Algebraic techniques in designing quantum synchronizable codes

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.Comment: 9 pages, no figures. The framework presented in this article supersedes the one given in arXiv:1206.0260 by the first autho

High-rate self-synchronizing codes

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication in the IEEE Transactions on Information Theory. Material presented in part at the International Symposium on Information Theory and its Applications, Honolulu, HI USA, October 201

Parsing a sequence of qubits

We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication such as a self-synchronizing quantum network where one can hop into the channel at any time, catch the next coming quantum information with a label indicating the sender, and reply by routing her quantum information with control qubits for quantum switches all without assuming prior frame synchronization between users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication in the IEEE Transactions on Information Theor

Coded DS-CDMA Systems with Iterative Channel Estimation and no Pilot Symbols

In this paper, we describe direct-sequence code-division multiple-access (DS-CDMA) systems with quadriphase-shift keying in which channel estimation, coherent demodulation, and decoding are iteratively performed without the use of any training or pilot symbols. An expectation-maximization channel-estimation algorithm for the fading amplitude, phase, and the interference power spectral density (PSD) due to the combined interference and thermal noise is proposed for DS-CDMA systems with irregular repeat-accumulate codes. After initial estimates of the fading amplitude, phase, and interference PSD are obtained from the received symbols, subsequent values of these parameters are iteratively updated by using the soft feedback from the channel decoder. The updated estimates are combined with the received symbols and iteratively passed to the decoder. The elimination of pilot symbols simplifies the system design and allows either an enhanced information throughput, an improved bit error rate, or greater spectral efficiency. The interference-PSD estimation enables DS-CDMA systems to significantly suppress interference.Comment: To appear, IEEE Transactions on Wireless Communication