally consecutive signals s0 and -si* are input to a path of the first antenna and signals si and sθ* are input to a path of the second antenna. Accordingly, since the signals s0 and -si* are consecutively output to the first antenna and the signals s 1 and sθ* are output to the second antenna, it may be considered thatthe output symbols are transmitted by the multi-input single-output method. FIG. 19 shows a simplest example using two antennas. The signals may be transmitted according to the method shown in FIG. 30 using more antennas.

[210] That is, when the example of FIG. 30 is described by the multi-input single-output method, the consecutive first and second symbols are multi- input and a minus of a complex conjugate of the second symbol and a complex conjugate of the first symbol are simultaneously output. The multi-input symbols may be encoded according to an Alamouti algorithm and the encoded symbols may be output.

[211] The multi- input/output encoder may transmit the signals which are interleaved by the second interleaver in the frequency domain,by the multi-input single-output method. The multi-input/output (including the multi-input single-output) shown in FIG. 30 is not applied to the pilot symbol interval shown in FIGs. 31 and 32 and is applied to only the data symbol interval.

[212] FIG. 31 is a view showing a structure of the pilot carriers in the pilot symbol intervals built by the first and second frame builders of FIG. 22. The pilot symbol intervals built by the frame builders of FIG. 22 may be output as shown in FIG. 31.

[213] The pilot carriers included in the frames output from the first and second frame builders are output to the first and second antennas, respectively. Accordingly, FIG. 31 shows the respective pilot symbols built by the first and second frame builders as the signals output from the first and second antennas.

[214] In the respective pilot symbol intervals output from the first and second frame builders of FIG. 22, an even-numbered pilot carrier and an odd-numbered pilot carrier are respectively interleaved as shown in FIG. 31 and the interleaved carriers may be output to the first and second antennas #1 and #2.

[215] For example, only the even-numbered pilot carrier information of the generated pilot carriers is included in the pilot symbol interval built by the first frame builder and is transmitted via the first antenna #1. Only the odd- numbered pilot carrier information of the generated pilot carriers is included in the pilot symbol interval built by the second frame builder and is transmitted via the second antenna. Accordingly, the receiver can distinguish between the transmission paths using the carrier indexes of the pilot symbol intervals received via the two signal paths. The structure of the pilot symbol interval of FIG. 31 may be used when the multi-input/output encoding is performed so as to have the two transmission paths as shown in FIG. 22.

[216] In the embodiment of FIG. 31, a channel corresponding to a subcarrier of a half of a frame may be estimated from a symbol. Accordingly, high channel estimation performance can be obtained with respect to a transmission channel having a short coherence time.

[217] FIG. 32 is a view showing another structure of the pilot carriers in the pilot symbol intervals. Even in the example of FIG. 32, different pilot carriers are transmitted to the pilot symbol intervals with respect to the paths according to the multi-input/output encoding method.

[218] The pilot carrier transmission structure of the pilot symbol intervals shown in FIG.

32 is called a Hadamard type pilot carrier transmission structure. In the embodiment of FIG. 32, Hadamard conversion is performed in the unit of a symbol interval in order to distinguish between the two transmission paths. For example, pilot carriers obtained by adding the two pieces of pilot carrier information for the transmission paths are transmitted to the even-numbered symbol interval and a difference between the two pieces of pilot carrier information is transmitted to the odd-numbered symbol interval.

[219] The pilot symbol interval includes even-numbered intervals and odd-numbered intervals which are arranged with time. A pilot carrier according to a sum of pilot carrier information which will be transmitted via a first path (first antenna (denoted by antenna #0)) and pilot carrier information which will be transmitted via a second path (second antenna (denoted by antenna #1)) is transmitted to the even-numbered interval. A pilot carrier according to a difference between pilot carrier information which will be transmitted via the first path (first antenna (denoted by antenna #0)) and pilot carrier information which will be transmitted via the second path (second antenna (denoted by antenna #1)) is transmitted to the odd-numbered interval. The receiver can recognize the sum of or difference between the two pieces of pilot carrier information via a received pilot index and distinguish between the transmission paths.

[220] In this embodiment, a channel corresponding to all subcarriers can be estimated and the estimation length of delay spread of the channel which can be processed by each transmission path can be extended by a symbol length.

[221] The example of FIG. 32 is shown for facilitating the distinguishment between the two pieces of pilot carrier information and shows both the two pieces of pilot carrier information in the frequency domain. In the even-numbered symbol interval and the odd-numbered symbol interval, impulses of the two pieces of pilot carrier information are located at the same frequency point.

[222] The embodiments of FIGs. 31 and 32 are examples of having two transmission paths. If the number of transmission paths is larger than 2, the pilot carrier information may be divided so as to be distinguished by the number of transmission paths similar to FIG. 31 or may be subjected to Hadamard conversion in the unit of a symbol interval and the converted information may be transmitted similar to FIG. 32.

[223] FIG. 33 is a schematic block diagram showing another example of an apparatus for receiving a signal according to an embodiment of the present invention. The embodiment of FIG. 33 shows the apparatus for receiving the signal transmitted according to the MIMO method.

[224] The embodiment of FIG. 33 includes a receiver 2500, a synchronizer 2510, a demodulator 2520, a frame parser 2530, a multi-input/output decoder 2540, a first dein- terleaver 2550, a linear pre-coding decoder 2560, a symbol demapper 2570, a second deinterleaver 2580, and a FEC decoder 2590. The embodiment of FIG. 33 will be described concentrating on a procedure of processing the signal by the signal receiving system.

[225] The receiver 2500 down-converts the frequency band of a received RF signal, converts the signal into a digital signal, and outputs the digital signal. The synchronizer 2510 acquires synchronization of the received signal output from the receiver 2500 in a frequency domain and a time domain and outputs the synchronization. The synchronizer 2510 may use an offset result of the data output from the demodulator 2520 in the frequency domain, for acquiring the synchronization of the signal in the frequency domain.

[226] The demodulator 2520 demodulates the received data output from the synchronizer 2510 and removes the guard interval. The demodulator 2520 may convert the received data into the frequency domain and obtain data values dispersed into the subcarriers.

[227] The frame parser 2530 may output symbol data of the data symbol interval excluding the pilot symbol according to the frame structure of the signal demodulated by the demodulator 2520.

[228] The frame parser 2530 may parse the frame using at least one of a dispersion pilot carrier of which the location is temporally shifted in the data carrier interval and a consecutive pilot carrier of which the location is temporally fixed in the data carrier interval.

[229] The multi-input/output decoder 2540 receives the data output from the frame parser 2530, decodes the data, and outputs a data stream. The multi-input/output decoder 2540 decodes the data stream received via the plurality of transmission antennas according to a method corresponding to the transmitting method of the multi- input/output encoder shown in FIG. 1 and outputs the data stream.

[230] The first deinterleaver 2550 deinterleaves the data stream output from the multi- input/output decoder 2540 and restores the data into the order of the data before interleaving. The first deinterleaver 2550 deinterleaves the data stream according to a method corresponding to the interleaving method of the second interleaver shown in FIG. 1 and restores the order of the data stream.

[231] The linear pre-coding decoder 2560 performs an inverse process of the process of dispersing the data in the apparatus for transmitting the signal. Accordingly, the data dispersed according to the linear pre-coding may be restored to the data before dispersing. The embodiment of the linear pre-coding decoder 2560 is shown in FIGs. 37 to 38.

[232] The symbol demapper 2570 may restore the coded symbol data output from the linear pre-coding decoder 2560 into a bit stream.

[233] The symbol demapper 2570 performs the inverse process of the symbol mapping process of the symbol mapper.

[234] The second deinterleaver 2580 deinterleaves the data stream output from the symbol demapper 2570 and restores the data into the order of the data before interleaving. The second deinterleaver 2580 deinterleaves the data according to a method corresponding to the interleaving method of the first interleaver 110 shown in FIG. 1 and restores the order of the data stream.

[235] The FEC decoder 2590 FEC-decodes the data, in which the order of the data stream is restored, detects an error generated in the received data, and corrects the error. The example of the FEC decoder 2590 is shown in FIG. 39.

[236] FIG. 34 is a schematic block diagram showing an example of the linear pre-coding decoder. The linear pre-coding decoder 2560 includes a serial/parallel converter 2562, a first decoder 2564 and a parallel/serial converter 2566. [237] The serial/parallel converter 2562 converts the input data into parallel data. The first decoder 2564 may restore the data, which is linearly pre-coded and is dispersed into the parallel data, as original data via a decoding matrix. The decoding matrix for performing decoding becomes an inverse matrix of the encoding matrix of the apparatus for transmitting the signal. For example, when the apparatus for transmitting the signal performs the encoding operation using the vanderMonde matrix, the Hadamard matrix and the Golden code shown in FIGs. 7 to 9, the first decoder 2564 restores the dispersed data as the original data using the inverse matrixes of the matrixes.

[238] The parallel/serial converter 2566 converts the parallel data received by the first decoder 2564 into the serial data and outputs the serial data.

[239] FIG. 35 is a schematic block diagram showing another example of the linear pre- coding decoder. The linear pre-coding decoder 2560 includes a serial/parallel converter 2561, a second decoder 2563 and a parallel/serial converter 2565.

[240] The serial/parallel converter 2561 converts the input data into parallel data, the parallel/serial converter 2565 converts the parallel data received from the second decoder 2563 into serial data and outputs the serial data. The second decoder 2563 may restore the original data, which is linearly pre-coded and is dispersed into the parallel data output from the serial/parallel converter 2561, using maximum likelihood (ML) decoding.

[241] The second decoder 2563 is the ML decoder for decoding the data according to the transmitting method of the transmitter. The second decoder 2563 ML-decodes the received symbol data according to the transmitting method and restores the data dispersed in the parallel data to the original data. That is, the ML decoder ML-decodes the received symbol data according to the encoding method of the transmitter.

[242] FIGs. 36 to 37 are views showing examples of a 2x2 code matrix for restoring the dispersed symbols. The code matrixes of FIGs. 36 to 37 show inverse matrixes corresponding to the 2x2 encoding matrixes of FIGs. 23 to 27. The code matrixes restore data which is dispersed into two pieces of data input to the decoding unit of the linear pre-coding decoder 2560 and output the restored data.

[243] FIG. 36 is a view showing an example of a 2x2 code matrix according to an embodiment of the present invention.

[244] In more detail, the 2x2 code matrix of FIG. 25 is a decoding matrix corresponding to the encoding matrix of FIG. 25.

[245] In the matrix of FIG. 36, first input data, of which phase is rotated by -45 degrees (- π T ), and second input data, of which phase is rotated by -45 degrees (- π 4

so as to be scaled.

[246] FIG. 37 shows another example of the 2x2 code matrix. The matrix of FIG. 37 is a decoding matrix corresponding to the encoding matrix of FIG. 26. In the matrix of FIG. 37, first input data which is multiplied by 0.5 and second input data are added and first output data is output. Then, second input data which is multipliedby 0.5 is subtracted from first input data and second output data is output. The output data is divided by

so as to be scaled. [247] FIG. 38 shows another example of the 2x2 code matrix. The matrix of FIG. 38 is a decoding matrix corresponding to the encoding matrix of FIG. 27. "*" of FIG. 38 denotes a complex conjugate of the input data. [248] In the matrix of FIG. 38, first input data, of which phase is rotated by -90 degrees (-

), and the complex conjugate of second input data are added and first output data is output. Then, the first input data and the complex conjugate of second input data, of which phase is rotated by -90 degrees (-

), are added, and second output data is output. The output data is divided by

V^ so as to be scaled. [249] FIG. 39 is a schematic block diagram showing a forward error correction (FEC) decoder according to an embodiment of the present invention. The FEC decoder 2590 corresponds to the FEC encoder 1300 of FIG. 14. As an inner decoder and an outer decoder, a LDPC decoder 2592 and a BCH decoder 2594 are included, respectively.

[250] The LDPC decoder 2592 detects a transmission error which occurs in a channel and corrects the error, and the BCH decoder 2594 corrects the remaining error of the data decoded by the LDPC decoder 2592 and removes an error floor.

[251] FIG. 40 is a block diagram of another embodiment of the apparatus for receiving the signal. Hereinafter, for convenience of description, it is assumed that the number of reception paths is two.

[252] The embodiment of FIG. 40 includes a first receiver 2900, a second receiver 2905, a first synchronizer 2910, a second synchronizer 2915, a first demodulator 2920, a second demodulator 2915, a first frame parser 2930, a second parser 2935, a multi- input/output decoder 2940, a third deinterleaver 2950, a linear pre-coding decoder 2960, a symbol demapper 2970, a fourth deinterleaver 2980, and a FEC decoder 2990.

[253] The first receiver 2900 and the second receiver 2905 receive respective RF signals, down-converts the frequency bands, converts the signals into digital signals, and outputs the converted digital signals. The first synchronizer 2910 and the second synchronizer 2915 acquire synchronizations of the received signals output from the first receiver 2900 and the second receiver 2905 in a frequency domain and a time domain and outputs the synchronizations. The first synchronizer 2910 and the second synchronizer 2915 may use an offset result of the data output from the first demodulator 2920 and the second demodulator 2925 in the frequency domain, for acquiring the synchronizations of the signals in the frequency domain.

[254] The first demodulator 2920 demodulates the received data output from the first synchronizer 2910. The first demodulator 2920 converts the received data into the frequency domain and decodes the data values dispersed into the subcarriers to values allocated to the subcarriers. The second modulatoer 2925 demodulates the received data output from the second synchronizer 2915.

[255] The first frame parser 2930 and the second frame parser 2935 may distinguish between the reception paths according to the frame structures of the signals demodulated by the first demodulator 2920 and the second demodulator 2925 and output the symbol data of the data symbol interval excluding the pilot symbol.

[256] The multi-input/output decoder 2940 receives the data output from the first frame parser 2930 and the second parser 2935 and decodes the received data streams such that one data stream is output.

[257] The signal processing procedure of the linear pre-coding decoder 2960, the symbol demapper 2970, the fourth deinterleaver 2980 and the FEC decoder 2990 is equal to that of the corresponding components shown in FIG. 33.

[258] FIG. 41 is a view showing an example of a decoding method of the multi- input/output decoder. That is, FIG. 41 shows a decoding example of the receiver when the transmitter multi-input/output encodes data by the STBC method and transmits the encoded data. The transmitter may use two transmission antennas. This is only exemplary and another multi-input/output method may be applied.

[259] In the equation, r(k), h(k), s(k) and n(k) represent a symbol received by the receiver, a channel response, a symbol value transmitted by the transmitter, and channel noise, respectively. Subscripts s, i, 0 and 1 represent a s' transmission symbol, an i reception antenna, 0 transmission antenna and 1st transmission antenna, respectively. "*" represents a complex conjugate. For example, h (k) represents a response of a s,l,i channel experienced by the transmitted symbol when a s symbol transmitted via the first transmission antenna is received by the i reception antenna, r (k) represents a s+l,i s+lth reception symbol received by the ith reception antenna. [260] According to the equation of FIG. 41, r (k) which is a s reception symbol received by the i reception antenna becomes a value obtained by adding the sth symbol value transmitted from the 0 transmission antenna to the ithreception antenna via the channel, the sthsymbol value transmitted from the 1st transmission antenna to the ith reception antenna via the channel and a sum n (k) of the channel noises of the channels. [261] r (k) which is the s+1 reception symbol received by the i reception antenna s+l,i becomes a value obtained by adding the s+l' symbol value h transmitted from the

Oth transmission antenna to the ith reception antenna via the channel, the s+l symbol value h transmitted from the lsttransmission antenna to the ithreception antenna s+l, l,i via the channel and a sum n (k) of the channel noises of the channels. s+l

[262] FIG. 42 is a view showing a detailed example of the reception symbol FIG. 41. FIG. 42 shows a decoding example when the transmitter multi- input/output encodes data by the STBC method and transmits the encoded data, that is, shows an equation which can obtain the received symbol when the data is transmitted using two transmission antennas and the data transmitted via the two transmission data is received using one antenna.

[263] The transmitter transmits a signal using two transmission antennas and the receiver receives the signal using one transmission antenna, the number of transmission channels may be two. In the equation, h0 and sOrespectively represent a transmission channel response from the Othtransmission antenna to the reception antenna and a symbol transmitted from the Oth transmission antenna, and hi and slrespectively represent a transmission channel response from the lsttransmission antenna to the reception antenna and a symbol transmitted from the Ith transmission antenna. "*" represents a complex conjugate and sθ' and si' of the following equation represent restored symbols.

[264] In addition, r and r respectively represent a symbol by the reception antenna at a time t and a symbol received by the reception antenna at a time t+T after a transmission period T is elapsed, and n and n represent values of sums of channel noises of the transmission paths at reception times.

[265] As expressed by the equation of FIG. 42, the signals r and r received by the reception antenna may be represented by values obtained by adding the signals transmitted by the transmission antennas and values distorted by the transmission channels. The restored symbols sθ' and si' are calculated using the received signals rO and rl and the channel response values h and h . o i

[266] FIG. 43 is a flowchart illustrating a method of transmitting a signal according to an embodiment of the present invention.

[267] Input data is FEC-encoded such that a transmission error of transmitted data is found and corrected (S3200). For FEC-encoding, an LDPC encoding method may be used as an inner encoder. A BCH encoding method may be used as an outer encoder for preventing error floor.

[268] The encoded data is interleaved so as to be robust against a burst error of a transmission channel, and the interleaved data is mapped to symbol data (S3210). As the mapping method, an optimal constellation mapping method may be used.

[269] In order to enable the symbol data to be robust against frequency selective fading of the channel, the mapped symbol data is pre-coded so as to be dispersed into several output symbols in the frequency domain (S3220) and the pre-coded symbol data is interleaved (S3230).

[270] Accordingly, it is possible to reduce a probability that all information is lost due to fading when experiencing frequency- selective fading of a channel and disable the dispersed symbol data to experience the same frequency selective fading. In the interleaving, a convolutional interleaver or a block interleaver may be used. This may vary according to the implementation examples.

[271] The interleaved data is converted into a transmission frame, the transmission frame is modulated, and the modulated frame is transmitted (S3240). For example, the transmission frame includes a pilot carrier symbol interval and a data symbol interval. The pilot carrier symbol interval may have a structure for distinguishing between transmission paths.

[272] In the case where the present embodiment is applied to a signal transmitting/ receiving system using the multi- input/output method instead of a signal transmitting/ receiving system using the single input/output method, the interleaved symbol data is multi-input/output encoded and converted into the transmission frame so as to be transmitted via a plurality of antennas. The number of antennas may be equal to the number of transmission paths. Data having the same information is transmitted via the paths in a spatial diversity method and different data is transmitted via the paths in a spatial multiplexing method.

[273] FIG. 44 is a flowchart illustrating an embodiment of a method of receiving a signal.

[274] In the apparatus for receiving the signal, the signal transmitted from the signal transmitting apparatus is synchronized and the synchronized signal is demodulated to frame data (S3300).

[275] After the demodulated data frame is parsed, the parsed data is deinterleaved in a manner inverse to the interleaving method of the signal transmitting apparatus (S3310). The data stream of which the sequence is restored is decoded in a manner inverse to the pre-coding method and original symbol data dispersed in several pieces of symbol data in the frequency domain is restored (S3320).

[276] The restored symbol data is demapped so as to be restored to bit data corresponding thereto and the bit data is deinterleaved so as to be restored to the original sequence (S3330). As the demapping method, a demapping method according to an optimal constellation method may be used.

[277] The restored data is FEC-decoded so as to correct the transmission error (S3340). For FEC-encoding, the LDPC decoding method may be used. As the outer decoder for preventing error floor, the BCH decoding method may be performed.

[278] In the case where the present embodiment is applied to a signal transmitting/ receiving system using the multi- input/output method instead of a signal transmitting/ receiving system using the single input/output method, the parsed frame data is multi- input/output decoded and the decoded data is then deinterleaved. In this case, the frame data is multi-input/output decoded in a state in which the transmission paths of the received data are distinguished.

[279] The method of transmitting/receiving the signal and the apparatus for transmitting/ receiving the signal are not limited to the above examples and are applicable to all signal transmitting/receiving systems such as broadcast or communication.

[280] It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents. Mode for the Invention

[281] The embodiments of the invention are described in the best mode of the invention. Industrial Applicability A method of transmitting/receiving a signal and an apparatus for transmitting/ receiving a signal of the present invention can be used in broadcast and communication fields.

Claims

[1] An apparatus for transmitting a signal, the apparatus comprising: a forward error correction (FEC) encoder which FEC-encodes input data; an interleaver which interleaves the FEC-encoded data; a symbol mapper which maps the interleaved data to symbol data according to a symbol mapping method for arranging symbols such that gaps between neighboring symbols in a constellation are equalized; and a transmitter which modulates and transmits the mapped symbol data. [2] The apparatus according to claim 1, wherein the symbol mapper enables three neighboring symbols in the constellation to be arranged in a regular triangle shape. [3] A method of transmitting a signal, the method comprising: forward error correction (FEC)-encoding input data; interleaving the FEC-encoded data; mapping the interleaved data to symbol data according to a symbol mapping method for arranging symbols such that gaps between neighboring symbols in a constellation are equalized; and modulating and transmitting the mapped symbol data. [4] The method according to claim 3, wherein the mapping step includes enabling three neighboring symbols in the constellation to be arranged in a regular triangle shape. [5] An apparatus for receiving a signal, the apparatus comprising: a demodulator which demodulates the received signal; a frame parser which outputs data obtained by parsing a frame of the demodulated signal; a symbol demapper which demaps symbols and outputs the demapped symbols if symbol data included in the data output from the frame parser is symbol data having the same gap between neighboring symbols; a deinterleaver which deinterleaves the data output from the symbol demapper; and a forward error correction (FEC) decoder which FEC-decodes the deinterleaved data. [6] The apparatus according to claim 5, wherein the symbol demapper includes: a plurality of decision units which decide whether the symbol data is positioned in a specific region of decision boundaries; and a plurality of rotation units which rotate the decision boundaries decided by the decision units. [7] The apparatus according to claim 6, wherein any one of the plurality of decision units includes a first decision unit which decides whether or not the symbol data is positioned in a rectangular region formed by two sides of a hexagonal region included in decision boundary regions. [8] The apparatus according to claim 7, wherein any one of the plurality of decision units includes a second decision unit which decides whether or not the symbol data is included in a region excluding the rectangular region formed by the two sides of the hexagonal region included in the decision boundary regions from the hexagonal region. [9] A method receiving a signal, the method comprising: demodulating the received signal; outputting data obtained by parsing a frame of the demodulated signal; demapping symbols if symbol data included in the output data is symbol data having the same gap between neighboring symbols; deinterleaving the demapped symbol data; and forward error correction (FEC)-decoding the deinterleaved data. [10] The method according to claim 9, wherein the step of the demapping the symbols includes: deciding whether the symbol data is positioned in a specific region of decision boundaries; and rotating the decision boundaries. [11] The method according to claim 10, wherein the deciding step includes deciding whether or not the symbol data is included in a region excluding a rectangular region formed by two sides of a hexagonal region included in decision boundary regions from the hexagonal region. [12] The method according to claim 11, wherein the deciding step further includes deciding whether or not the symbol data is included in a region excluding the rectangular region formed by the two sides of the hexagonal region included in the decision boundary regions.