Broadcast Coded Modulation: Multilevel and Bit-Interleaved Construction

The capacity of the AWGN broadcast channel is achieved by superposition coding, but the superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Hierarchical modulations, which appear in the literature mostly in the context of unequal error protection, can approach only a few isolated points on the boundary of the broadcast capacity region. This paper studies multilevel coding (MLC) for constellation-constrained broadcast-coded modulation. The conditions under which multilevel codes can achieve the constellation-constrained capacity of the AWGN broadcast channel are derived. We propose a pragmatic multilevel design technique with near-constellation-constrained-capacity performance where the coupling of the superposition inner and outer codes is localized to each bit-level. It is shown that this can be further relaxed to a code coupling on only one bit-level, with a little or no penalty under natural labeling. The rate allocation problem between the bit levels of the two users is studied and a pragmatic method is proposed, again with near-capacity performance. In further pursuit of lower complexity, a hybrid MLC-bit-interleaved-coded modulation is proposed, whose performance is shown to be very close to the boundary of the constellation-constrained capacity region. Simulation results show that good point-to-point LDPC codes produce excellent performance in the proposed coded modulation framework.

[1]  Gottfried Ungerboeck,et al.  Channel coding with multilevel/phase signals , 1982, IEEE Trans. Inf. Theory.

[2]  Stephan Pfletschinger,et al.  Multilevel coding for non-orthogonal broadcast , 2014, 2014 48th Asilomar Conference on Signals, Systems and Computers.

[3]  Aria Nosratinia,et al.  Multi-level coding and multi-stage decoding in MAC, broadcast, and relay channel , 2014, 2014 IEEE International Symposium on Information Theory.

[4]  Shu Lin,et al.  QPSK block-modulation codes for unequal error protection , 1995, IEEE Trans. Inf. Theory.

[5]  Tie Liu,et al.  Symmetrical Multilevel Diversity Coding and Subset Entropy Inequalities , 2014, IEEE Transactions on Information Theory.

[6]  Lutz H.-J. Lampe,et al.  Multilevel coding for multiple-antenna transmission , 2004, IEEE Transactions on Wireless Communications.

[7]  Giuseppe Caire,et al.  Bit-Interleaved Coded Modulation , 2008, Found. Trends Commun. Inf. Theory.

[8]  Raymond W. Yeung,et al.  Multilevel diversity coding with distortion , 1995, IEEE Trans. Inf. Theory.

[9]  Felix A. Taubin Performance of BICM transmission over Gaussian broadcast channels , 2008, 2008 International Conference on Telecommunications.

[10]  L. Goddard Information Theory , 1962, Nature.

[11]  Rudiger Urbanke,et al.  Approaching the AWGN channel capacity without active shaping , 1997, Proceedings of IEEE International Symposium on Information Theory.

[12]  R.H. Morelos-Zaragoza,et al.  Coded modulation for satellite broadcasting , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[13]  Shlomo Shamai,et al.  A broadcast approach for a single-user slowly fading MIMO channel , 2003, IEEE Trans. Inf. Theory.

[14]  Volker Kühn,et al.  On Superposition Multilevel Coding for the 3-Node Relay Channel Exploiting Decode and Forward , 2015, 2015 IEEE 82nd Vehicular Technology Conference (VTC2015-Fall).

[15]  Abbas El Gamal,et al.  Network Information Theory , 2021, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT).

[16]  Udo Wachsmann,et al.  Design of Multilevel Codes , .

[17]  Richard D. Wesel,et al.  Superposition turbo TCM for multirate broadcast , 2004, IEEE Transactions on Communications.

[18]  Robert F. H. Fischer,et al.  Multilevel codes: Theoretical concepts and practical design rules , 1999, IEEE Trans. Inf. Theory.

[19]  A. Calderbank,et al.  Multilevel Codes for Unequal Error Protection , 1993, Proceedings. IEEE International Symposium on Information Theory.

[20]  Hideki Imai,et al.  A new multilevel coding method using error-correcting codes , 1977, IEEE Trans. Inf. Theory.

[21]  Pierre Duhamel,et al.  Achievable rates optimization for broadcast channels using finite size constellations under transmission constraints , 2013, EURASIP J. Wirel. Commun. Netw..

[22]  Shlomo Shamai,et al.  Superposition coding for side-information channels , 2006, IEEE Transactions on Information Theory.

[23]  A. Sridharan Broadcast Channels , 2022 .

[24]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[25]  Antonio Ortega,et al.  Multiresolution broadcast for digital HDTV using joint source-channel coding , 1992, [Conference Record] SUPERCOMM/ICC '92 Discovering a New World of Communications.

[26]  U. Wachsmann,et al.  Capacities of equivalent channels in multilevel coding schemes , 1994 .

[27]  Giuseppe Caire,et al.  Bit-Interleaved Coded Modulation , 2008, Found. Trends Commun. Inf. Theory.

[28]  Khaled A. S. Abdel-Ghaffar,et al.  Multilevel error-control codes for data storage channels , 1991, IEEE Trans. Inf. Theory.

[29]  W. Marsden I and J , 2012 .

[30]  Suhas N. Diggavi,et al.  Asymmetric Multilevel Diversity Coding and Asymmetric Gaussian Multiple Descriptions , 2010, IEEE Transactions on Information Theory.

[31]  M. Feder,et al.  On the optimality of multilevel coding and multistage decoding , 2008, 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel.

[32]  Raymond W. Yeung,et al.  Symmetrical multilevel diversity coding , 1997, IEEE Trans. Inf. Theory.

[33]  Alex Alvarado,et al.  Signal Shaping for BICM at Low SNR , 2013, IEEE Transactions on Information Theory.

[34]  G. David Forney,et al.  Modulation and Coding for Linear Gaussian Channels , 1998, IEEE Trans. Inf. Theory.

[35]  Lee-Fang Wei,et al.  Coded modulation with unequal error protection , 1993, IEEE Trans. Commun..

[36]  Krishna R. Narayanan,et al.  Multilevel Coding Schemes for Compute-and-Forward With Flexible Decoding , 2013, IEEE Transactions on Information Theory.