IEEE TRANSACTIONS ON BROADCASTING, VOL. 62, NO. 1, MARCH 2016
`
`197
`
`Non-Uniform Constellations for ATSC 3.0
`
`Nabil Sven Loghin, Jan Zöllner, Belkacem Mouhouche, Daniel Ansorregui, Jinwoo Kim,
`and Sung-Ik Park, Senior Member, IEEE
`
`the concept of a non-
`Abstract—This paper introduces
`uniform constellation (NUC) in contrast to conventional uniform
`quadrature-amplitude modulation (QAM) constellations. Such
`constellations provide additional shaping gain, which allows
`reception at lower signal-to-noise ratios. ATSC3.0 will be the first
`major broadcasting standard, which completely uses NUCs due
`to their outstanding properties. We will consider different kinds
`of NUCs and describe their performance: 2-D NUCs provide
`more shaping gain at the cost of higher demapping complex-
`ity, while 1-D NUCs allow low-complexity demapping at slightly
`lower shaping gains. These NUCs are well suited for very large
`constellations sizes, such as 1k and 4k QAM.
`Terms—Non-uniform constellations,
`Index
`shaping, QAM, ATSC3.0, terrestrial broadcast.
`
`constellation
`
`spectral efficiencies, the constellations had to be changed.
`While conventional quadrature-amplitude modulation (QAM)
`employed signal points on a regular orthogonal grid, so-
`called non-uniform constellations
`(NUCs)
`loosened this
`restriction.
`Constellation shaping techniques have a long history:
`already in 1974, Foschini (now well known for his ground-
`breaking work on multi-antenna systems) and his colleagues
`proposed constellations, which minimize symbol error rates
`over an additive white Gaussian noise (AWGN) channel [4].
`Ten years later, Forney et al. provided a mathematical proof
`of the ultimate shaping gain limit [5]. This limit however
`only applies to the so-called signal set capacity. A more
`realistic capacity limit is given by the bit interleaved coded
`modulation (BICM) capacity [7]. In [8], several known con-
`stellations (e.g., square or rectangular grids) were compared
`with respect to this BICM capacity. Other methods to obtain
`shaping gain tried to heuristically force the constellation to
`look Gaussian-like [9], however lacking a mathematical proof.
`The optimization of constellations in the 1-dimensional space
`with respect to BICM capacity was first described in [10].
`In [11], constellations up to 32-QAM have been optimized in
`the 2-dimensional space to maximize BICM capacity for the
`AWGN channel and a range of SNR values. A summary of
`both optimized NUCs in both 1- and 2-dimensional space is
`given in [12], where constellations up to 1048576 points are
`examined.
`In general, signal shaping can be classified into two groups:
`probabilistic shaping, which tackles the symbol probabilities
`by using a shaping encoder, and geometrical shaping by mod-
`ifying the location of the constellation points. The former
`approach requires a shaping decoder at receiver side, which
`increases the overall complexity. The latter only requires to
`Manuscript received August 4, 2015; revised October 20, 2015; accepted
`store a new set of constellation points and may require finer
`October 22, 2015. Date of publication February 25, 2016; date of current
`quantization in hardware implementations. This paper focuses
`version March 2, 2016. This work was supported by the ICT Research
`only on geometrically shaped NUCs.
`and Development Program of MSIP/IITP under Grant R0101-15-294 through
`the Development of Service and Transmission Technology for Convergent
`In March 2013,
`the Advanced Television Systems
`Realistic Broadcast.
`Committee announced a ‘call for proposals’ for the ATSC 3.0
`N. S. Loghin is with Sony Deutschland GmbH, European Technology
`physical layer, with one of the goals being to maximize spec-
`Center, Stuttgart 70327, Germany (e-mail: nabil@sony.de).
`J. Zöllner
`is with
`the Technische Universitaet Braunschweig,
`tral efficiencies [13]. It was thus not completely unexpected
`Braunschweig 38106, Germany (e-mail: zoellner@ifn.ing.tu-bs.de).
`that the proposed technologies included both LDPC codes
`B. Mouhouche and D. Ansorregui are with Samsung, Staines TW18 4QE,
`for FEC, and NUCs for constellations. ATSC3.0 may most
`U.K. (e-mail: b.mouhouche@samsung.com; d.ansorregui@samsung.com).
`J. Kim is with LG Electronics, Seoul 137-130, Korea
`(e-mail:
`likely become the first major broadcast system deploying such
`jinwoo03.kim@lge.com).
`constellations.
`S.-I. Park is with Broadcasting System Research Group, Electronics and
`This paper is structured as follows: Section II provides an
`Telecommunication Research Institute, Daejeon 305-700, Korea (e-mail:
`psi76@etri.re.kr).
`introduction to the limits imposed by information theory, with
`Color versions of one or more of the figures in this paper are available
`focus on BICM capacity, which will be used as optimization
`online at http://ieeexplore.ieee.org.
`criterion for NUCs, as discussed in Section III. Here, we will
`Digital Object Identifier 10.1109/TBC.2016.2518620
`0018-9316 c(cid:2) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
`See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
`
`I. INTRODUCTION
`
`T HE TRANSITION from first to second generation digi-
`
`tal terrestrial broadcast systems, such as transition from
`DVB-T to DVB-T2 [1], offered a variety of new technolo-
`gies and algorithms, which reduced the gap to the famous
`Shannon limits [2]. One major trend was the adoption of more
`powerful forward error correction (FEC) schemes. Cutting-
`edge low-density parity-check (LDPC) codes together with an
`outer BCH code replaced the long established combination
`of a convolutional code with an outer Reed-Solomon (RS)
`code. Similar data throughput was thus achieved at about
`5dB less signal-to-noise ratio (SNR) [3]. Subsequent activities
`to further improve FEC schemes resulted in minor addi-
`tional gains in the order of 0.01-0.3dB. Larger FEC gains
`were obtained at
`the price of higher complexity, e.g., by
`LDPC parity check matrices with higher density and or
`longer codeword lengths. Obviously, the new FEC schemes
`were already close to optimum. In order to further increase
`
`LG Electronics, Inc. v. Constellation Designs, LLC
`
`
`
`Constellation Exhibit 2007
`Page 1 of 7
`
`IPR2023-00319
`
`IPR2023-00228
`
`

`

`198
`
`IEEE TRANSACTIONS ON BROADCASTING, VOL. 62, NO. 1, MARCH 2016
`
`distinguish between 2-dimensional NUCs and low-complexity
`1-dimensional NUCs. Simulation results are presented in
`Section IV, the conclusions are drawn in Section V.
`
`II. ULTIMATE COMMUNICATION LIMITS
`A. Channel Capacity
`In his seminal work, Shannon defined the maximum pos-
`sible throughput over any given channel as the channel
`capacity [2]. The channel is fully described by its transition
`probabilities p(rk|sk = xl), where we assume a memoryless
`channel. The index k denotes the discrete time index, sk and
`rk are transmitted and received symbols at time k, respec-
`tively. The particular transmit symbol xl
`is taken from an
`alphabet X, which may be finite or infinite. For an AWGN
`channel, p(rk|sk = xl) is simply a Gaussian distributed proba-
`bility density function, centered around the transmitted symbol
`(assuming zero-mean noise), with noise variance according
`to SNR. Shannon’s channel capacity is the maximum mutual
`information (MI) between channel input sk and output rk,
`where maximization is performed over the distribution of
`the input alphabet X. To keep the amount of mathemati-
`cal details to a minimum, the interested reader is referred
`to [14]. Here, we will simply explain MI between two ran-
`dom variables A and B as the amount of information, which
`can be gained about B by observing A (or vice versa, since
`MI is commutative). The receiver of a communication system
`has an uncertainty about the potentially transmitted symbols
`sk. But luckily, it can observe the channel output rk, which
`helps reducing this uncertainty, and this reduction is exactly
`the MI. For the AWGN channel, Shannon proved that the
`maximum MI can be achieved, if the transmit alphabet X is
`itself Gaussian distributed, resulting in the famous capacity
`of CC = log2(1+SNR), given in bits/s/Hz. This serves as an
`ultimate limit for the channel itself, but can never be achieved
`by a practical system, since an infinite number of transmit
`symbols has to be realized.
`
`B. Signal Set Capacity
`Another capacity limit includes the particular modulation
`format, in general a QAM constellation with symbols from
`a finite alphabet X. The number of symbols m, i.e., the car-
`dinality of X, is usually a power of 2, M = log2(m) being
`the number of bits, which are mapped to a symbol via a bit
`labelling function µ. The resulting capacity CS is called signal
`set capacity (or sometimes coded modulation (CM) or multi-
`level coding (MLC) capacity), and is given by the maximum
`MI between the input bits of the QAM mapper and the channel
`output, as indicated in Figure 1. We assume equiprobable sym-
`bols xl, i.e., each symbol occurs with probability p(xl) = 1/m.
`Thus, no maximization of MI has to be performed, assum-
`ing that the symbols are defined by a particular constellation
`(e.g., located on an equidistant uniform grid). No restriction
`has been made about the receiver of this system, so it is
`assumed that a perfect receiver is decoding the symbols rk.
`This can be realized by a joint symbol detector and decoder,
`where demapping and FEC decoding are considered as a com-
`bined unit. Multilevel codes (MLC) are one way to approach
`
`Fig. 1. Definition of channel, signal set and BICM capacity.
`
`this limit [15], with trellis coded modulation (TCM) [16] as
`a special form thereof. Another way to approach CS is to use
`iterative demapping and decoding as deployed in BICM-ID
`schemes [17], [18].
`
`C. BICM Capacity
`Finally, a more pragmatic communication system decou-
`ples symbol demapping from FEC decoding, and assumes that
`a QAM demapper computes soft values once, which will be
`forwarded to the subsequent FEC decoding stage. To fully
`decouple FEC encoding and mapping (especially for fading
`channels), an interleaver is placed between these blocks. The
`resulting system is thus called bit-interleaved coded modula-
`tion (BICM) [6], and the ultimate throughput limit is termed
`BICM capacity CB [7], see Figure 1. An optimum demapper
`at receiver side computes a posteriori probabilities (APP) as
`soft values, typically in the form of (extrinsic) log-likelihood
`ratios (LLR), called LE,k in Figure 1. This vector comprises
`all M LLRs for each of the M bits per symbol.
`If CB (in bits/s/Hz) is smaller than the overall FEC code
`rate, error free reception is not possible. Hence, CB has to be
`large enough to provide the FEC decoder with LLRs exceeding
`a particular reliability level to provide low bit error rates. For
`a given channel realization, the only way to maximize CB is
`to apply shaping to the constellations.
`
`D. Capacity Comparisons
`For the AWGN channel, the above three capacities are com-
`pared in Figure 2. The signal set capacity (here called CM
`capacity) and the BICM capacity are plotted for well-known
`uniform constellations with Gray labelling. In general CC >
`CS ≥ CB, but the difference between CS and CB is hardly
`visibly for Gray mappings. Both CS and CB converge towards
`M bits/s/Hz, when the SNR tends towards infinity. As can be
`observed, the CB curve has a gap to the Shannon limit, which
`becomes larger, the bigger the constellation size is. This gap
`can be further reduced by using NUCs instead of conventional
`constellations, as described later.
`While the signal set capacity is independent of the labelling
`function µ, the BICM capacity does depend on bit labelling.
`Usually, Gray labelling is deployed, where adjacent symbols
`differ in one bit only. It is interesting to note that constellations
`with more than 16 points do not have a unique class of Gray
`labellings, but allow for several kinds of Gray labellings, with
`
`Constellation Exhibit 2007, Page 2 of 7
`
`

`

`LOGHIN et al.: NUCs FOR ATSC 3.0
`
`199
`
`Fig. 2. Shannon’s channel capacity, CM and BICM capacity.
`
`The task is to maximize CB by modifying the QAM sym-
`bols xl, considering constraint (1). Since CB depends on the
`channel transition probabilities p(rk|sk= xl), this optimization
`has to be performed for each particular channel. In particular,
`a different optimum NUC may result for an AWGN channel
`for each SNR value. For modern FEC codes, such as LDPC,
`with their steep bit error rate (BER) curves as a function of
`the SNR, the target SNR of the NUC is easily selected accord-
`ing to the SNR of the code’s waterfall region (the SNR where
`the BER curve drops by several orders of magnitude), i.e.,
`for each code rate a different NUC is used [20]. This allows
`for optimum performance, independent of the SNR at each
`user’s location. When a user suffers worse SNR than the tar-
`get SNR of the FEC code (and the NUC), successful decoding
`is anyhow not possible due to the cliff behaviour of “all-or-
`nothing” FEC codes. In contrast, when the actual SNR is better
`than the target SNR, decoding is still possible even though the
`constellation may not be optimal for the actual SNR. NUCs
`for ATSC3.0 have been optimized both with respect to per-
`formance over flat AWGN channel and over independent and
`identically distributed Rayleigh fading with perfect side infor-
`mation at receiver side. To further optimize the combination
`of coding and modulation, the bit interleaver was carefully
`optimized as well for each combination of constellation size
`and code rate.
`The degrees of freedom (DOF) for the optimization are the
`m complex symbols xl ∈ X. In the following, we will describe
`two different optimization approaches.
`
`A. Two Dimensional NUCs
`All m complex DOFs will be considered to optimize 2D
`NUCs, i.e., 2m real-valued DOFs have to be optimized. For
`a 16QAM, this results in 32 DOFs. To reduce the number
`of DOFs of 2D NUCs by a factor of four, quadrant symmetry
`can be assumed [12]. In general, one DOF can be fixed due to
`power constraint (1), but this depends on the way the optimiza-
`tion problem is solved. Since capacity functions are in general
`
`Fig. 3. Uniform 16QAM constellation with binary reflected Gray labeling.
`
`the so-called binary reflected Gray labelling offering the maxi-
`mum BICM capacity for a uniform constellation [19]. Figure 3
`depicts such a labelling for a 16QAM constellation, which is
`deployed in systems like DVB-T or DVB-T2. The constella-
`tion points are uniformly located on an orthogonal grid with
`the same minimum Euclidean distance of points to their closest
`neighbours. Such constellations are called uniform constella-
`tions (UCs) in contrast to non-uniform constellations, which
`will be discussed in the following chapter.
`
`III. OPTIMIZATION OF NON-UNIFORM CONSTELLATIONS
`When optimizing NUCs of a given constellation size m
`for a transmission system using a BICM chain, we need to
`maximize the BICM capacity CB. The only constraint on the
`constellation is that the average transmit power should be con-
`stant, usually normalized to unity, i.e., the transmit symbols
`need to fulfil the following power constraint
`m−1(cid:2)
`|xl|2 !=1.
`Px = 1
`m
`l=0
`
`(1)
`
`Constellation Exhibit 2007, Page 3 of 7
`
`

`

`200
`
`IEEE TRANSACTIONS ON BROADCASTING, VOL. 62, NO. 1, MARCH 2016
`
`Fig. 4. Optimized 2D 16NUC for ATSC3.0 for LDPC of rate 7/15.
`
`Fig. 5. Optimized 2D 16NUC for ATSC3.0 for LDPC of rate 2/15.
`
`non-convex, optimization thereof relies on numerical tools
`such as non-linear gradient search algorithms. Some optimiza-
`tion methods consider a two-step approach of an unconstrained
`optimization followed by a radial contraction to comply the
`power constraint in a second step [4], others apply constrained
`quadratic programming methods [21] or yet other tools.
`As an example, Figure 4 shows a NUC with 16 constella-
`tion points (called 16NUC), which has been optimized for
`ATSC3.0 for a combination with an LDPC code of code
`rate 7/15. The bit labels are given as integer numbers, with
`0000 corresponding to 0, 0001 to 1, and so on (least signif-
`icant bit is the right-most label). The constellation resembles
`a 16APSK (amplitude phase shift keying), but a closer view
`reveals four different amplitudes, not only two. Nevertheless,
`all 2D NUCs from ATSC3.0 offer a symmetry with respect
`to the four quadrants, i.e., the complete constellation can be
`derived from the first quadrant by simple rotation rules. The
`target SNR for the AWGN channel of this NUC was about
`5.3dB. At this SNR, the uniform 16QAM from Figure 3 offers
`a BICM capacity of CB(5.3dB, 16QAM) = 2.00 bits/s/Hz.
`The optimized 16NUC from Figure 4 offers at
`the same
`SNR CB(5.3dB, 16NUC) = 2.04 bit/s/Hz, i.e., 0.04 bits/s/Hz
`more, which corresponds to a theoretical SNR gain of about
`0.16dB. In practice, the gain in bit error rates simulations was
`about 0.2dB.
`To understand the outcome of an optimized NUC, let us
`focus on an extreme case, where the target SNR for the
`AWGN channel is chosen extremely low. The outcome can
`be seen in Figure 5, which is a 16NUC for code rate 2/15.
`This very low code rate allows receiving this constellation at
`about -2.6dB SNR. Only four points are visible, resembling the
`classical quadrature phase shift keying (QPSK) constellation,
`but in fact, these are four clusters consisting of four almost
`identical points. The reason why this constellation still works
`fine at very low SNR is that at least two out of M = 4 bit
`labels offer robust MI: the first two most significant bits (left-
`most labels) offer similar robustness as the two bit positions
`of a QPSK, which is optimum for four constellation points
`(maximizing Euclidean distance, while maintaining indepen-
`dent dimensions for each bit). The other two weaker bit levels
`
`are “sacrificed” for this purpose, since they cannot be resolved
`anymore from the (almost) overlapping points. The bit-wise
`MI of those weak bits is close to 0 and will remain so, even
`for very large SNR. In general, NUCs of all constellation sizes
`converge towards a “QPSK-like” constellation, if target SNR
`goes to very small values, i.e., four clusters will remain with
`m/4 overlapping points each.
`As another extreme case, consider the application for very
`large code rates, i.e., very large target SNR. In such cases, the
`NUCs tend to become uniform QAM constellations, with the
`BICM capacity converging towards M bits/s/Hz. This implies
`that conventional uniform QAM constellations are only opti-
`mum for uncoded systems,
`if SNR is significantly large,
`but in combination with FEC coding, they are outperformed
`by NUCs.
`levels cannot be
`the four bit
`Note from Figure 4 that
`demapped independently. A uniform QAM such as the one
`from Figure 3 on the other hand allows demapping half of the
`bits independently from the other half. In case of the depicted
`16QAM, the first and third bit label are mapped to the real part
`of the constellation, while the second and forth bit label are
`mapped to the imaginary part. Thus, demapping can be split
`into two independent demappers for each dimension: effec-
`tively, only a real-valued pulse amplitude modulation (PAM)
`is demapped on each axis, resulting in much lower complexity.
`
`B. One Dimensional NUCs
`To exploit the properties of two independent dimensions
`as in uniform QAM constellations, the NUC is reduced to
`a one-dimensional PAM with non-uniform points. Both real
`√
`and imaginary component of the NUC are formed by the same
`PAM. An m-ary complex constellation is thus reduced to
`m
`√
`real-valued points. We may further assume symmetry to the
`origin, resulting in only
`m/2 real-value points (again, one of
`these points may be normalized due to power constraint (1)).
`The resulting NUC will be called 1D NUC.
`For example, a 1024QAM (also called 1k QAM) has
`2048 real-valued DOFs for 2D NUCs, but only 16 DOFs for
`1D NUCs. The optimization process itself is greatly eased by
`
`Constellation Exhibit 2007, Page 4 of 7
`
`

`

`LOGHIN et al.: NUCs FOR ATSC 3.0
`
`201
`
`Fig. 6. Optimized 1D 1k NUC for ATSC3.0 for LDPC of rate 7/15.
`
`Fig. 7. Shaping gain of conventional uniform constellation (UC) versus NUC
`for 256QAM and 64k LDPC of rate 10/15 over AWGN channel.
`
`points for APP computation, but only 2·√
`
`this limitation, but mostly, the complexity reduction for the
`demapper is an important feature. Maximum likelihood (ML)
`demapping of a 2D NUC has to consider all m constellation
`m candidates for 1D
`NUCs (the factor 2 arises from 2 independent PAM demapping
`processes).
`For ATSC3.0, 16QAM, 64QAM and 256QAM have been
`optimized as 2D NUCs, but for 1k and 4k constellations, lower
`complexity 1D NUCs have been proposed. The drawback of
`1D NUCs is that the restriction of DOFs results in slightly
`smaller shaping gains compared with the 2D variants. Figure 6
`shows as an example a 1D NUC with 1024 constellation points
`(1k NUC), optimized for an LDPC of rate 7/15. Both real and
`imaginary component apply the same 32PAM, and half of the
`bit labels (not shown in the figure) are mapped independent
`of the other half to each dimension.
`It can be shown empirically (not shown here) that 2D NUCs
`offer about 0.2-0.3dB more shaping gain compared with 1D
`NUCs of the same constellation size due to the larger number
`of DOFs for NUC optimization.
`
`IV. SIMULATION RESULTS
`ATSC3.0 offers a large variety of modulation and cod-
`ing combinations, called MODCODs [22]: LDPC codes have
`either 64800 or 16200 bits as codeword lengths (64k or 16k
`codes, respectively), with code rates ranging from 2/15 to
`13/15,
`in steps of 1/15 [23]. 64k codes have better per-
`formance than their shorter counterparts, but require more
`memory for decoding and have some impact on latency and
`power consumption. Constellations in ATSC3.0 range from
`very robust QPSK modulation over 16NUC to 4096NUC,
`each constellation carefully optimized for the LDPC code rate.
`The same constellation is used for both 16k and 64k LDPC,
`since the LDPC performance difference is rather small (less
`than 0.5dB on average) and to reduce the amount of different
`constellations.
`Figure 7 depicts bit and frame error rates (BER and ER,
`resp.) over the AWGN channel, when using a 64k LDPC of
`rate 10/15 and an outer BCH code together with a traditional
`
`Fig. 8. Shaping gain of conventional uniform constellation (UC) versus NUC
`for 256QAM and 64k LDPC of rate 7/15 over Rayleigh i.i.d. channel.
`
`uniform 256QAM, in comparison with the optimized 256NUC
`−4, the NUC
`from ATSC3.0 for this MODCOD. At FER = 10
`constellation allows reception at SNR level (here Es/N0) being
`0.91dB lower than that for the uniform counterpart.
`As pointed out before, ATSC3.0 NUCs have been designed
`considered both AWGN and Rayleigh fading channels.
`Figure 8 demonstrates the performance of a 256NUC, using
`64k LDPC of lower rate 7/15. The channel is a passive one-tap
`Rayleigh fading channel, with fading coefficients being inde-
`pendent identically distributed (i.i.d.), which models a fully
`interleaved fading channel. Compared with the state-of-the-art
`uniform constellation, the SNR gain at FER = 10
`−4 is 0.9dB.
`Such SNR gains, also called shaping gains, in dB, are sum-
`marized in Figure 9 for 64k codes of rates 2/15 until 13/15 for
`the AWGN channel of NUCs proposed for ATSC3.0 ver-
`sus conventional uniform constellations of the same size. As
`a rule-of-thumb, shaping gains tend towards 0 for extremely
`small or large code rates (“(almost) all constellations are
`equally bad or good, respectively”), with a maximum shaping
`gain for rates around 7/15. However, for lower constellation
`sizes, such as 16QAM and 64QAM, an impressive gain is still
`
`Constellation Exhibit 2007, Page 5 of 7
`
`

`

`202
`
`IEEE TRANSACTIONS ON BROADCASTING, VOL. 62, NO. 1, MARCH 2016
`
`[4] G. J. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-
`dimensional signal constellations in the presence of Gaussian noise,”
`IEEE Trans. Commun., vol. 22, no. 1, pp. 28–38, Jan. 1974.
`[5] G. D. Forney, Jr., R. G. Gallager, G. Lang, F. M. Longstaff, and
`S. U. Qureshi, “Efficient modulation for band-limited channels,”
`IEEE J. Sel. Areas Commun., vol. 2, no. 5, pp. 632–647, Sep. 1984.
`[6] G. Caire, G. Taricci, and E. Biglieri, “Bit-interleaved coded modulation,”
`IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May 1998
`[7] G. Caire, G. Taricco, and E. Biglieri, “Capacity of bit-interleaved
`channels,” IEE Electron. Lett., vol. 32, no. 12, pp. 1060–1061, Jun. 1996.
`[8] S. Y. L. Goff, “Signal constellations for bit-interleaved coded modula-
`tion,” IEEE Trans. Inf. Theory, vol. 49, no. 1, pp. 307–313, Jan. 2003.
`[9] C. Fragouli, R. D. Wesel, D. Sommer, and G. P. Fettweis, “Turbo codes
`with non-uniform constellations,” in Proc. IEEE ICC, Helsinki, Finland,
`Jun. 2001, pp. 70–73.
`[10] M. F. Barsoum, C. Jones, and M. Fitz, “Constellation design via capac-
`ity maximization,” in Proc. IEEE Int. Symp. Inf. Theory, Nice, France,
`Jun. 2007, pp. 1821–1825.
`[11] N. S. Muhammad, “Coding and modulation for spectral efficient
`transmission,” Ph.D. dissertation, Inst. Nachrichtenübertragung, Univ.
`Stuttgart, Stuttgart, Germany, 2010.
`[12] J. Zoellner and N. Loghin, “Optimization of high-order non-
`uniform QAM constellations,” in Proc. IEEE Int. Symp. Broadband
`Multimedia Syst. Broadcast.(BMSB), London, U.K., Jun. 2013, pp. 1–6.
`[13] Call for Proposals for ATSC 3.0 Physical Layer—A Terrestrial Broadcast
`Standard, ATSC Technology Group 3 (ATSC 3.0), Mar. 2013.
`[14] R. G. Gallager, Information Theory and Reliable Communication.
`New York, NY, USA: Wiley, 1968.
`[15] U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes:
`Theoretical concepts and practical design rules,” IEEE Trans. Inf.
`Theory, vol. 45, no. 5, pp. 1361–1391, Jul. 1999.
`[16] G. Ungerböeck, “Channel coding with multilevel/phase signals,”
`IEEE Trans. Inf. Theory, vol. 28, no. 1, pp. 55–67, Jan. 1982.
`[17] S.
`ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping and
`decoding for multilevel modulation,” in Proc. IEEE Glob. Telecommun.
`Conf. (GLOBECOM), vol. 1. Sydney, NSW, Australia, Nov. 1998,
`pp. 579–584.
`[18] N. S. Muhammad and J. Speidel, “Joint optimization of signal constella-
`tion and bit labeling for bit-interleaved coded modulation with iterative
`decoding,” IEEE Commun. Lett., vol. 9, no. 9, pp. 775–777, Sep. 2005.
`[19] C. Stierstorfer and R. F. H. Fischer, “(Gray) mappings for bit-interleaved
`coded modulation,” in Proc. IEEE Veh. Technol. Conf. (VTC), Dublin,
`Irleand, Apr. 2007, pp. 1703–1707.
`[20] B. Mouhouche, D. Ansorregui, and A. Mourad, “High order non-uniform
`constellations for broadcasting UHDTV,” in Proc.
`IEEE Wireless
`Commun. Netw. Conf., Istanbul, Turkey, Apr. 2014, pp. 600–605.
`[21] E. Çela, The Quadratic Assignment Problem: Theory And Algorithms.
`Boston, MA, USA: Kluwer Academic, 1998.
`[22] L. Michael and D. Gómez-Barquero, “Bit interleaved coding and mod-
`ulation for ATSC 3.0,” IEEE Trans. Broadcast., vol. 63, no. 1, pp. 1–8,
`Mar. 2016.
`[23] K. Kim et al., “Low density parity check code for ATSC 3.0,”
`IEEE Trans. Broadcast., vol. 63, no. 1, Mar. 2016.
`
`Nabil Sven Loghin received the Diploma degree
`in electrical engineering and the Ph.D. degree from
`the University of Stuttgart, Germany, in 2004 and
`2010, respectively, both with summa cum laude.
`Since 2009, he has been with Sony, working on
`DTV standardization and communication systems.
`His research interests include channel coding, iter-
`ative decoding, QAM mapping optimization, and
`multiple-antenna communications.
`
`Performance gains in dB of ATSC3.0 NUCs versus uniform
`Fig. 9.
`constellations over AWGN channel.
`
`possible also for low code rates like 2/15. Further, shaping
`gains become larger the larger the constellation size is. The
`reasons are that more DOFs are available for optimization, but
`also that larger uniform constellations result in a bigger gap
`to the Shannon limit, as shown in Figure 2. For 16NUC, only
`0.2dB gains can be expected for 2D NUCs (almost no gain for
`1D NUCs – not shown), while 256NUCs already exceed 1dB
`of shaping gains. For 1k and larger NUCs, up to 1.8dB are
`possible, which is well above the famous shaping gain limit
`of 1.53dB derived in [5]. However, this limit holds only for
`NUCs optimized with respect to signal set capacity CS. The
`ultimate shaping gain limit with respect to BICM capacity CB
`is still to be derived.
`
`V. CONCLUSION
`In this paper, we presented non-uniform constella-
`tions (NUCs), carefully designed for the ATSC3.0 physical
`layer. The design considered different channel realizations,
`and took the combination of LDPC code and bit interleaver
`into account. Results showed that shaping gains of more than
`1.5dB are possible, which can be seen as a major step towards
`the ultimate limits of communications and which qualifies
`ATSC3.0 to become a future-proof cutting-edge terrestrial
`broadcast standard.
`
`ACKNOWLEDGMENT
`The authors like to thank the members of ATSC3.0 physi-
`cal layer standardization groups for promising contributions
`in various fields, accurate evaluation processes and fruitful
`discussions.
`
`REFERENCES
`
`[1] I. Eizmendi et al., “DVB-T2: The second generation of terrestrial digital
`video broadcasting system,” IEEE Trans. Broadcast., vol. 60, no. 2,
`pp. 258–271, Jun. 2014.
`[2] C. E. Shannon, “A mathematical theory of communication,” Bell Lab.
`Syst. J., vol. 27, p. 535, Jul./Oct. 1948.
`[3] Digital Video Broadcasting (DVB),
`Implementation Guidelines for
`a Second Generation Digital Terrestrial Television Broadcasting System,
`document ETSI TS 102 831 V1.2.1, ETSI, Sophia Antipolis, France,
`2012.
`
`Constellation Exhibit 2007, Page 6 of 7
`
`

`

`LOGHIN et al.: NUCs FOR ATSC 3.0
`
`203
`
`Jan Zöllner
`received the Diploma degree in
`computer
`science and communications
`technol-
`ogy engineering from Technische Universitaet
`Braunschweig, in 2010. His diploma thesis resulted
`in the implementation of a DVB-C measure-
`ment receiver in MATLAB. He joined the Institut
`für Nachrichtentechnik, Technische Universitaet
`Braunschweig, where he was involved in the devel-
`opment of DVB-NGH. He is currently the Chair of
`DVB’s Study Mission on co-operative spectrum use.
`
`Belkacem Mouhouche received the Ph.D. degree
`in signal processing from the l’Ecole Nationale
`Superieure des Telecoms (Telecom ParisTech), in
`2005. He joined Freescale Semiconductor to work
`on advanced receivers for 3GPP HSPA+. He later
`held different positions related to 3GPP standard-
`ization and implementation for major telecommu-
`nication companies. Since 2012, he has been with
`Samsung Electronics where his research focuses on
`the physical layer of future broadcast and broadband
`systems.
`
`Daniel Ansorregui received the M.S. degree in
`telecommunications engineering from the University
`of the Basque Country, Spain, in 2011. Since 2013,
`he has been with Samsung Electronics Research,
`U.K., at the Standard Department. His main work
`focuses on ATSC 3.0 standard PHY layer develop-
`ment with special focus on LDPC and modulation
`and synchronization systems. He is currently work-
`ing with Android Graphics Technologies.
`
`Jinwoo Kim received the B.S.E.E. degree from
`Hanyang University, Seoul, Korea, in 2001, and the
`M.S.E.E. degree from POSTECH, Pohang, Korea, in
`2003. Since 2003, he has been with LG Electronics.
`His research interests include digital communica-
`tions and signal processing.
`
`Sung-Ik Park received the B.S.E.E. degree
`from Hanyang University, Seoul, Korea, in 2000,
`the M.S.E.E. degree from POSTECH, Pohang,
`Korea,
`in 2002, and the Ph.D. degree from
`Chungnam National University, Daejeon, Korea,
`in 2011. Since 2002, he has been with the
`Broadcasting System Research Group, Electronics
`and Telecommunication Research Institute, where he
`is a Senior Member of Research Staff. His research
`interests are in the area of error correction codes and
`digital communications, in particular, signal process-
`ing for digital television. He currently serves as an Associate Editor of the
`IEEE Transactions on Broadcasting and a Distinguished Lecturer of the IEEE
`Broadcasting Technology Society.
`
`Constellation Exhibit 2007, Page 7 of 7
`
`