In discrete multi-tone (DMT) transmission based digital subscriber line (DSL) systems, a cyclic prefix (CP) is added to each symbol before transmission, where the length of the CP is larger than the estimated channel impulse response (CIR) length. This ensures the elimination of inter-symbol interference (ISI) and inter-carrier interference (ICI) between the carriers of the same symbol, and allows for single tap frequency domain equalizers and crosstalk cancellation at the receiver. Recently, long reach xDSL (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. With the extended loop lengths, the required CP length increases, in order to match the larger CIR length. The longer CP adds a large overhead and results in overall throughput loss. A more efficient way to deal with extended loop lengths is to use a channel shortening filter -commonly referred as a time domain equalizer (TEQ), to reduce the length of the CIR to the length of CP. This paper focuses on minimum mean square error (MMSE) based multiple input multiple output (MIMO) TEQ design for LR-xDSL MIMO channel shortening. Constraints are applied to the minimization problem to eliminate the trivial solution. This paper proposes two new constraints for the MMSE based MIMO TEQ design for upstream scenarios, which result in a lower complexity and provide better (or similar) performance compared to existing MMSE based MIMO TEQ design methods. Furthermore, a diagonal MIMO TEQ with lower memory requirement and lower computational complexity is presented based on the proposed constraints, which can be applied in upstream as well as downstream scenarios.

This paper presents an overview of quantum errors and noise channels, their mathematical modeling and its implementation in quantum one time password (QOTP) based user authentication. Quantum noise plays a pivotal role in understanding quantum information theory which is important to build up quantum communication theory. The Kraus operators provide a powerful mathematical tool in understanding and modeling various quantum channels. Use of QOTP provides an impressive method of carrying out user authentication involving quantum operations based on user biometrics. However, the efficiency of this method can be better envisaged by incorporating noise models during qubit transmission.

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The Discrete Wavelet Transform (DWT) has gained attention in the area of Multi-Carrier Modulation (MCM) because it can overcome some well known limitations of Discrete Fourier Transform (DFT) based MCM systems. Its improved spectral containment removes the need for a cyclic prefix, be it that appropriate equalization then has to be added as the cyclic convolution property no longer holds. Most DWT based MCM systems in the literature use Time-domain EQualizers (TEQs) to mitigate the channel distortion. In this paper, a Per-Wavelet EQualizer (PWEQ) is proposed which directly maximizes the Signal-to-Interference-plus-Noise Ratio (SINR) per symbol and is applicable to any wavelet family.The proposed PWEQ provides a performance upper bound for the TEQs for DWT based MCM systems. The computational complexity of the PWEQ is reduced by modifying the Filter Bank (FB) structure of the DWT. Simulations are performed to compare the PWEQ performance against the TEQs for DWT based MCM systems and the similar Per-Tone EQualizer (PTEQ) for DFT based MCM systems. The simulations are performed using measured Asymmetric Digital Subscriber Line (ADSL) and G.fast channels with Fejér-Korovkin (FK) wavelets. The proposed PWEQ increases the SINR on the received symbols compared to the TEQs at the cost of an increased computational complexity.INDEX TERMS multi-carrier modulation, discrete wavelet transform, channel equalization, ADSL, G.fast, wireline communication.

Recently, long reach x-digital subscriber line (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. The extended loop lengths are characterized by a longer channel impulse response (CIR), which requires a similarly longer cyclic prefix (CP) to successfully eliminate the inter-symbol interference (ISI) between successive time-domain discrete multi-tone (DMT) symbols and inter-carrier interference (ICI) between the carriers or tones of the same DMT symbol. This adds a large overhead to the transmitted symbols and results in throughput loss. A per-tone equalizer (PTEQ) is an attractive alternative to deal with extended loop lengths. However, it imposes a large initialization computational complexity and memory requirement, hindering the use of a PTEQ in practical multiple-input multiple-output (MIMO) scenarios. To tackle this problem, a specific structure in the MIMO DSL channel, namely that the combined ISI and ICI signal power from the crosstalk channels is significantly lower than the desired and combined ISI and ICI signal power from the direct channels, may be exploited in deriving a novel low complexity/memory solution, here referred as sparse MIMO PTEQ, with negligible impact (≈ 0.5% drop) on performance compared to a full MIMO PTEQ. For a conventional DSL binder size of 16 lines and a PTEQ order of 3, the proposed sparse MIMO PTEQ performs at 42% of the initialization computational complexity and 29.7% of the memory requirement, with negligible performance degradation, compared to a full MIMO PTEQ. The initialization computational complexity and memory requirement is further reduced by the proposed diagonal MIMO PTEQ which operates at 0.4% of the initialization computational complexity of a full MIMO PTEQ and requires 6.25% memory compared to a full MIMO PTEQ, with some degradation in the performance compared to the full MIMO PTEQ. The diagonal MIMO PTEQ has the additional benefit that it can be applied in both upstream and downstream scenarios, in contrast to the full and sparse MIMO PTEQ which can be used only in upstream scenarios.