EXIT-Chart-Aided Near-Capacity Quantum Turbo Code Design

High detection complexity is the main impediment in future gigabit-wireless systems. However, a quantum-based detector is capable of simultaneously detecting hundreds of user signals by virtue of its inherent parallel nature. This, in turn, requires near-capacity quantum error correction codes for protecting the constituent qubits of the quantum detector against undesirable environmental decoherence. In this quest, we appropriately adapt the conventional nonbinary EXtrinsic Information Transfer (EXIT) charts for quantum turbo codes (QTCs) by exploiting the intrinsic quantum-to-classical isomorphism. The EXIT chart analysis not only allows us to dispense with the time-consuming Monte Carlo simulations but facilitates the design of near-capacity codes without resorting to the analysis of their distance spectra as well. We have demonstrated that our EXIT chart predictions are in line with the Monte Carlo simulation results. We have also optimized the entanglement-assisted QTC using EXIT charts, which outperforms the existing distance-spectra-based QTCs. More explicitly, the performance of our optimized QTC is as close as 0.3 dB to the corresponding hashing bound.

[1]  Lajos Hanzo,et al.  Near-Capacity Turbo Trellis Coded Modulation Design , 2007, 2007 IEEE 66th Vehicular Technology Conference.

[2]  Lajos Hanzo,et al.  EXIT Charts for System Design and Analysis , 2014, IEEE Communications Surveys & Tutorials.

[3]  Lajos Hanzo,et al.  Maximum-Throughput Irregular Distributed Space-Time Code for Near-Capacity Cooperative Communications , 2010, IEEE Transactions on Vehicular Technology.

[4]  Lajos Hanzo,et al.  Reduced-Complexity Syndrome-Based TTCM Decoding , 2013, IEEE Communications Letters.

[5]  Mark M. Wilde,et al.  Entanglement boosts quantum turbo codes , 2011, ISIT.

[6]  David Poulin,et al.  Quantum Serial Turbo Codes , 2009, IEEE Transactions on Information Theory.

[7]  Jean-Pierre Tillich,et al.  Description of a quantum convolutional code. , 2003, Physical review letters.

[8]  Yonghui Li,et al.  Transactions Papers Near-Capacity Turbo Trellis Coded Modulation Design Based on EXIT Charts and Union Bounds , 2008 .

[9]  Reiner S. Thomä,et al.  EXIT Chart-Aided Adaptive Coding for Multilevel BICM With Turbo Equalization in Frequency-Selective MIMO Channels , 2007, IEEE Transactions on Vehicular Technology.

[10]  S. Brink Rate one-half code for approaching the Shannon limit by 0.1 dB , 2000 .

[11]  Lajos Hanzo,et al.  Quantum Search Algorithms, Quantum Wireless, and a Low-Complexity Maximum Likelihood Iterative Quantum Multi-User Detector Design , 2013, IEEE Access.

[12]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[13]  Zunaira Babar,et al.  Entanglement-Assisted Quantum Turbo Codes , 2010, IEEE Transactions on Information Theory.

[14]  Martin Rötteler,et al.  Constructions of Quantum Convolutional Codes , 2007, 2007 IEEE International Symposium on Information Theory.

[15]  Gottesman Class of quantum error-correcting codes saturating the quantum Hamming bound. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[16]  Lajos Hanzo,et al.  On the MIMO channel capacity of multidimensional signal sets , 2006, IEEE Transactions on Vehicular Technology.

[17]  B. Moor,et al.  Clifford group, stabilizer states, and linear and quadratic operations over GF(2) , 2003, quant-ph/0304125.

[18]  Mark M. Wilde,et al.  Recursive Quantum Convolutional Encoders are Catastrophic: A Simple Proof , 2012, IEEE Transactions on Information Theory.

[19]  Sandor Imre,et al.  Quantum Computing and Communications: An Engineering Approach , 2005 .

[20]  Markus Grassl,et al.  Convolutional and Tail-Biting Quantum Error-Correcting Codes , 2005, IEEE Transactions on Information Theory.

[21]  Jing Li,et al.  Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions , 2010, IEEE Transactions on Information Theory.

[22]  Debbie W. Leung,et al.  Quantum data hiding , 2002, IEEE Trans. Inf. Theory.

[23]  R. Schumann Quantum Information Theory , 2000, quant-ph/0010060.

[24]  Richard Cleve Quantum stabilizer codes and classical linear codes , 1997 .

[25]  Lajos Hanzo,et al.  Near-Capacity Code Design for Entanglement-Assisted Classical Communication over Quantum Depolarizing Channels , 2013, IEEE Transactions on Communications.

[26]  David Poulin,et al.  Degenerate Viterbi Decoding , 2012, IEEE Transactions on Information Theory.

[27]  Stephan ten Brink,et al.  Convergence behavior of iteratively decoded parallel concatenated codes , 2001, IEEE Trans. Commun..

[28]  Lajos Hanzo,et al.  Near-capacity turbo trellis coded modulation design based on EXIT charts and union bounds - [transactions papers] , 2008, IEEE Transactions on Communications.

[29]  T. H. Liew,et al.  Turbo Coding, Turbo Equalisation and Space-Time Coding: EXIT-Chart-Aided Near-Capacity Designs for Wireless Channels , 2011 .

[30]  Jong-Moon Chung,et al.  Multihop Hybrid Virtual MIMO Scheme for Wireless Sensor Networks , 2012, IEEE Transactions on Vehicular Technology.

[31]  Seung-Hwan Lee,et al.  A Compressed Analog Feedback Strategy for Spatially Correlated Massive MIMO Systems , 2012, 2012 IEEE Vehicular Technology Conference (VTC Fall).

[32]  M. Wilde Quantum Information Theory: Noisy Quantum Shannon Theory , 2013 .

[33]  Matthew R. McKay,et al.  Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation , 2010, IEEE Transactions on Vehicular Technology.

[34]  David J. C. MacKay,et al.  Sparse-graph codes for quantum error correction , 2004, IEEE Transactions on Information Theory.

[35]  B. L. Yeap,et al.  Turbo Coding, Turbo Equalisation and Space-Time Coding , 2002 .

[36]  Lajos Hanzo,et al.  Efficient Computation of EXIT Functions for Nonbinary Iterative Decoding , 2006, IEEE Transactions on Communications.

[37]  A. Grant,et al.  Convergence of non-binary iterative decoding , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).