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IEEE Open Journal of the Communications Society

Quantum Codes in Classical Communication: A Space-Time Block Code From Quantum Error Correction

Travis C. Cuvelier, S. Andrew Lanham, Brian R. La Cour, Robert W. Heath

Published Jan 1, 2021• 8 citations
Publisher

Abstract

We propose a general framework for noncoherent communication using techniques from the field of quantum error correction (QEC). We first propose an approach for analyzing a classical communication channel as a quantum channel, and develop an extension of the QEC conditions to the classical case. We derive a quantum analogue of the noncoherent multiantenna wireless channel. Restricting to the case in which the number of transmitter and receiver antennas are equal and a power of two, we use the framework to develop a family of space-time block codes for noncoherent multiple-input multiple-output (MIMO) communication. Under a Rayleigh fading assumption, we derive the optimal decoder and bound the probability of symbol detection error. We compare our performance to comparable coherent and noncoherent approaches and achieve competitive performance for various antenna geometries and rates.

DOI
10.1109/ojcoms.2021.3121183

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We propose a general framework for noncoherent communication using techniques from the field of quantum error correction (QEC). We first propose an approach for analyzing a classical communication channel as a quantum channel, and develop an extension of the QEC conditions to the classical case. We derive a quantum analogue of the noncoherent multiantenna wireless channel. Restricting to the case in which the number of transmitter and receiver antennas are equal and a power of two, we use the framework to develop a family of space-time block codes for noncoherent multiple-input multiple-output (MIMO) communication. Under a Rayleigh fading assumption, we derive the optimal decoder and bound the probability of symbol detection error. We compare our performance to comparable coherent and noncoherent approaches and achieve competitive performance for various antenna geometries and rates.
In this work, we develop a space-time block code for noncoherent communication using techniques from the field of quantum error correction. We decompose the multiple-input multiple-output (MIMO) channel into operators from quantum mechanics, and design a non-coherent space time code using the quantum stabilizer formalism. We derive an optimal decoder, and analyze the former through a quantum mechanical lens. We compare our approach to a comparable coherent approach and a noncoherent differential approach, achieving comparable or better performance.
The engineering problem of building scalable quantum computers has prompted the development of a rich theory modeling the evolution of quantum systems as well as techniques to preserve quantum information in the presence of noise. Such techniques offer systems-level approaches to the problem of robustly encoding and preserving information and, as a result, see applicability in a wide variety of architectures for computing systems. In this thesis, we visit the mathematical underpinnings of quantum information and apply strategies inspired by quantum information processing to two non-quantum systems to demonstrate advantage. We first describe the construction of a quantum emulation device, an analog electronic system with the same mathematical structure as a gate-based quantum computer, and introduce novel time-domain information encoding methods to increase the computational capacity of the device. We confirm the sustained performance of the improved system by successfully transforming emulated states by randomly selected quantum gates. We then visit similarities between quantum information processing and signal processing in the noncoherent wireless communication setting, the latter being an environment characterized by a lack of instantaneous channel knowledge. We describe the theoretical underpinnings of the noncoherent communication environment from both an information theoretic and signal processing perspective. This leads us to propose a multi-antenna space-time code construction based on a family of quantum error correcting codes known as stabilizer codes. For this code, we derive the optimal decoder in Rayleigh and Ricean fading and benchmark the its performance against coherent and differential coding at comparable rates.
Multiple-input multiple-output (MIMO) technology utilizes multiple antennas at the transmitter and receiver to enhance data transmission speeds and reliability. Traditional MIMO decoding methods, however, can become increasingly complex as the number of antennas and modulation order rises. Quantum computing brings forth a new realm of information processing with significant potential. This study investigates the applicability of quantum algorithms for decoding information in MIMO wireless communication systems. Specifically, the Dürr-Høyer quantum search, based on Grover’s algorithm, and optimal quantum sorting algorithms are leveraged to reduce the query complexity with an analysis of the complexity and achievable bit error rate performance of the quantum-assisted decoders. The study considers cases of MIMO diversity, spatial modulation, and multiplexing transmission using both maximum-likelihood and fixed-complexity sphere decoders. By examining a variety of communication scenarios, this work aims to assess the applicability of quantum algorithms across different operational regimes and aids in extending the methodology to other communication systems.
In upcoming generations of wireless communication (6G), Quantum Information Technology (QIT) will be integrated for high computational speeds and unprecedented security features. Quantum states are very delicate and may be lost or suffer from excessive noise as a result of decoherence during transmission. This especially applies to long-distance quantum links that are required for a global 6G network. The use of Quantum Error Correction (QEC) techniques will be necessary in order to achieve fault-tolerant quantum communication. In this work, the most actionablle QEC and hybrid (quantum-classical) error correction techniques are analyzed, especially with respect to the difficult channel conditions and high Key Performance Indicators (KPI) regarding 6G. In particular, the error suppression, qubit overhead, and decoding time required for various codes (Surface Code, Steane Code, hybrid Reed-Solomon (RS)/Turbo Codes, etc.) will be analyzed in the context of a 6G quantum channel (free-space or noisy fiber) to provide 6G. In the wireless 6G network, the simulation will show that while high-distance QEC codes provide the best ultimate logical error suppression, the enormous resource costs and 6G’s strict latency requirements will lead to the first proposed hybrid classical-QEC.
We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a proof of the rate region stated in Yard et al., IEEE Trans. Inf. Theory 57 (10), 2011. Our second result is a quantum generalization of the Marton coding scheme. The error analysis for the quantum Marton region makes use of ideas in our earlier work and an idea recently presented by Radhakrishnan et al. in arXiv:1410.3248. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.
Abstract A confidential communication over multiple-input multiple-output (MIMO) fading channels is considered, in which a transmitter communicates with a group of receivers in the presence of multiple eavesdroppers. The antenna correlation depends on both the antenna spacing and the angular spectrum of the incoming radio waves. We derive the closed-form analytical expressions of the ergodic secrecy multicast capacity for Rayleigh and Ricean fading MIMO channels considering a linear array with equally spaced antennas and employing the classical Jakes correlation. Then, we compare the performance of Rayleigh and Ricean fading channels showing the effects of fading, antenna correlation and the spacing between antenna elements. Our results show that antenna correlations significantly reduces the ergodic secrecy multicast capacity of Rayleigh as well as Ricean fading MIMO channels and this effect is more severe in the case of Rayleigh fading channel compared to Ricean fading.