The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

Four-Group Decodable Space-Time Block Codes

Two new rate-one full-diversity space-time block codes (STBC) are proposed. They are characterized by the \emph{lowest decoding complexity} among the known rate-one STBC, arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection. The first and the second codes are delay-optimal if the number of transmit antennas is a power of 2 and even, respectively. The exact pair-wise error probability is derived to allow for the performance optimization of the two codes. Compared with existing low-decoding complexity STBC, the two new codes offer several advantages such as higher code rate, lower encoding/decoding delay and complexity, lower peak-to-average power ratio, and better performance.Comment: 1 figure. Accepted for publication in IEEE Trans. on Signal Processin

Two-tier channel estimation aided near-capacity MIMO transceivers relying on norm-based joint transmit and receive antenna selection

We propose a norm-based joint transmit and receive antenna selection (NBJTRAS) aided near-capacity multiple-input multiple-output (MIMO) system relying on the assistance of a novel two-tier channel estimation scheme. Specifically, a rough estimate of the full MIMO channel is first generated using a low-complexity, low-training-overhead minimum mean square error based channel estimator, which relies on reusing a modest number of radio frequency (RF) chains. NBJTRAS is then carried out based on this initial full MIMO channel estimate. The NBJTRAS aided MIMO system is capable of significantly outperforming conventional MIMO systems equipped with the same modest number of RF chains, while dispensing with the idealised simplifying assumption of having perfectly known channel state information (CSI). Moreover, the initial subset channel estimate associated with the selected subset MIMO channel matrix is then used for activating a powerful semi-blind joint channel estimation and turbo detector-decoder, in which the channel estimate is refined by a novel block-of-bits selection based soft-decision aided channel estimator (BBSB-SDACE) embedded in the iterative detection and decoding process. The joint channel estimation and turbo detection-decoding scheme operating with the aid of the proposed BBSB-SDACE channel estimator is capable of approaching the performance of the near-capacity maximumlikelihood (ML) turbo transceiver associated with perfect CSI. This is achieved without increasing the complexity of the ML turbo detection and decoding process

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

A universal space-time architecture for multiple-antenna aided systems

In this tutorial, we first review the family of conventional multiple-antenna techniques, and then we provide a general overview of the recent concept of the powerful Multiple-Input Multiple-Output (MIMO) family based on a universal Space-Time Shift Keying (STSK) philosophy. When appropriately configured, the proposed STSK scheme has the potential of outperforming conventional MIMO arrangements

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor