BR112016017945B1 - TRANSMISSION METHOD - Google Patents

Abstract

TRANSMISSION APPARATUS A transmission apparatus is disclosed. The transmission apparatus includes an encoder for performing bit-wise channel coding and generating a codeword, an interleaver for interleaving the codeword, and a modulator for mapping the interleaved codeword to a non-uniform constellation in accordance with a scheme. of modulation, and the constellation may include constellation points defined based on various tables according to the modulation scheme.

Description

Technical Field

[0001] Apparatus and methods consistent with the exemplary modalities of the inventive concept refer to the transmission and reception of data using broadcasting, more particularly, to the design of non-uniform constellations used in a Bit Interleaved Coded Modulation Modulation (BICM)) that maps bits from an encoder and interleaver output to complex constellations.

Background of the Technique

[0002] Current broadcasting systems consistent with Second Generation Digital Terrestrial Video Broadcasting (DVB-T2) use a chain of Bit Interleaving and Coded Modulation (BICM) in order to encode the bits to be transmitted. The BICM chain includes a channel encoder as a Low Density Parity Check (LDPC) encoder followed by a bit interleaver and a Quadrature Amplitude Modulation (QAM) mapper. ). The role of the QAM mapper is to map the different bit outputs from the channel encoder and interleaved using the QAM cell bit interleaver. Each cell represents a complex number with a real part and an imaginary part. The QAM mapper groups M bits into a single cell. Each cell is translated into a complex number. M, which is the number of bits per cell, is equal to 2 for QPSK, 4 for 16QAM, 6 for 64QAM, and 8 for 256. It is possible to use a larger QAM size in order to increase throughput. For example - 1K QAM is a constellation containing 1024 possible points and used to map M = 10 bits. DVB-T2 and earlier standards use uniform QAM. Uniform QAM has two important properties: possible constellation points are rectangular, and the spacing between each two successive points is uniform. Uniform QAM is very easy to map and unmap.

[0003] QAM is also easy to use, as it does not need to be optimized depending on the signal-to-noise ratio (SNR) or the coding rate of the channel code like the LDPC code.

[0004] However, uniform QAM capability leaves a large gap from the theoretical limit, known as the Shannon limit. Performance in terms of bit error rate (BER) or frame error rate (FER) can be far from ideal.

Disclosure Technical problem

[0005] In order to reduce the Shannon limit difference and provide better BER/FER performance, a non-uniform constellation (NUC) is generated by relaxing the two properties of uniform QAM, namely: the square shape and the uniform distance between constellation points.

Technical Solution

[0006] It is an objective of certain exemplary embodiments of the present invention to address, resolve and/or mitigate, at least partially, at least one of the problems and/or disadvantages associated with the related technique, for example, at least one of the problems and /or disadvantages described above. It is an object of certain exemplary embodiments of the present invention to provide at least one advantage over the related art, for example, at least one of the advantages described below.

[0007] The present invention is defined in the independent claims. Advantageous features are defined in the dependent claims.

[0008] Other relevant aspects, advantages and characteristics of the invention will be evident to those skilled in the art from the detailed description that follows, which, taken together with the attached drawings, describe exemplary embodiments of the invention.

Advantageous Effects Description of the Drawings

[0009] The aforementioned and/or other aspects will be more evident through the description of certain exemplary embodiments with reference to the attached drawings, in which: FIG. 1 is a schematic diagram of a first algorithm according to an exemplary embodiment; FIG. 2 is a flowchart illustrating the operations of the first algorithm, according to an exemplary embodiment; FIG. 3 illustrates the convergence of C_last with respect to one of the parameters as the first algorithm of FIGs. 1 and 2 is carried out, according to an exemplary embodiment; FIG. 4 illustrates a second algorithm according to an exemplary embodiment for determining an ideal constellation at a given SNR value S on an AWGN channel; FIG. 5 illustrates the convergence of the C_best constellation as the second algorithm of FIG. 4 is carried out, according to an exemplary embodiment; FIG. 6 illustrates a third algorithm according to an exemplary embodiment for determining the optimal constellation at a given SNR value S in a Rician fading channel for a desired Rician_rice factor k; FIG. 7 illustrates a fourth algorithm according to an exemplary embodiment for determining the ideal constellation at a given SNR value S in a Rayleigh fading channel; FIG. 8 illustrates a fifth algorithm according to an exemplary embodiment for determining an ideal constellation; FIG. 9 illustrates a process for obtaining an ideal constellation for a specific system, according to an exemplary embodiment; FIG. 10 illustrates a plot of BER versus SNR for 64-QAM using a low-density parity checker, LDPC, coding rate (CR) of 2/3 of DVB-T2, on an AWGN channel, according to an exemplary embodiment; FIG. 11 illustrates a sixth algorithm according to an exemplary embodiment for determining an ideal constellation; FIG. 12 further illustrates the sixth algorithm illustrated in FIG. 11, according to an exemplary embodiment; FIG. 13 illustrates a process for obtaining cascaded SNR for a given channel type according to an exemplary embodiment; FIG. 14 schematically illustrates a process for obtaining a weighted performance measurement function for an input constellation based on different transmission scenarios according to an exemplary embodiment; FIG. 15 illustrates a process for obtaining an ideal constellation according to an exemplary embodiment; FIGS. 16a and 16b illustrate alternative schemes for generating a candidate constellation from a previous constellation in accordance with exemplary embodiments; FIG. 17 illustrates a technique for reducing complexity according to an exemplary embodiment; FIG. 18 illustrates an apparatus for implementing an algorithm according to an exemplary embodiment; FIGS. 18 to 34 illustrate non-uniform constellations according to various exemplary embodiments; FIG. 35 is a block diagram for describing a configuration of a transmission apparatus in accordance with an exemplary embodiment; FIG. 36 is a block diagram for describing a configuration of a receiving apparatus in accordance with an exemplary embodiment; and FIG. 37 is a flowchart for describing a modulation method in accordance with an exemplary embodiment.

Invention Mode

[00010] Various exemplary embodiments will now be described in greater detail with reference to the accompanying drawings.

[00011] In the following description, the same drawing reference numbers are used for the same elements, even in different drawings. The matters defined in the description, such as construction and detailed elements, are provided to assist in a comprehensive understanding of the invention. Thus, it is clear that the exemplary embodiments can be realized without these specifically defined elements. Furthermore, well-known functions or constructs are not described in detail as this would obscure the exemplary embodiments with unnecessary detail.

[00012] The following description of the exemplary embodiments with reference to the accompanying drawings is provided to assist in the comprehensive understanding of the inventive concept, as defined by the claims. The description includes several specific details to aid understanding, but these should be considered as examples only. Thus, those skilled in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope of the inventive concept.

[00013] The same or similar components may be designated by the same or similar reference numbers, although they may be illustrated in different drawings.

[00014] Detailed descriptions of techniques, structures, constructions, functions or processes known in the art may be omitted for clarity and brevity, and to avoid obscuring the object of the exemplary embodiments.

[00015] The terms and words used here are not limited to standard or bibliographical meanings, but are merely used by the inventors to allow a clear and consistent understanding of the exemplary modalities.

[00016] Throughout the description and claims of this specification, the words "comprise", "contain" and "include", and variations thereof, for example, "comprising", "containing" and "including" mean "including , but not limited to", and are not intended to (and do not) exclude other features, elements, components, integers, steps, operations, functions, processes, features and the like.

[00017] Throughout the description and claims of this specification, the singular form, for example, "a", "an" and "the", encompass the plural unless the context requires otherwise. For example, reference to "an object" includes reference to one or more such objects.

[00018] Throughout the description and claims of this specification, language in the general form of "X to Y" (where Y is some action, process, function, activity or step and , function, activity or step) comprises adapted means X, configured or arranged specifically, but not necessarily exclusively, to do Y.

[00019] Features, elements, components, integers, steps, operations, processes, functions, characteristics, and the like, "described in conjunction with a particular aspect, embodiment, example or claim of the inventive concept should be understood to be applicable to any other aspect, embodiment, example or claim described herein, unless incompatible therewith.

[00020] Exemplary embodiments may be applied in the form of any method, system and/or apparatus suitable for use in digital broadcasting, for example, in the form of a mobile/portable terminal (e.g. mobile phone), device laptop, personal computer, digital television and/or digital radio transmitter and/or receiving device, set-top box, etc. Any system and/or apparatus may be compatible with any existing or future suitable digital broadcasting system and/or standard, for example, one or more of the digital broadcasting systems and/or standards referred to herein.

[00021] A non-uniform constellation (NUC) according to an exemplary embodiment can be generated or obtained using any suitable method, or algorithm including steps (or operations) for generating or obtaining such a non-uniform constellation. The non-uniform constellation according to the embodiment may be generated or obtained by any suitably arranged apparatus or system, which includes means for generating or obtaining such a non-uniform constellation. The methods or algorithms described in this document may be implemented in any suitably arranged apparatus or system, which includes means for carrying out the steps of the method or algorithm.

[00022] Certain exemplary embodiments provide an algorithm for obtaining a non-uniform constellation. The non-uniform constellation obtained in certain exemplary embodiments may provide greater capacity than an equivalent uniform constellation (e.g., a uniform constellation of the same order). Certain exemplary embodiments can obtain an optimized non-uniform constellation using an algorithm with relatively low complexity and relatively high computational efficiency. For example, an algorithm in certain exemplary embodiments can obtain an optimized non-uniform constellation much faster than an algorithm using a brute force method that searches all (or a high proportion of) possible candidate constellations. Certain exemplary embodiments provide an algorithm for obtaining optimized non-uniform constellations suitable for very high order constellation (e.g., having more than 1024 constellation points). Various embodiments are described below in which non-uniform (NU) Quadrature Amplitude Modulation (QAM) constellations are obtained. However, one skilled in the art will appreciate that the inventive concept is not limited to QAM constellations, but can be applied to other types of constellations.

[00023] As mentioned above, a constellation can be characterized by a number of parameters, for example, specifying spacings between constellation points, or specifying the position of each positive real level (complete constellations can be obtained from these parameters, because the constellations are the same for the real and imaginary axes and the same for positive and negative values). In order to obtain an optimal constellation, a brute force approach can be taken in which combinations of values for each of the parameters are searched with a given step size up to a given maximum value. Each combination of values for each parameter corresponds to a different constellation. The constellation having the best performance is selected.

[00024] However, in certain exemplary embodiments, the number of parameters can be reduced by imposing one or more certain geometric and/or symmetry restrictions on the constellations. For example, a constraint might be that the constellations are symmetrical across the four quadrants of the constellations. Furthermore, constellations can be constrained by the fact that the constellation points are arranged in a QAM-type network in which, within each quadrant, (i) constellation points are arranged in horizontal and vertical lines, (ii) the number of horizontal lines is the same as the number of vertical lines, (iii) the same number of constellation points are arranged on each horizontal line, and (iv) the same number of constellation points are arranged on each vertical line. In another example, a constellation may be constrained to be a circular constellation (e.g., a constellation having circular symmetry). Furthermore, constellations having the same relative arrangement, differing only in size, can be considered as equivalent. In this case, one of the parameters can be set to a fixed value. One skilled in the art will appreciate that the inventive concept is not limited to the above examples, and that one or more additional or alternative restrictions may be used.

[00025] In certain exemplary embodiments, a non-uniform QAM (NU-QAM) constellation may have a constellation conforming to one or more geometric and/or symmetry constraints, e.g., one or more, or all, of the above constraints , or a rotation and/or scaling thereof. A non-uniform N-QAM constellation may be a non-uniform QAM constellation including N constellation points.

[00026] By applying the restrictions described above, the number of parameters can be reduced, for example, to 1, 3, 7, 15, 31 and 63 parameter(s) of constellations including 16, 64, 256, 1024, 4096 and 16384 constellation points respectively. The number of parameters in a reduced parameter set can be denoted by b. For example b = 1 for 16-QAM (in which there are 16 positions that are symmetrical on real/imaginary and positive/negative axes). So there are only 2 points to define. Since the total power of the constellation is typically normalized to one, fixing one parameter will correct the other. So b = 1 for a square 16QAM.

[00027] In certain exemplary embodiments, combinations of values for each of the parameters b are searched with a step size d up to a maximum value A. Thus, the number of search iterations is equal to (A/d)b.

[00028] A first algorithm according to certain exemplary embodiments for obtaining an ideal non-uniform constellation for a given SNR will now be described. The algorithm uses an iterative scheme to gradually modify the initial constellation until the constellation converges. For example, the initial constellation may be a uniform constellation, the constellation may be modified by changing parameter values between iterations, and convergence occurs when the values of all parameters change by less than a threshold amount between iterations. An ideal constellation can be defined as the constellation having the best performance according to any suitable measure. For example, the measure may include a coded modulation (CM) capability or a BICM capability. In the following example, a non-uniform 64-QAM constellation is obtained, in which the (reduced) number of variable parameters, b, is equal to 3.

[00029] FIG. 1 is a schematic diagram of a first algorithm, according to an exemplary embodiment, and FIG. 2 is a flowchart of operations illustrating the first algorithm, according to an exemplary embodiment. In the algorithm, the following variables are used. A C_last parameter indicates a particular constellation, which corresponds to a particular set of B parameter values. A C_last parameter starts with a certain starting constellation, for example, a uniform constellation. The SNR parameter indicates a signal-to-noise ratio. The SNR parameter is set to a desired value equal to an SNR for which an ideal constellation is desired. The C_best parameter indicates a constellation that maximizes performance, for example, maximizes CM capacity or BICM capacity, for a given SNR. The d parameter indicates a first step size used in the algorithm. The parameter d (or step) is initialized to a suitable value that can be determined theoretically and/or experimentally. A Min_Step parameter indicates a minimum allowable value for d, and is set to a fixed value.

[00030] In operation 201, C_last is initialized for an input constellation. In a next operation 203, step d is initialized to an Ini_step value. In operation 205, a set of candidate constellations is obtained. The set of candidate constellations includes the C_last constellation and one or more modified constellations, wherein each modified constellation is obtained by modifying one or more of the parameter values that define C_last using any suitable scheme. In the illustrated example, the set of candidate constellations is created based on C_last and step size d, indicated by the CreateSet (C_Last, d) function. For example, for each constellation point, three derived constellations are generated [C_last, C_last + d, C_last - d]. Specifically, a set of constellations is derived such that the values of the parameters b in C_last are each set to one of the new values n that vary around the current parameter value. For example, three new values (n = 3) can be used, which include (i) the current parameter value, (ii) a value of d is greater than the current parameter value, and (iii) a value of d less than the current parameter value. For example, if there are two constellation levels to be defined, then the number of combinations to be tested are 3 X 3 (corresponding to three positions for each level). All combinations of the new parameter values are used to generate the constellation set. Thus, the set of constellations includes a total of nb constellations. Although three new values for each of the parameters are used in the embodiment described above, any suitable number of new values can be used in another embodiment. The set of new values may include the old (or current) value, or may not include the old value.

[00031] In certain exemplary embodiments, three values from each level are chosen so that the total number of possibilities to be tested is 3b, where b is the number of levels (parameters) to be optimized. In the case of higher order constellations, for example above IK, 3b may be too high. In this case, all levels can be fixed except one, for which three possibilities are tested, C_last, C_last d + and C_last - d until convergence is reached. The same operation can then be repeated for the other levels. The cost of this operation is multiplicative and not exponential (for example, it is assumed that each level converges in one iteration, so the cost will be 3 x b instead of 3b).

[00032] In operation 207, the performance of each constellation in the set of derived (candidate) constellations is calculated or determined using any suitable performance measure (e.g., capacity). In operation 209, the candidate constellation having the best performance (e.g., the candidate constellation that maximizes capacity) is assigned to C_best. In operation 211, it is determined whether C_best differs from C_last by more than a threshold amount. For example, in the illustrated example, the threshold quantity is equal to zero, so it is determined whether C_best = C_last. In other words, it is determined whether there is any difference between the C_best constellation and the C_last constellation (for example, within a certain resolution). The difference may be any suitable measure of difference, for example, including a geometry-based difference (e.g., differences in constellation point locations of constellations) and/or a performance measure (e.g., a difference of a certain performance measure between constellations). If it is determined in operation 211 that C_best + C_last, then in operation 213, C_last takes the value C_best (i.e., so that the value of C_last in the next iteration is equal to the value of C_best in the current iteration) and the method returns for operation 205 in which a set of candidate constellations is created based on C_last and step size d, CreateSet (C_Last, d). On the other hand, if it is determined in operation 211 that C_best = C_last, then in operation 215, C_last takes the value C_best and the method moves to operation 217.

[00033] In operation 217, it is determined whether d <Min_Step. If it is determined in operation 217 that d > Min_Step then, the method moves to operation 219 in which the step size d is reduced. For example, d is divided by a certain factor of (e.g., 2). After operation 219, the method returns to operation 205 in which a set of candidate constellations is created based on C_last and the step size d (i.e. reduced d), CreateSet (C_Last, d). On the other hand, if it is determined in operation 217 that d <Min_Step then the value of C_best is saved and the algorithm ends.

[00034] FIG. 3 illustrates the convergence of C_last with respect to one of the parameters as the first algorithm of FIGs. 1 and 2 is performed. Initially, the parameter value converges to a certain value. When the parameter value has converged within a certain resolution, the step size d is reduced and the parameter value converges further, until the step size d has reached the minimum step size.

[00035] In the example shown in FIG. 3, for each iteration, three new parameter values are tried, as represented by the vertical columns of circles. The best new parameter for each iteration is indicated in FIG. 3 as a filled circle. The best parameter value in one iteration is used as the new parameter value for the next iteration. Thus, in the example illustrated in FIG. 3, in which three new parameter values are tested (including the current parameter and parameters by an amount d above and below the current parameter), the filled circle for an iteration corresponds to the average of the three circles arranged in a column for the iteration Following. In certain exemplary embodiments, operations 217 and 219 of the algorithm illustrated in FIG. 2 can be omitted so that operations 205, 207, 209, 211, 213 and 215 are performed using the initial step. In this case, when it is determined in operation 215 that C_best = C_last, the step size is not reduced, but rather the value of C_best is saved and the algorithm ends. By omitting operations 217 and 219, the algorithm can potentially complete more quickly. However, in this case, the C_best output constellation may differ from the true ideal constellation more than the C_best output constellation obtained in the algorithm illustrated in FIG. 2, in which the step size d is decreased. This can be seen in FIG. 3, where it can be seen that the best parameter value in the final iteration is closer to the ideal value (indicated by the horizontal line) than the best parameter value in the convergence stage with the initial step.

[00036] The first algorithm described above determines an optimized constellation based on a certain performance measure (e.g. capacity). The following are several algorithms for determining an optimal constellation for a transmission system defined by a set of one or more system parameter values, where the constellation is optimized for a given desired value of a system parameter (e.g. a certain SNR value or a certain Ricean factor). In these embodiments, a system parameter value is set to an initial value (e.g., a relatively high value) and an ideal constellation is generated using an algorithm described above (e.g., the algorithm illustrated in FIG. 2), wherein The performance measurement is based on a defined transmission system having the defined system parameter value. The system parameter value is then reset to a modified value (e.g., by reducing the value by a certain step size) and the algorithm is tested again. Other system parameter values can remain fixed. This process is repeated until the system parameter value reaches a certain desired value.

[00037] For example, FIG. 4 illustrates a second algorithm for determining an optimal constellation at a given SNR value S in an additive white Gaussian noise (AWGN) channel. In operation 401, the algorithm is started by setting an SNR parameter to a high N value, where N is large. For example, the initial SNR value may be set to a value above which a non-uniform SNR constellation provides no better performance than an equivalent uniform constellation. This value can be determined, for example, theoretically and/or experimentally. In operation 401, the C_last parameter is also initialized for a given constellation, for example, a uniform constellation.

[00038] In operation 403, the first algorithm described above is performed using the initialized C_last constellation as the input constellation and using the initialized SNR ratio. When applying the first algorithm, the C_last constellation will converge to an ideal C_best constellation for a specific input value of SNR. An output of operation 403 is C_best obtained using the first algorithm. In operation 405 the SNR value is reduced by a certain value, for example, a unit or step size. In operation 405, C_last takes the value of C_best (that is, so that the value of C_last in the next iteration is equal to the value of C_best in the current iteration). In operation 407 it is determined whether SNR < S. If it is determined in operation 407 that SNR > S, then the method returns to operation 403, in which the first algorithm is performed with new values of C_last and SNR. On the other hand, if it is determined in operation 407 that SNR < S, then the value of C_best is saved and the algorithm ends. When applying the second algorithm, the resulting C_best constellation is the optimal constellation for the desired SNR value S.

[00039] FIG. 5 illustrates the convergence of the C_best constellation as the second algorithm in FIG. 4 is accomplished. Each of the three curves represents the variation in the value of one of the respective three variable parameters. The constant solid line represents the fixed value of a fixed parameter. As shown in FIG. 5, at the beginning of the second algorithm, starting from the right side of FIG. 5, the SNR value is high and the constellation is a uniform constellation, as defined by the parameter values on the right side of FIG. 5, marked as "initial condition". In each iteration, an optimal constellation is obtained for the specific SNR value (indicated in FIG. 5 by markers). The SNR is then reduced and the ideal constellation is obtained for the new SNR (this process being indicated for one of the parameters by the dotted line in FIG. 5). As shown in FIG. 5, the parameter values corresponding to the ideal constellation vary smoothly with different SNR values. The iterations are repeated until the SNR value reaches the desired SNR value S.

[00040] When performing the second algorithm illustrated in FIG. 4, an ideal constellation is derived from each of a set of SNR values. These constellations can be stored in association with corresponding SNR values, for example, in a look-up table.

[00041] FIG. 6 illustrates a third algorithm for determining an optimal constellation at a given SNR value S in a Rician fading channel for a desired Rician factor K_rice. The Rician channel is given by: [Equation 1]

[00042] In Equation 1, K is the Rician factor and h is Rayleigh distributed (centered and normalized). Initially, the third algorithm applies the second algorithm described above to obtain the ideal constellation C_best at an SNR value S for an AWGN channel, C_best (AWGN). In operation 601, the C_last parameter is initialized to C_best (AWGN). In operation 601, the Rician K factor is initialized to a high value, which can be determined theoretically and/or experimentally. For example, K can be initialized to a value K_rice + N, where N is large. In operation 603, the first algorithm described above is performed using the initialized C_last constellation as the input constellation and using the initialized Rician K factor to obtain an optimal C_best constellation. In operation 605, the Rician k factor is reduced by a certain value, for example, by one unit. In operation 605, C_last takes the value of C_best (that is, so that the value of C_last in the next iteration is equal to the value of C_best in the current iteration). In operation 607 it is determined whether K <K_rice. If it is determined in operation 607 that K > K_rice, then the method returns to operation 603, in which the first algorithm is performed with new values of C_last and K. On the other hand, if it is determined in operation 607 that K < K_rice, then the value of C_best is saved and the algorithm ends. When applying the third algorithm, the resulting constellation C_best is the ideal constellation for the desired Rician factor K_rice.

[00043] FIG. 7 illustrates a fourth algorithm for determining an optimal constellation at a given SNR value S in a Rayleigh fading channel. A Rayleigh fading channel is a special case of Rician fading with the Rician factor K = 0. Thus, the fourth algorithm is the same as the third algorithm described above, except that K_rice is set to zero.

[00044] Table 1 below compares the number of capacity calculation function calls to obtain optimal constellations for various constellation sizes (16-QAM, 64-QAM, and 256-QAM) using an exhaustive search, an exhaustive search restricted and an algorithm according to the present embodiment. The values presented in Table 1 are based on a step size d of 0.0125 and a maximum parameter value of 10. Table 1 also indicates a factor difference between using a restricted exhaustive search and a search using a algorithm according to the present embodiment. As can be seen, the algorithm according to the present embodiment is significantly more efficient, for example, by a factor of 1.15xl010 for 256-QAM [Table 1]

[00045] In Table 1, the difference between exhaustive search and exhaustive restrictive search is as follows. It is assumed below that there are 4 levels (parameters) between 0 and 10. In exhaustive search, each of the 4 parameters is searched over the entire range [0-10] with a certain granularity. In the case of restricted exhaustive search, the range in which each level will fall is fixed. For example, level 1 (first parameter) will be in the range [0-2.5], level 2 in the range [2.5-5], level 3 in the range [5-7.5], level 4 in the range [7.5-10], thus, the number of possibilities is reduced.

[00046] FIG. 8 illustrates a fifth algorithm for determining an ideal constellation. This algorithm closely corresponds to the algorithm illustrated in FIG. 2, but is modified to increase overall efficiency. This algorithm includes an internal circuit for operations (operations 803819) corresponding to operations 203-219 of FIG. 2. However, operation 805 for creating a set of candidate constellations is modified from the corresponding operation 205 of FIG. 2. Specifically, in the algorithm of FIG. 8, instead of modifying each of the b parameters and trying all combinations of the new parameters as in the algorithm of FIG. 2, only one parameter is modified at a time. For example, within one iteration of the 803-819 inner loop, only one parameter (parameter i) is modified to produce a set of candidate constellations. The capabilities of these constellations are calculated and the best constellation is selected, as in FIG. two.

[00047] In the algorithm of FIG. 8, the value of i is varied from 1 to b using an external circuit (operations 821-825). The algorithm of FIG. 8 is initialized at operation 801, which corresponds to operation 201 of FIG. 2. It can be seen that, using the algorithm in FIG. 8, instead of the algorithm of FIG. 2, the total number of candidate constellations tested (i.e., the total number of capacity calculations) is significantly reduced. However, in simulations, the ideal constellation obtained using the algorithm in FIG. 8 is very close to the ideal constellation obtained using the algorithm in FIG. 2, which in turn is very close to the true ideal constellation obtained using an exhaustive search. The improvement in computational efficiency using the algorithms according to the above embodiments, when compared to an exhaustive search, increases as the constellation order increases.

[00048] As with the algorithm illustrated in FIG. 2, in certain exemplary embodiments, operations 817 and 819 of the algorithm illustrated in FIG. 8 can be omitted.

[00049] According to the above embodiments, ideal constellations can be obtained for particular parameters, e.g., SNR, Rician factor, etc. These ideal constellations are obtained independently of any particular system implementation, namely, for example, independent of a particular coding scheme. Next, several modalities for obtaining an ideal constellation for a specific transmission system are described.

[00050] A transmission system may include a number of processes that may affect the optimal constellation, for example, FEC coding, bit interleaving, demultiplexing of bits to cells, mapping of cells to constellations, cell interleaving, rotation constellation, in-phase and quadrature-phase component interleaving (I/Q mapping), inter-frame convolution and inter-frame block interleaving, and multiple-input-single-output (MIS0) precoding. A QAM mapper is used in the Bit Interleaved Coded Modulation (BICM) chain to map bits to symbols. The QAM mapper can use a uniform constellation to map bits to cells (for example, as done in DVB-T2). However, an increase in capacity can be achieved through the use of a fixed non-uniform constellation. A non-fixed non-uniform constellation (e.g. QAM) can be used to further increase capacity. BICM capability depends on the bit for cell mapping used. Optimizations are desirable in LDPC design, QAM mapping, and bit-to-cell mapping.

[00051] In certain exemplary embodiments, different constellations are generated using a certain step size. A bit error rate (BER), a block error rate, and/or a packet error rate corresponding to the constellations are obtained, and the best constellation is selected based on one or more of the above-mentioned error rates.

[00052] In certain exemplary embodiments, the process illustrated in FIG. 9 can be performed to obtain an optimal constellation for a specific system. In operation 901, a uniform constellation (e.g., uniform QAM) is selected. In operation 903, BER values for the selected uniform constellation are obtained over a range of SNR values (e.g., using simulation or by obtaining BER values theoretically or experimentally). These values can be obtained based on a specific system, for example, using a particular coding scheme (e.g. LDPC coding with a certain parity check matrix) with a certain coding rate and a certain bit interleaver and cell interleaver. FIG. 10 illustrates an exemplary plot for 64-QAM using a coding rate of 2/3 of LDPC DVB-T2, on an AWGN channel.

[00053] In operation 905, an SNR at which the BER falls below a threshold value (e.g., 0.001) is determined. The threshold value can be selected such that the resulting SNR falls within a "cascade zone" of the BER curve (i.e., the zone in which BER falls relatively quickly with increasing SNR). The determined SNR value can be denoted S and referred to as a "cascade" SNR.

[00054] Then, an ideal constellation can be obtained for the SNR value S determined in operation 905.

[00055] For example, in some exemplary embodiments, in operation 907a, an ideal constellation may be selected from ideal constellations obtained during execution of the algorithms described above in relation to FIGs. 1 to 8 (and stored in a lookup table). Specifically, a previously determined optimal constellation for the SNR value S can be retrieved from the lookup table.

[00056] Alternatively, an iterative process can be carried out to obtain an ideal (non-uniform) constellation. Specifically, after operation 905, the process moves to operation 907b in which the algorithms described above with respect to FIGs. 1 to 8 are used to obtain an ideal constellation for SNR value S (or a value close to S). After operation 907b, the process returns to operation 903, in which BER values are obtained over a range of SNR values. In this iteration, the BER values are obtained for the ideal constellation obtained in operation 907b (instead of for the initial uniform constellation as in the first iteration). In a similar manner, as described previously, the SNR value at which the BER falls below a threshold value (using the new set of BER values for the ideal constellation) is determined in operation 905, and a new ideal constellation for the newly determined SNR value is obtained in operation 907b. The previously described operations 903, 905, 907 can be repeated a certain number of times (e.g., a predetermined number of times). Alternatively, the algorithm can terminate when the cascaded SNR stops decreasing between iterations, and instead starts increasing.

[00057] FIGS. 11 and 12 illustrate a sixth algorithm for determining an ideal constellation. This algorithm closely corresponds to the algorithm illustrated in FIG. 8, but is modified to improve performance. In particular, this algorithm introduces a concept of a direction of convergence of a parameter value. For example, within the algorithm's internal loop, the direction is initialized to 0. When creating a set of candidate constellations, the candidate set depends on the direction parameter. When the best constellation is selected in operation 1109, the convergence direction of the value of parameter i is obtained. For example, if the parameter value is converging upward, then the direction parameter can be set to +1, if the parameter is converging downward, then the direction parameter can be set to -1, and if the parameter does not change, then the direction parameter can be set to 0. As illustrated in FIG. 12, the number of candidate constellations can be reduced when the parameter value is converging up or down.

[00058] As described above, an ideal constellation can be obtained for a particular application system, and/or for certain system parameter values. For example, an ideal constellation (e.g., a constellation that optimizes BICM capacity) can be obtained for a given type of propagation channel (e.g., AWGN, Rayleigh, or typical urban channel, TU6) and for a given SNR. However, in some cases, data may be transmitted in different scenarios. For example, data may be transmitted over different types of channels and may be received with different SNRs. Furthermore, it may be desirable or necessary for a data transmission system to use the same constellation regardless of the scenario (e.g., channel type or SNR), for example, in order to reduce system complexity. In some cases, a transmission system may use a certain constellation for many different scenarios (e.g., channel types and SNRs).

[00059] FIGS. 13 to 16 illustrate an algorithm for obtaining a constellation that is optimized (e.g., achieves the best capacity) with respect to two or more different scenarios (e.g., different types of channels and/or SNR values). The algorithm includes a number of different parts. First, the cascaded SNR for each channel type (e.g., the propagation channel type) is obtained using an algorithm similar to the algorithm illustrated in FIG. 9. The weighted performance measurement function (e.g., weighted capacity) for an input constellation is defined, based on different scenarios (e.g., different channel types and SNR values). Then, an algorithm similar to the algorithm illustrated in FIGs. 2, 8, or 11 is applied to determine an ideal constellation, where the performance measure is used, based on the weighted performance measure.

[00060] FIG. 13 illustrates a process for obtaining cascaded SNR for each channel type. Each channel type is treated separately in order to obtain its cascaded SNR. In particular, the process illustrated in FIG. 13 is repeated for each channel type to obtain a respective cascaded SNR for the channel type. The process illustrated in FIG. 13 operates in substantially the same manner as the algorithm illustrated in FIG. 9, and therefore a detailed description will be omitted for brevity. However, instead of producing an ideal constellation, as in the algorithm illustrated in FIG. 9, the process illustrated in FIG. 13 produces the cascaded SNR determined in the final iteration of the process. The process illustrated in FIG. 13 (including BER simulation and capacity optimization operations) is performed based on a certain channel type, and the output cascaded SNR is determined as the cascaded SNR associated with that channel type.

[00061] FIG. 14 schematically illustrates a process for obtaining a weighted performance measurement function for an input constellation based on different transmission scenarios. In this example, the weighted performance measure is a weighted capacity, and the different scenarios include different channel types and associated cascaded SNR values. As illustrated in FIG. 14, a candidate constellation is provided as an input. For each channel type and associated cascaded SNR, the BICM capacity for the input constellation is obtained based on the channel type and cascaded SNR. Each obtained BICM capacity is then multiplied by a respective weight and the weighted BICM capacities are summed to obtain an output weighted average BICM capacity. Weights can be selected according to suitable criteria. For example, a relatively common or important channel type may be associated with a relatively large weight.

[00062] FIG. 15 illustrates a process for obtaining an ideal constellation. The process illustrated in FIG. 15 operates in substantially the same manner as the algorithm illustrated in FIGS. 2, 8, or 11, and therefore a detailed description will be omitted for brevity. However, when determining the performance of a candidate constellation in the process illustrated in FIG. 15, performance is determined based on the weighted performance measure described above in relation to FIG. 14.

[00063] In the process illustrated in FIG. 15, in some situations, a given constellation may achieve the best performance with respect to the weighted performance measure, even though the performance of the constellations with respect to individual channel-based BICM capacity and SNR may be relatively low. In certain exemplary embodiments, to ensure that a constellation obtained using the algorithm is capable of achieving at least a certain level of performance for one or more, or all, transmission scenarios, an additional criterion may be applied when testing each constellation. candidate to obtain the C_best constellation. Specifically, any candidate constellation that does not achieve at least a threshold performance with respect to one or more given individual scenarios, or all scenarios, is ignored and cannot be selected as C_best, even if that constellation achieves the best performance with respect to the measure. weighted performance.

[00064] In the process illustrated in FIG. 15, a set of candidate constellations may be derived using any suitable method, for example, the method described above with respect to FIG. 9 based on a step size d. FIGS. 16a and 16b illustrate alternative schemes for generating a candidate constellation from a previous constellation, C_last, which can be used in certain exemplary embodiments. In FIGS. 16a and 16b, the open circles represent the constellation points of a previous constellation, C_last. For each constellation point of the previous constellation, a respective set of N modified constellation points is defined, as indicated in FIGs. 16a and 16b as filled circles. Each set of modified constellation points forms a pattern of constellation points situated relatively close to the respective constellation point of the previous constellation.

[00065] For example, as illustrated in FIG. 16a, each set of modified constellation points can form a square or rectangular network of n = 8 constellation points around a respective constellation point of the previous constellation. The lattice spacing is equal to d.

[00066] Alternatively, as illustrated in FIG. 16b, each set of modified constellation points can form a ring of N = 8 constellation points around a respective constellation point of the previous constellation. The radius of the ring is equal to d.

[00067] A candidate constellation can be obtained by selecting, for each constellation point in the previous constellation, either the constellation point of the previous constellation itself or one of the constellation points of a respective set of modified constellation points.

[00068] In the examples described above, a weighted performance measure is defined based on different transmission scenarios. For example, in the case illustrated in FIG. 14, each transmission scenario includes a different channel type and an associated cascaded SNR value. As a consequence, a constellation optimized for a range of associated channel types and SNR values can be obtained. In an alternative embodiment, an ideal constellation can be obtained in different transmission scenarios, in which case each of the transmission scenarios includes the same channel type but involves different SNR values (e.g., a set of S1 values of SNR, S1 + d, S1 + 2d, S1 + 3d, • ••, S2, where d is a step dimension). That is, an ideal constellation can be obtained by a fixed channel type that is intended to be used over a range of SNR values. In this case, the algorithm described above with respect to FIGs. 13 to 16 may be used, except that when determining the weighted performance measure as illustrated in FIG. 14, instead of determining individual BICM capabilities based on their respective channel types and associated cascaded SNR values, individual BICM capabilities are determined based on fixed channel type and respective SNR values S1, S1+ d, S1 + 2d, S1 + 3d, • ••, S2.

[00069] In the algorithms described above, the technique can be applied to reduce overall complexity. In particular, when a set of candidate constellations is generated and the performance of the candidate constellations is tested, those candidate constellations that were previously tested (i.e., one or more previous iterations) are not tested again. That is, in a current iteration, only candidate constellations that were not tested in previous iterations are tested.

[00070] For example, as described above, a first set of candidate constellations, A, is generated in one iteration, and the best performing candidate constellation, a (aeA), is selected from this set. In a next iteration, a second set of candidate constellations, B, is generated based on the previously selected constellation a (a and B). In this next iteration, the best performing candidate constellation b (beB) from set B needs to be determined.

[00071] Typically, there will be at least some overlap between the two sets of candidate constellations A and B, such that one or more candidate constellations belong to both sets A and B (i.e., A A B + 0), including a constellation . Since it is known that a constellation has the best performance of all constellations in set A, then it is also known that a constellation has the best performance of all constellations belonging to the overlap between sets A and B (i.e. A A B).

[00072] Thus, when testing the constellations in set B to determine the best performing constellation, b, it is not necessary to retest those constellations belonging to the overlap between series A and B (i.e., it is not necessary to retest those constellations in the set A A B) . Instead, instead of testing all constellations in set B, only constellations belonging to the smaller set of constellations B*, including constellations belonging to set B, but excluding any constellations that also belong to set A (i.e., B * = B-A) are tested. Then, the best-performing constellation from the set formed from the union of B* and the previous best-performing constellation, a (i.e., the best-performing constellation from the set B*u{a}) is selected as the constellation of best performance, b, of set B.

[00073] An example of the above principle in relation to the example shown in FIG. 16a is illustrated in FIG. 17. In the example of FIG. 17, in iteration i, it was found that the constellation point indicated as a black circle is the best performing constellation. In iteration i+1, there is no need to test the common subset (including the white circles and the black circle) because it has already been tested before and underperformed. That is, in iteration i + 1, only the dark gray circles need to be tested. As a consequence, in the illustrated example, a complexity reduction of 44% (= 4/9) is obtained.

[00074] FIG. 18 illustrates an apparatus for implementing an algorithm according to one or more of the embodiments described above. The device is configured to generate a non-uniform constellation. The apparatus includes a block for carrying out a first process. The block for carrying out the first process includes: a block for obtaining a first constellation defined by one or more parameter values; and a block for generating a second constellation based on the first constellation using a second process. The block for generating the second constellation based on the first constellation using the second process includes: a block for obtaining a set of candidate constellations, wherein the set of candidate constellations includes the first constellation and one or more modified constellations, wherein each modified constellation is obtained by modifying the values of the parameters that define the first constellation; a block for determining the performance of each candidate constellation according to a predetermined performance measure; and a block for selecting the candidate constellation having better performance than the second constellation. The block for carrying out the first process further includes a block for determining a difference between the first constellation and the second constellation; and a block for, if the second constellation differs from the first constellation by more than a threshold amount, to cause the block for performing the first process to repeat the first process that uses the second constellation generated in a current iteration of the first process, as the first constellation in a next iteration.

[00075] One skilled in the art will appreciate that the functions of any two or more blocks illustrated in FIG. 18 can be performed by a single block, and that the functions of any block illustrated in FIG. 18 can be performed by two or more blocks. A block may be implemented in any suitable form, for example, hardware, software, firmware, or any suitable combination of hardware, software and firmware.

[00076] A constellation obtained by a method according to the exemplary embodiments described above can be used in a digital broadcasting system to transmit data from a transmitter side to a receiver side. In certain exemplary embodiments, the system includes a transmitter arranged to obtain data (e.g., a data stream), perform any required encoding and/or other data processing, modulate a signal using the data in accordance with a modulation that corresponds to the constellation, and transmit the modulated signal. The system further includes a receiver configured to receive a modulated signal, demodulate the signal in accordance with a demodulation scheme corresponding to the constellation (or a similar or corresponding constellation), and perform any necessary decoding and/or other processing to recover the original data. . Certain exemplary embodiments may include a transmit-side apparatus only, a receive-side apparatus only, or a system that includes both a transmit-side apparatus and a receive-side apparatus.

[00077] In the case of non-uniform constellations, it is possible to design constellations by relaxing only one restriction, that is, maintaining a square constellation, but changing the distance between the constellation points. This form of non-uniform constellations (NUCs) can be called one-dimensional constellations (1D NUCs). The 1D NUCs can be described by levels at which constellations occur in the positive real part. The other points can be deduced using the symmetry of the four quadrants, as well as real and imaginary symmetry. 1D NUCs are simple to decode because of the independence of the real and imaginary part. Two (2) pulse amplitude modulator (PAM) demappers can be used to decode the 1D NUCs.

[00078] It is possible to design a different type of NUC, relaxing both restrictions: the square shape and the uniform distance between the constellation points. Ideal constellations will have a tendency to resemble a circular constellation. This type of NUC can be called 2D-NUC. The 2D-NUC has a higher capacity than the 1D-NUC and a better BER/FER performance. However, 2D-NUC performance is achieved at the expense of a more complex receiver demapper.

[00079] Since the real and imaginary axes are not symmetric, a 2D demapper is necessary in order to decode a 2D-NUC constellation. In the case of 2D-NUC, a complete set of points needs to be specified. It is possible to specify only the points belonging to the first quadrant, and deduce the other points assuming that the constellation is symmetric.

[00080] The optimization of 1D and 2D NUCs depends on an SNR in which a capacity has to be optimized. In the case of a BICM chain, an SNR can be selected to be a cascaded SNR of a BER/FER curve. Cascade BER/FER can be defined as an SNR in which a BER curve drops below a certain level, for example, 10e-6. Cascaded SNR depends on a coding rate of an LDPC encoder/decoder. As the code rate increases, the cascaded SNR increases. For this reason, a different NUC is associated with each LDPC encoder coding rate. The cascaded SNR also increases with a QAM constellation size (M). This is because the receiver needs a higher SNR to decode a higher QAM constellation. Thus, a constellation size and coding rate define the cascaded SNR. Cascaded SNR is used to optimize constellations. Here the encoding rates include: 2/15, 3/15 and 4/15. NUC sizes are: 16QAM, 64QAM, 256QAM and 1K QAM. For the first three QAM sizes only 2D constellations are proposed. For 1K QAM both 1D and 2D constellations are proposed.

[00081] Next, an example of constellation points of a constellation obtained by applying the algorithms described above by rate coding will be described.

[00082] In the following exemplary embodiment, a restriction is added to the process of determining capacity according to SNR with respect to the existing NUC modeling method.

[00083] When the SNR is given, it is general to calculate the maximum transmission capacity that can be transmitted error-free. In other words, when calculating SNR holding capacity with respect to cascaded BER/FER, SNR indicates an area where a bit error or frame error occurs, but actual capacity indicates transmission capacity under circumstances free from error and therefore cannot be a contradiction.

[00084] As a consequence, in the present disclosure, when calculating capacity with respect to SNR, a correction factor is added.

[00085] For example, when SNR1 is decided with respect to CH1 in FIG. 1, if the capacity value in error-free state is C1, corrected C1 value, which is C1' is defined as shown below. [Equation 2]

[00086] Here, Pb indicates a BER value that determines a cascade area, and H(x) function indicates the binary entropy function, H(x) = -X log2(X) - (1-X) x log2(1-X).

[00087] In this case, the reason why the value of (1-H(Pb)) which is less than or equal to 1 is multiplied by the value of the existing capacity, as indicated in Equation 2, is as shown below.

[00088] With respect to a case where a bit error occurs as much as the probability of Pb in a transmission channel, if it is assumed that a bit error as much as Pb was occurred before transmitting source information, and error does not occur As long as the source information is being transmitted, there is no difference in terms of a bit error at the transmitting end/receiving end. As described above, when the probability of error occurrence with respect to a channel is considered a loss of source information, there is an effect, as if lossy compression is applied, as much as H (Pb) compared to the data provided , by the Shannon rate distortion theory. That is, in conclusion, it can be considered that the amount of data that can be transmitted through, firstly given channel, which is the capacity, will be reduced compared to the channel (L-H (Pb)) without an error or loss.

[00089] When the same value is applied to all channels that consider Pb in FIG.14, the same factor (1-H(Pb)) is multiplied, and, therefore, the same factor (1-H(Pb)) is multiplied with the weighted capacity value. Thus, there is no difference in the constellation points of the optimized NUC. However, target BER may be different for each channel and therefore the order of magnitude of the weighted capacity may be different. As a consequence, the optimized NUC constellation points may be different. For example, an AWGN channel is applied to a generally fixed device and therefore very low BER is required. Therefore, when calculating capacity, BER = le-8 can be considered. As the Rayleigh channel is largely considered a moving channel that experiences fading, a higher BER than that of the AWGN channel is required. Thus, BER = le-6 can be considered. As described above, if different BER requirements are defined for the respective channels, the factor values for final capacity become different and therefore this value may be different from the NUC constellation points that are obtained taking into account only the capacity without reflect BER.

[00090] To be more specific, Table 2 indicates the constellation point values of a normalized 2D NU 16-QAM (2D 16NUC) constellation that is obtained by applying the algorithms described above, using the respective 2/15 coding rates, 3/15 and 4/15 for a single SNR value. [Table 2]

[00091] In this case, the constellation points of the 2D NU 16-QAM constellation for the respective coding rates of 2/15, 3/15, and 15/4 are indicated in FIGs. 19 to 21.

[00092] Table 3 indicates the constellation point values of a normalized 2D NU 64-QAM constellation (2D 64NUC) that is obtained by applying the algorithms described above, using the respective coding rates 2/15, 3/15 and 4 /15 for a single SNR value. [Table 3]

[00093] In this case, the constellation points of the 2D NU 64-QAM constellation for the respective coding rates of 2/15, 3/15 and 4/15 are indicated in Figs. 22 to 24.

[00094] Table 4 indicates the values of the constellation points of a normalized 2D NU 256-QAM constellation (2D 256NUC) that is obtained through the application of the algorithms described above, using the respective coding rates 2/15, 3/15 and 4/15 for a single SNR value. [Table 4]

[00095] In this case, the constellation points of the 2D NU 256-QAM constellation for the respective coding rates of 2/15, 3/15, 4/15 and are illustrated in FIGs. 25 to 27

[00096] However, according to Tables 2 to 4, when the values of constellation points are determined from one quadrant, the values of constellation points in other quadrants can be deduced by symmetry. For example, for each constellation point A in the upper right quadrant, corresponding constellation points may be present in three different quadrants (bottom right, bottom left and top left) respectively, and they can be denoted as A*, -A*, and -A. Here, * indicates complex conjugation.

[00097] Table 5 indicates constellation point values of a normalized 1D NU 1024-QAM constellation (1D 1024NUC) that is obtained by applying the algorithms described above, using the respective coding rates 2/15, 3/15 and 4/ 15 for a single SNR value. [Table 5]

[00098] In this case, the constellation points of the 1D NU 1K QAM constellation for the respective coding rates 2/15, 3/15 and 4/15 can be illustrated in FIGs. 28 to 30.

[00099] For example, FIG. 28 illustrates an exemplary 1D NU 1024-QAM constellation obtained by applying the algorithms described above, using the coding rate of 2/15.

[000100] According to FIG. 28, a complete set of points on the right side of the drawing. The values of the constellation points in the upper right quadrant are indicated on the upper left side of the drawing.

[000101] In the case of 1D NU 1K QAM constellation, instead of giving the values of the constellation points explicitly, a set of levels of the constellation points is given instead, from which the actual values of the constellation points can be be deducted. To be more specific, given a set of m levels A = [A1, A2, ..., An], a set of m2 constellation point values C + Di can be deduced. Here, C and D can each include a value selected from a set of level A. A complete set of constellation points in the upper right quadrant can be obtained by considering all possible pairs of values of C and D According to FIG. 28, the values of the constellation points in the remaining three quadrants can similarly be deduced by symmetry. As an example, according to Table 5, when the encoding rate is 2/15, A = {1, 1.000988842, ..., 2.818221832}, and a group of C + Di corresponding to a constellation point set of the first quadrant has 256 elements, such as {1 + i, 1 + 1.000988842 X i, 1.000988842 + i, •••, 2.818221832 2.818221832 + Full set of 1D NU 1024-QAM constellation points can be obtained by indicating an arbitrary element in the group, such as a*, -a* and -a. Here, * indicates complex conjugation.

[000102] Table 6 indicates the constellation point values of a normalized 1D NU 4096-QAM constellation (1D 4096NUC) that is obtained by applying the algorithms described above, using the respective coding rates 2/15, 3/15, 4 /15 and 5/15 for a single SNR value [Table 6]

[000103] In this case, the constellation points of the 1D NU 4096-QAM constellation for the respective coding rates 2/15, 3/15, 4/15 and 5/15 can be illustrated in FIGs. 31 to 34.

[000104] In the case of 1D NU 4K QAM constellation, instead of giving the values of the constellation points explicitly, a set of levels of the constellation points are given instead, from which the actual values of the constellation points can be be deducted. To be more specific, given a set of m levels A = [A1, A2, • • •, Am, and a set of m2 constellation point values C + Di can be deduced. Here, C and D can each include a value selected from a set of level A. A complete set of constellation points in the upper right quadrant can be obtained by considering all possible pairs of values of C and D That is, the values of constellation points in the remaining three quadrants can be similarly deduced by symmetry. As an example, according to Table 6, when the coding rate is 2/15, A = {1, 1.020833333, 5.1875}, and a group of C + Di corresponding to a set of points constellation of the first quadrant has 256 elements, such as {1 + i, 1 + 1.020833333 X i, 1.020833333 + i, •••, 5.1875 + 5.1875 X i}, the complete set of 1D constellation NU 4096-QAM can be obtained by indicating an arbitrary element a in the group, such as a*, -a* and -a. Here, * indicates complex conjugation.

[000105] As described above, in the 1D-NUC of Tables 5 and 6, the constellation can be described by the levels at which the constellations occur in the positive real part. Constellation points can be deduced using real/imaginary symmetry, but also four quadrant symmetry.

[000106] However, the inventive concept is not limited to the constellations defined in Tables 2 to 6. For example, when different sizes of normalization and rounding are applied to the constellation point values defined in Tables 2 to 6, the values can be indicated as in Tables 7 to 11. In this case, the constellation defined in Tables 7 to 11 may be an exemplary embodiment.

[000107] Tables 7 to 11 illustrate the set of constellation points for just one quadrant, but it is obvious to obtain a complete set of constellation points by indicating the constellation point a in the quadrant, such as a*, -a* , and the. Here, * indicates complex conjugation.

[000108] To be more specific, Table 7 indicates the constellation point values of the 2D NU-16QAM constellation (2D 16NUC) which is obtained by applying normalization and rounding of the constellation point values defined in Table 2. Table 7]

[000109] In this case, the values of the constellation points of other quadrants can be determined by symmetry.

[000110] Table 8 indicates constellation point values of a 2D NU 64-QAM (2D 64NUC) constellation that is obtained by applying normalization and rounding of the constellation point values defined in Table 3. [Table 8]

[000111] In this case, the values of the constellation points of other quadrants can be determined by symmetry.

[000112] Table 9 indicates the constellation point values of a 2D NU 256-QAM (2D 256NUC) constellation that is obtained by applying normalization and rounding of the constellation point values defined in Table 4. [Table 9]

[000113] In this case, the values of the constellation points of other quadrants can be determined by symmetry.

[000114] Table 10 indicates the constellation point values of a 1D NU 1024-QAM (1D 1024NUC) constellation that is obtained by applying normalization and rounding of the constellation point values defined in Table 5. [Table 10]

[000115] Table 11 indicates the constellation point values of a 1D NU 4096-QAM (1D 4096NUC) constellation that is obtained by applying normalization and rounding of the constellation point values defined in Table 6. [Table 11]

[000116] However, it should be noted that the method for obtaining a complete set of constellation points as in Tables 10 and 11 is completely the same as the method described in Tables 5 and 6.

[000117] However, those skilled in the art may recognize that rotation, scaling (here, the scale factor applied to a real axis and an imaginary axis may be the same or different) or any other transformation may be applied with respect to the constellation described above. The constellation indicates a comparative position of the constellation points, and another constellation can be deduced through rotation, scaling, or any other transformation.

[000118] Furthermore, those skilled in the art can recognize that the inventive concept is not limited to the constellation defined in Tables 2 to 11 described above.

[000119] For example, in certain exemplary embodiments, a constellation having a different order and/or a constellation including a different arrangement or in a comparative position of the constellation points can be used. As another example, a constellation that is similar to one of the constellations defined in Tables 2 through 11 can be used.

[000120] For example, a constellation that has constellation point values with differences that do not exceed a predetermined threshold (or error) from the values indicated in Tables 2 to 11 can be used. Here, the threshold value can be expressed as comparative numbers (e.g. 0.1%, 1%, 5%, etc.), absolute numbers (e.g. 0.001, 0.01, 0.1, etc.) or appropriate methods (rounding, minimization, maximization or similar). As an example of rounding, the constellation point "0.707316 + 0.707473i" can be approximated to "0.7073 + 0.7075i" by rounding to five decimal places.

[000121] Furthermore, a transmitter and a receiver may use different constellations. For example, a transmitter and a receiver may use respective constellations that have at least one constellation point that has a difference that does not exceed a predetermined threshold value. For example, a receiver may use a constellation that has at least one rounded-down/rounded-down constellation point (e.g., A2) to unmap the constellation points, while a transmitter may use a constellation having unrounded constellation points. approximated/rounded down (e.g. A1).

[000122] Furthermore, even if an order of values in Tables 2 to 11 is changed, the set of constellation points itself is not changed, and thus, it is possible to arrange the values by changing the order of values as in Tables 2 to 11.

[000123] Hereinafter, an example of a normalization method and an example embodiment of the 2D constellation of constituting a 1D level set will be described.

[000124] For example, in Table 12, it is assumed that the constellation point values of a 1D NU 1K QAM constellation for a 13/15 coding rate are as shown below. [Table 12]

[000125] Here, when a level A vector is indicated as A = (ai), (i = 0, 1, 2, •••, L-1), first of all, the A vector is normalized, using the equation 3 below, and the normalized vector It can be obtained. [Equation 3]

[000126] In Equation 3 above, L indicates the level number (i.e. dimensionality of A). For example, in the case of 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM, the level dimensionality can be 4, 6, 8, 10, and 12, respectively.

[000127] In the example described above, the normalized vector can be indicated as Table 13 shown below. [Table 13]

[000128] If the normalization method described above applied to Tables 5 and 6, respectively, it can be easily recognized that Tables 10 and 11 will be obtained, respectively.

[000129] Then, a final constellation is generated such that all possible combinations of the real part and the imaginary part, which are the same as one of the inputs (i.e., components). In this case, for example, gray mapping can be used.

[000130] In the example described above, the constellation points in the first final quadrant can be indicated as in Table 14 below. [Table 14]

[000131] FIG. 35 is a block diagram for describing a configuration of a transmission apparatus in accordance with an exemplary embodiment. With reference to FIG. 35, transmission apparatus 3500 includes an encoder 3510, an interleaver 3520, and a modulator 3530 (or, "constellation mapper").

[000132] Encoder 3510 performs channel coding relative to the input bits and generates a keyword.

[000133] For example, encoder 3510 can perform LDPC encoding with respect to bits and generate an LDPC codeword using an LDPC encoder (not shown).

[000134] Specifically, the encoder 3510 can perform LDPC coding with the input bits as the information word bits, and generate the LDPC code word that constitutes the information word bits and parity bits (i.e., the LDPC parity bits). In this case, the code is a systematic LDPC code, the information word can be included in the LDPC code word as it is.

[000135] Here, the LDPC codeword consists of information word bits and parity bits. For example, the LDPC code word has Nldpc bits, and may include the information word bits formed from Kldpc bits and parity bits formed from Nparity = Nldpc - Kldpc parity bits.

[000136] In this case, the encoder 3510 can perform LDPC encoding based on a parity check matrix and generate the LDPC code word. That is, a process of realizing LDPC coding is a process of generating the LDPC code word that satisfies H. CT = 0, and therefore the encoder 3510 can use the parity check matrix when performing LDPC encoding. Here, H is a parity check matrix and C is an LDPC code word.

[000137] To achieve this, the transmission apparatus 3500 may include a separate memory and pre-store various types of a parity check matrix.

[000138] However, this is merely exemplary, and channel coding can be performed in various schemes.

[000139] The encoder 3510 can perform channel coding using different coding rates, such as 2/15, 3/15, 4/15, 5/15, 6/15, 7/15, 8/15, 9/ 15, 10/15, 11/15, 12/15 and 13/15. Furthermore, the encoder 3510 can generate a codeword with different lengths, such as 16200 and 64800 based on a bit length and coding rate.

[000140] An interleaver 3520 interleaves the code word. That is, the interleaver 3520, based on various interleaving rules, can perform interleaving of codeword bits generated by the encoder 3510.

[000141] A modulator 3530 maps the code word that is interleaved according to a modulation scheme to a non-uniform constellation.

[000142] Specifically, modulator 3530 can perform series-to-parallel conversion with respect to the interleaved codeword, and demultiplex the interleaved codeword to a cell (or a cell word) formed by a certain number of bits.

[000143] For example, the modulator 3530 may receive the codeword bit output Q = (q0, q1, q2, ...) from the interleaver 3520, and generate cells.

[000144] In this case, the number of bits that constitute each of the cells may be the same as the number of bits that constitute a modulation symbol (i.e., a modulation order). For example, when the modulator 3530 performs modulation using QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, 4096-QAM, the number of qMOD bits constituting the modulation symbol may be 2, 4, 6, 8, 10 and 12.

[000145] For example, when the modulation scheme is 64-QAM, qMOD is 6 (qMOD = 6), and thus, each cell can be composed of (q0, q1, q2, q3, q4, q5), (q6 , q7, q8, q9, q10, q11), (q12, q13, q14, q15, q16, q17), ...

[000146] Furthermore, the modulator 3530 can perform modulation by mapping the cells in the non-uniform constellation.

[000147] Specifically, each cell includes bits as much as the number constituting the modulation symbol, and thus the modulator 3530 can generate the modulation symbol by sequentially mapping each of the cells to a constellation point of the non-uniform constellation. Here, the modulation symbol corresponds to a constellation point of a constellation.

[000148] In this case, constellation may include constellation points that are defined based on Tables 2 to 11, according to a modulation scheme.

[000149] To be more specific, the constellation may include the constellation points, which are defined by a constellation position vector as in Tables 2 to 4 and 7 to 9, according to a modulation scheme. Or, the constellation may include the constellation points, which are defined by the constellation position vector that is generated based on the level defined as in Tables 5, 6, 10, and 11 according to a modulation scheme.

[000150] That is, modulator 3530, taking into account the coding rate used for coding by encoder 3510, can perform modulation by mapping cells to the set of constellation points that correspond to the coding rate between the sets of constellation points that are defined based on Tables 2 to 11 according to coding rates.

[000151] For example, constellation may include constellation points that are defined based on Table 8, when a modulation scheme is 64-QAM.

[000152] To be more specific, modulator 3530, when coding is performed with the coding rate of 2/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_64_2 /15 of Table 8.

[000153] That is, when the coding rate is 2/15 and the modulation is performed to 2D 64 NUC, the constellation points in the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2, ..., W14, W15} = {0.6474 + 0.9831i, 0.6438 + 0.9829i, 0.6471 + 0.9767i, + 0.6385 + 0.4656i, 0.6353 + 0 ,4653i} which is defined as NUC_64_2/15 from Table 8.

[000154] Furthermore, modulator 3530, when coding is performed with the coding rate of 3/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_64_3/15 from Table 8.

[000155] That is, when the coding rate is 3/14 and the modulation is performed to 2D 64NUC, the constellation points in the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2, ..., W14, W15} = {0.5472 + 1.1591i, 0.5473 + 1.1573i, 0.5467 + 1.1599i, ..., 0.5087 + 0.3163i, 0.5087 + 0.3163i} which is defined as NUC_64_3/15 from Table 8.

[000156] Furthermore, modulator 3530, when coding is performed with the coding rate of 4/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_64_4/15 from Table 8.

[000157] That is, when the coding rate is 4/15 and the modulation is performed at 2D 64NUC, the constellation points of the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2 , ..., W14, W15} = {0.5008 + 1.2136i, 0.4994 + 1.2194i, 0.5313 + 1.1715i, ... 0.4791 + 0.2773i, 0.4791 + 0.2758i} which is defined as NUC_64_4/15 from Table 8.

[000158] Table 8 indicates the constellation points in a constellation quadrant, and the constellation points in the remaining constellation quadrants can be obtained by indicating each constellation point a, which is defined in Table 8, as a*, -a *, and -a, respectively. (Here, * indicates complex conjugation).

[000159] As another example, when the modulation scheme is 256-QAM, constellation points that are defined based on Table 9 can be included.

[000160] Specifically, the modulator 3530, when coding is performed with the coding rate of 2/15 by the encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_256_2/15 of the Table 9.

[000161] That is, when the coding rate is 2/15 and the modulation is performed to 2D 256NUC, the constellation points of the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2 , ... W62, W63} = {0.5553 + 1.1262i, 0.5673 + 0.1336i, 0.5593 + 1.1204i, ..., 0.5319 + 0.3381i, 0.5327 + 0.3395i} which is defined as NUC_256_2/15 from Table 9.

[000162] Furthermore, modulator 3530, when coding is performed with the coding rate of 3/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_256_3/15 from Table 9.

[000163] That is, when the coding rate is 3/15 and the modulation is performed at 2D 256NUC, the constellation points of the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2 , ..., W62, W63} = {0.5229 + 1.1810i, 0.5384 + 1.1625i, 0.5148 + 1.1943i, 0.4734 + 0.2696i, 0.4749 + 0.2711i } which is defined as NUC_256_3/15 from Table 9.

[000164] Furthermore, modulator 3530, when coding is performed with the coding rate of 4/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_256_4/15 from Table 8.

[000165] That is, when the coding rate is 4/15 and the modulation is performed at 2D 256NUC, the constellation points of the first quadrant of the constellation can be expressed as the constellation position vector {W0, W1, W2 , ..., W62, W63} = {0.2975 + 1.0564i, 0.5862 + 0.9617i, 0.2909 + 1.0696i, 0.3762 + 0.1998i, 0.3689 + 0.2114i } which is defined as NUC_256_4/15 from Table 9.

[000166] Table 9 indicates the constellation points in a quadrant of the constellation, and the constellation points in the remaining quadrants of the constellation can be obtained by indicating each constellation point a, which is defined in Table 9, as a*, -a * and -a respectively (Here, * indicates complex conjugation).

[000167] As another example, the constellation, when the modulation scheme is 1024-QAM, may include constellation points, which are defined based on Table 10.

[000168] Specifically, modulator 3530, when coding is performed with the coding rate of 2/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_lk_2/15 of the Table 10.

[000169] That is, when the coding rate is 2/15 and modulation is performed for 1D 1024NUC, the level set can be A = {0.3317, 0.3321, 0.3322, ..., 0.9394, 0.9349} as NUC_lk_2/15 from Table 10, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.3317 + 0.3317i, 0.3317 + 0 .3321i, 0.3321 + 0.3317i, ..., 0.9349 + 0.9349i}.

[000170] Furthermore, modulator 3530, when coding is performed with the coding rate of 3/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_lk_3/15 from Table 10.

[000171] That is, when the coding rate is 3/15 and the modulation is performed for 1D 1024NUC, the level set can be A = {0.2382, 0.2556, 0.2749, ..., 0.9459, 1.4299} as NUC_1k_3/15 from Table 10, and the constellation position vector indicating the constellation points of the first quadrant can be expressed as {0.2382 + 0.2382i, 0.2382 + 0 .2556i, 0.2556 + 0.2382i, ..., 1.4299 + 1.4299i}.

[000172] Furthermore, modulator 3530, when coding is performed with the coding rate of 4/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_1k_4/15 from Table 10.

[000173] That is, when the coding rate is 4/15 and modulation is performed for 1D 1024NUC, the level set can be A = {0.1924, 0.1940, 0.2070, ..., 1.1332, 1.4761} as NUC_1k_4/15 from Table 10, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.1924 + 0.1924i, 0.1924 + 0 ,1940i, 0.1940 + 0.1924i, ..., 1.4761 + 1.4761i}.

[000174] Table 10 is used to define the constellation points in a constellation quadrant, and the constellation points in the remaining quadrants can be obtained by indicating each constellation point, which is defined based on Table 10, as a*, -a*, and -a (Here, * indicates complex conjugation).

[000175] As another example, the constellation, when the modulation scheme is 4096-QAM, may include constellation points, which are defined based on Table 11.

[000176] Specifically, modulator 3530, when coding is performed with the coding rate of 2/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_4k_2/15 of the Table 11.

[000177] That is, when the coding rate is 2/15 and the modulation is performed for 1D 4096NUC, the level set can be A = {0.2826, 0.2885, 0.2944, ..., 1.0185, 1.4660} as NUC_4k_2/15 from Table 11, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.2826 + 0.2826i, 0.2826 + 0.2885i , 0.2885 + 0.2826i, ..., 1.4660 + 1.4660i}.

[000178] Furthermore, modulator 3530, when coding is performed with the coding rate of 3/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_4k_3/15 from Table 11.

[000179] That is, when the coding rate is 3/15 and the modulation is performed for 1D 4096NUC, the level set can be A = {0.2038, 0.2038, 0.2155, ..., 1.0658, 1.6424} as NUC_4k_3/15 from Table 11, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.2038 + 0.2038i, 0.2038 + 0, 2155i, 0.2155 + 0.2038i, ..., 1.6424 + 1.6424i}.

[000180] Furthermore, modulator 3530, when coding is performed with the coding rate of 4/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_4k_4/15 from Table 11.

[000181] That is, when the coding rate is 4/15 and the modulation is performed for 1D 4096NUC, the level set can be A = {0.1508, 0.1468, 0.1456, ..., 1.1683, 1.6391} as NUC_4k_4/15 from Table 11, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.1508 + 0.1508i, 0.1508 + 0 ,1468i, 0.1468 + 0.1508i, ..., 1.6391 + 1.6391i}.

[000182] Furthermore, modulator 3530, when coding is performed with the coding rate of 4/15 by encoder 3510, can map the interleaved codeword into the non-uniform constellation, which includes the constellation points defined by NUC_4k_5/15 from Table 11.

[000183] That is, when the coding rate is 5/15 and modulation is performed for 1D 4096NUC, the level set can be A = {0.1257, 0.1257, 0.1257, ..., 1.1882, 1.6566} as NUC_41k_5/15 from Table 11, and the constellation position vector indicating the constellation points in the first quadrant can be expressed as {0.1257 + 0.1257i, 0.1257 + 0, 3599i, 0.3599 + 0.1257i, ..., 1.6566 + 1.6566.}.

[000184] Table 11 is used to define the constellation points in quadrant a, and the constellation points with respect to the remaining quadrants of the constellation can be obtained by indicating each constellation point a, which is defined based on Table 11, as a*, -a*, and -a (Here, * indicates complex conjugation).

[000185] In the examples described above, it is described that the cells are mapped to the set of constellation points that correspond to the coding rate used for coding, but this is merely exemplary and, in some cases, the modulator 3530 can map the cells in the set of constellation points that does not match the encoding rate that is used for encoding.

[000186] As an example, when 64-QAM is used, even if coding is performed with the coding rate of 2/15, the modulator 3530 can map the cells to the set of constellation points that are defined as NUC_64_3/ 15 or NUC_64_4/15 of Table 8, instead of the set of constellation points that are defined as NUC_64_2/15 of Table 8.

[000187] The transmitting apparatus 3500 can modulate a signal that is mapped into the constellation and transmit the signal to a receiving apparatus (e.g., 3600 of FIG. 36). For example, the transmission apparatus 3500 may map the signal that is mapped to the constellation into an orthogonal frequency division multiplexing (OFDM) frame using an OFDM scheme, and may transmit the signal to the receiving apparatus 3600 via an assigned channel.

[000188] In other words, in the mapping method for 16-QAM, 64-QAM and 256-QAM, each input data cell word (y0,s, ..., yπMOD-1.s) must be modulated using a 2D non-uniform constellation to produce a constellation point zs. The index S indicates the discrete time index, , where M is the number of constellation points, for example, M = 64 for 64-QAM. The complex constellation point vector X = (x0,..., XM-1) includes all constellation points M from the QAM alphabet. The Kth element of this vector, s being the most significant bit (MSB), and ynMOD-1.s being the least significant bit (LSB)). Due to quadrant symmetry, the full vector x can be derived by defining only the first quarter of the complex constellation points, i.e. (X0, ..., XM/4-1), which corresponds to the first quadrant. The generation rule for the remaining points is described below. Setting b = M/4, in the first quarter of complex constellation points is denoted as the NUC position vector w = (w0, ..., wb-1). Position vectors are defined in the tables above. As an example, the NUC position vector for a 16-QAM comprises the complex constellation points with markings corresponding to 0 decimal values, i.e., (y0,s, ..., ynMOD-1.s) = 0000, for b - 1, that is, (y0,s, ..., ynMOD-1.s) = 0011. The remaining constellation points are derived as follows: (X0, ..., Xb-1) = w (first quarter) (Xb, ..., X2b-1) = -conj (w) (second quarter) (X2b, ..., X3b-1) = conj (w) (third quarter) (X3b, .. ., X4b-1) = - w (fourth quarter), with “conj” being the complex conjugate.

[000189] As an example, the NUC position vector for 16-QAM and the code rate of 2/15 are constructed as follows. From Table 7, W = (0.7073 + 0.7075i, 0.7073 + 0.7074i, 0.7060 + 0.7077i, 0.7065 + 0.7071i). Here and hereafter, it is imaginary unity. Assuming the input data cell word is (y0,s, ..., yπM0D-i.s) = (1100), the corresponding QAM constellation point at time index s is Zs = x12 = -w0 = -0 .7073-0.7075i.

[000190] Furthermore, in the 1024-QAM and 4096-QAM mapping method, each input data cell word (y0,s, ..., ynMOD-1.s) at the discrete time index s must be modulated using a non-uniform single-dimensional QAM constellation to produce a ZS constellation point before normalization. Monodimensional refers to the fact that a two-dimensional QAM constellation can be separated into two one-dimensional PAM constellations, one for each I and Q component. The exact values of the real and imaginary components Re(ZS) and Im(ZS) for each relevant input cell word combination (y0,s, ..., yπMOD-1.s) are given by a 1D-NUC position vector u = (U0, ..., UV), which defines the positions of the constellation points of non-uniform constellation in one dimension. The number of elements in the position vector u is defined by

[000191] As an example, the 2/15 code rate 1024-NUC is defined by the NUC position vector NUC_1k_2/15. From Table 10, u = (u0, ..., u15) = (0.3317, 0.3321, 0.3322, 0.3321, 0.3327, 0.3328, 0.3322, 0.3322 , 0.9369, 0.9418, 0.9514, 0.9471, 0.9448, 0.9492, 0.9394, 0.9349). Assuming that the input data cell (y0,s, ..., ynMOD-1.s) = (0010011100) the corresponding QAM constellation point ZS has Re(ZS) = u3 = 0.3321 (defined by the same markings of index bits, i.e. 01010) and Im(ZS) = u11 = 0.9471 (defined by marking odd index bit, i.e. 00110).

[000192] FIG. 36 is a block diagram for describing a configuration of receiving apparatus in accordance with an exemplary embodiment. With reference to FIG. 36, the receiving apparatus 3600 includes a demodulator 3610, a deinterleaver 3620, and a decoder 3630.

[000193] The demodulator 3610 receives and demodulates a signal transmitted from the transmission apparatus 3500. Specifically, the demodulator 3610 can generate a value that corresponds to the code word by demodulating the received signal.

[000194] In this case, the demodulator 3610 can perform demodulation to match the modulation scheme that is used by the transmitting apparatus 3500. To do this, the transmitting apparatus 3500 can transmit information about the modulation scheme to the receiving apparatus 3600 , or the transmitting apparatus 3500 may perform modulation using the modulation scheme that is predefined between the transmitting apparatus 3500 and the receiving apparatus 3600. However, a value corresponding to the code word may be expressed as a channel value with respect to the received signal. There may be several methods for determining the channel value, for example, a method for determining a log likelihood ratio (LLR) value is an example of the method for determining the channel value.

[000195] The LLR value may indicate a log value for a ratio of the probability that the bit transmitted from the transmission apparatus 3500 is 0 and the probability that the bit is 1. Additionally, the LLR value may be a bit value, which is determined by a hard decision, or it may be a representative value, which is determined according to a section in which there is a probability that the bit transmitted from the transmission apparatus 3500 is 0 or 1 .

[000196] The demodulator 3610 can perform cell-to-bit conversion with respect to a value corresponding to the code word and output an LLR value in the bit unit.

[000197] The deinterleaver 3620 deinterleaves an output value from the demodulator 3610, and outputs the value to the decoder 3630.

[000198] To be more specific, the deinterleaver 3620 is an element corresponding to the interleaver 3520 of the transmission apparatus 3500 and performs an operation corresponding to the interleaver 3520. That is, the interleaver 3620 performs the interleaving operation of the interleaver 3520 inversely and deinterleaves a LLR value.

[000199] The decoder 3630 can perform channel decoding based on the output value of the deinterleaver 3620.

[000200] Specifically, the decoder 3630 is an element corresponding to the encoder 3510 of the transmission apparatus 3500, which can correct an error when performing decoding using the LLR value output of the deinterleaver 3620.

[000201] For example, decoder 3630 may include an LDPC decoder (not shown) to perform LDPC decoding.

[000202] In this case, decoder 3630 can perform LDPC decoding using an iterative decoding scheme based on a sum product algorithm. Here, the sum product algorithm refers to an algorithm by which messages (e.g., LLR value) are exchanged across an edge in a bipartite graph of a message passing algorithm, and an output message is calculated from incoming messages to variable nodes or check nodes, and is updated.

[000203] However, decoder 3630 may use a parity check matrix for LDPC decoding. In this case, the parity check matrix that is used for decoding may have the same structure as the parity check matrix that is used for encoding.

[000204] However, parity check matrix information or code rate information used for LDPC decoding may be pre-stored in the receiving apparatus 3600 or provided by the transmitting apparatus 3500.

[000205] The foregoing is merely exemplary, and channel decoding may be performed by various schemes that correspond to channel coding, which is performed by transmitting apparatus 3500. A non-transitory computer readable medium may be provided which stores a program for operating the above-described methods of various exemplary embodiments, in accordance with an exemplary embodiment. Non-transitory recording medium refers to a medium that can store data semi-permanently rather than storing data for a short period of time, such as a register, a cache, and a memory, and can be read by a device. Specifically, this medium may be a non-temporal recording medium, such as compact disc (CD), Digital Versatile Disc (DVD), hard disk, Blu-ray disc, Universal Serial Bus (USB), memory card, or memory read-only (ROM), not limited to them.

[000206] The components, elements, modules or units represented by a block, as illustrated in FIGs. 18, 35 and 36 can be embodied as various numbers of hardware, software and/or firmware structures that perform the respective functions described above, according to an exemplary embodiment. For example, these components, elements, modules or units may utilize a direct circuit structure, such as a memory, processing, logic, a look-up table, etc., which may perform respective functions through the control of one or more microprocessors. or other control devices. Furthermore, these components, elements, modules or units may be specifically incorporated by a program or a piece of code, which contains one or more executable instructions to perform specified logical functions. Furthermore, at least one of these components, elements, modules or units may further include a processor, such as a central processing unit (CPU), which performs respective functions, a microprocessor, or the like. A bus is not illustrated in the block diagrams above FIGS. 18, 35 and 36. However, communications between respective components, elements, modules or units can be carried out via the bus.

[000207] The previous modalities and advantages are merely exemplary and should not be interpreted as limiting the inventive concept. Furthermore, the description of exemplary embodiments of the inventive concept is intended to be illustrative, and not to limit the scope of the claims, and many alternatives, modifications, and variations will be apparent to those skilled in the art.

[000208] FIG. 37 is a flowchart for describing a method for transmitting a transmission apparatus in accordance with an exemplary embodiment.

[000209] First of all, a codeword is generated (S3710) by performing channel coding with respect to bits, and the codeword is interleaved (S3720).

[000210] Thereafter, the interleaved codeword is mapped onto the non-uniform constellation according to a modulation scheme (S3730).

[000211] In this case, the constellation may include the constellation points, which are defined based on Tables 2 to 11, according to a modulation scheme.

[000212] As an example, when the modulation scheme is 64-QAM, the constellation may include constellation points that are defined based on Table 8.

[000213] Specifically, when coding is performed with the coding rate of 2/15, in S3730, an interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined by UC_64_2/15 of Table 8 .

[000214] When coding is performed with the coding rate of 3/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points, which are defined by UC_64_3/15 of Table 8.

[000215] Furthermore, when coding is performed with the coding rate of 4/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined by NUC_64_4/15 of Table 8.

[000216] As another example, the constellation may include constellation points that are defined based on Table 9, where the modulation scheme is 256-QAM.

[000217] Specifically, when coding is performed with the coding rate of 2/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined by NUC_256_2/15 of Table 9 .

[000218] Furthermore, when coding is performed with the coding rate of 3/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points that are defined by NUC_256_3/15 from Table 9.

[000219] When coding is performed with the coding rate of 4/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined by NUC_256_4/15 of Table 9.

[000220] Tables 8 and 9 indicate the constellation points in a quadrant of the constellation, and the constellation points in the remaining quadrants of the constellation can be obtained by indicating each point of a constellation that is defined in Tables 8 and 9, as a* , -a*, and -a respectively (Here, * indicates complex conjugation).

[000221] As another example, the constellation may include, when the modulation scheme is 1024-QAM, the constellation points, which are defined based on Table 10.

[000222] Specifically, when coding is performed with the coding rate of 2/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined based on NUC_lk_2/15 of the Table 10.

[000223] Furthermore, when coding is performed with the coding rate of 3/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined based on NUC_lk_3/15 from Table 10.

[000224] Furthermore, when coding is performed with the coding rate of 4/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined based on NUC_1k_4/15 from Table 10.

[000225] As another example, the constellation may include the constellation points, which are defined based on Table 11, when the modulation scheme is 4096-QAM.

[000226] Specifically, when coding is performed with the coding rate of 2/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined based on NUC_4k_2/15 of the Table 11.

[000227] Furthermore, when coding is performed with the coding rate of 3/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points defined based on UC_4k_3/15 from Table 11.

[000228] When coding is performed with the coding rate of 4/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points, which are defined based on NUC_4k_4/15 from Table 11.

[000229] When coding is performed with the coding rate of 5/15, in S3730, the interleaved codeword can be mapped to the non-uniform constellation, which includes the constellation points, which are defined based on NUC_4k_5/15 from Table 11.

[000230] However, Tables 10 and 11 are used to define the constellation points in a quadrant, and the constellations in the remaining quadrants of the constellation can be obtained by indicating each point of a constellation, which is defined based on tables 10 and 11 , such as a*, -a*, and -a respectively (Here, * indicates complex conjugation).

[000231] In the present specification, to generate the optimized constellation, the capacity must be determined. For this, SNR is an important parameter. However, optimization with respect to SNR does not necessarily mean that an environment that satisfies SNR is necessary. However, it is highly likely that optimized performance can be obtained in the environment that satisfies the SNR, but in general, the reception SNR may change frequently according to the system environment, and it is obvious that a different SNR or rate Different channel coding can be used according not only to complexity of realizing the system, but also for various purposes to support various channel environments utilizing the modulation scheme to which a NUC constellation point is applied.

[000232] A non-transitory computer-readable medium in which a program that sequentially performs the non-uniform constellation generation method is stored therein can be provided.

[000233] The non-transitory computer-writable medium is not a medium configured to temporarily store data, such as a register, a cache, or a memory, but a reading apparatus medium configured to store data semi-permanently. Specifically, the various applications or programs described above may be stored on a non-transitory device readable medium, such as a compact disc (CD), a digital versatile disc (DVD), a hard disk, a Blu-ray disc, a universal bus serial (USB), a memory card, or read-only memory (ROM), and are provided.

[000234] In the block diagram illustrating the transmitting device and the receiving device, the bus is not illustrated, but communication between the elements of each device can be done via the bus. Furthermore, each device may further include a CPU that performs the steps described above and processors, such as a microprocessor.

[000235] The previous exemplary modalities and advantages are merely exemplary and should not be interpreted as limiting the inventive concept. The exemplary embodiments can be readily applied to other types of devices or apparatus. Furthermore, the description of exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art.

Claims (10)

1. TRANSMISSION METHOD, characterized by comprising: encoding input bits to generate parity bits based on a low density parity check code (LDPC); interleaving a codeword comprising input bits and parity bits; map bits of the interleaved codeword into constellation points for 64 quadrature amplitude modulation (QAM); and transmitting a signal comprising information about the constellation points to which the bits of the interleaved codeword are mapped, wherein the constellation points comprise constellation points as defined in a table below: 0.5472 + 1.1591i 0.5473 + 1.1573i 0.5467 + 1.1599i 0.5479 + 1.1585i 1.1578 + 0.5478i 1.1576 + 0.5475i 1.1591 + 0.5475i 1.1591 + 0.5475i 0.3163 + 0 .5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.5087 + 0.3163i 0.5087 + 0.3163i 0.5087 + 0.3163i 0.5087 + 0, 3163i 2. Method according to claim 1, characterized in that the encoding comprises encoding the input bits based on the low density parity check code (LDPC) with a encoding rate of 3/15. 3. Method according to claim 1, characterized in that the table indicates the constellation points in a quadrant of a constellation, and in which the constellation points in the remaining quadrants of the constellation are obtained by indicating each constellation point to which it is defined by the table as a*, -a* and -a respectively, where * indicates complex conjugation. 4. TRANSMISSION APPARATUS, characterized by comprising: an encoder configured to encode input bits to generate parity bits based on a low density parity check code (LDPC); an interleaver configured to interleave a codeword comprising input bits and parity bits; a mapper configured to map bits of the interleaved codeword into constellation points for quadrature amplitude modulation (QAM); and a transmitter configured to transmit a signal comprising information about the constellation points to which the interleaved codeword bits are mapped, wherein the constellation points comprise constellation points as defined in a table below: 0.5472 + 1.1591i 0.5473 + 1.1573i 5. Apparatus according to claim 4, characterized in that the encoder is configured to encode the input bits based on the low density parity check code (LDPC) having a coding rate of 3/15. 6. Apparatus according to claim 4, characterized in that the table indicates constellation points in a quadrant of a constellation, and in which the constellation points in the remaining quadrants of the constellation are obtained by indicating each constellation point to which it is defined by the table as a*, -a* and -a respectively, where * indicates complex conjugation. 7. RECEIVING APPARATUS, characterized by comprising: a receiver configured to receive a signal from a transmission apparatus; a demodulator configured to demodulate the signal to generate values in accordance with quadrature amplitude modulation (QAM); a deinterleaver configured to deinterleave the values; and a decoder configured to decode the deinterleaved values based on a low density parity check code (LDPC) having a code rate being 3/15, wherein the demodulator is configured to demodulate the signal based on at least one constellation point between the constellation points represented as a table below: 0.5472 + 1.1591i 0.5473 + 1.1573i 0.5467 + 1.1599i 0.5479 + 1.1585i 1.1578 + 0.5478i 1 .1576 + 0.5475i 1.1591 + 0.5475i 1.1591 + 0.5475i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0, 5087 + 0.3163i 0.5087 + 0.3163i 0.5087 + 0.3163i 0.5087 + 0.3163i 8. Apparatus according to claim 7, characterized in that the table indicates the constellation points in a quadrant of a constellation, and in which the constellation points in the remaining quadrants of the constellation are obtained by indicating each constellation point to which it is defined by the table as a*, -a* and -a respectively, where * indicates complex conjugation. 9. RECEIVING METHOD, characterized by comprising: receiving a signal from a transmission device; demodulating the signal to generate values according to 64 quadrature amplitude modulation (QAM); deinterleave the values; and decoding the deinterleaved values based on a low density parity check code (LDPC) having a code rate being 3/15, wherein the demodulation demodulates the signal based on at least one constellation point between the deinterleaved values constellation represented as a table below: 0.5472 + 1.1591i 0.5473 + 1.1573i 0.5467 + 1.1599i 0.5479 + 1.1585i 1.1578 + 0.5478i 1.1576 + 0.5475i 1 .1591 + 0.5475i 1.1591 + 0.5475i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.3163 + 0.5072i 0.5087 + 0.3163i 0, 5087 + 0.3163i 0.5087 + 0.3163i 0.5087 + 0.3163i 10. Method according to claim 9, characterized in that the table indicates constellation points in a quadrant of a constellation, and in which the constellation points in the remaining quadrants of the constellation are obtained by indicating each constellation point that is defined by the table as a*, -a* and -a respectively, where * indicates complex conjugation.