Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes

Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here we present an efficient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code 'sheets'. We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.Comment: 23 pages, 15 figures, accepted for publication in Phys. Rev.

An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor Product Code with Application to Data Storage

Joint morphological-lexical language modeling for processing morphologically rich languages with application to dialectal Arabic

Language modeling for an inflected language such as Arabic poses new challenges for speech recognition and machine translation due to its rich morphology. Rich morphology results in large increases in out-of-vocabulary (OOV) rate and poor language model parameter estimation in the absence of large quantities of data. In this study, we present a joint morphological-lexical language model (JMLLM) that takes advantage of Arabic morphology. JMLLM combines morphological segments with the underlying lexical items and additional available information sources with regards to morphological segments and lexical items in a single joint model. Joint representation and modeling of morphological and lexical items reduces the OOV rate and provides smooth probability estimates while keeping the predictive power of whole words. Speech recognition and machine translation experiments in dialectal-Arabic show improvements over word and morpheme based trigram language models. We also show that as the tightness of integration between different information sources increases, both speech recognition and machine translation performances improve

Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems

In this work, decision feedback (DF) detection algorithms based on multiple processing branches for multi-input multi-output (MIMO) spatial multiplexing systems are proposed. The proposed detector employs multiple cancellation branches with receive filters that are obtained from a common matrix inverse and achieves a performance close to the maximum likelihood detector (MLD). Constrained minimum mean-squared error (MMSE) receive filters designed with constraints on the shape and magnitude of the feedback filters for the multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive implementation of the proposed MB-MMSE-DF detector is developed along with a recursive least squares-type algorithm for estimating the parameters of the receive filters when the channel is time-varying. A soft-output version of the MB-MMSE-DF detector is also proposed as a component of an iterative detection and decoding receiver structure. A computational complexity analysis shows that the MB-MMSE-DF detector does not require a significant additional complexity over the conventional MMSE-DF detector, whereas a diversity analysis discusses the diversity order achieved by the MB-MMSE-DF detector. Simulation results show that the MB-MMSE-DF detector achieves a performance superior to existing suboptimal detectors and close to the MLD, while requiring significantly lower complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications, 201

Towards robust real-world historical handwriting recognition

In this thesis, we make a bridge from the past to the future by using artificial-intelligence methods for text recognition in a historical Dutch collection of the Natuurkundige Commissie that explored Indonesia (1820-1850). In spite of the successes of systems like 'ChatGPT', reading historical handwriting is still quite challenging for AI. Whereas GPT-like methods work on digital texts, historical manuscripts are only available as an extremely diverse collections of (pixel) images. Despite the great results, current DL methods are very data greedy, time consuming, heavily dependent on the human expert from the humanities for labeling and require machine-learning experts for designing the models. Ideally, the use of deep learning methods should require minimal human effort, have an algorithm observe the evolution of the training process, and avoid inefficient use of the already sparse amount of labeled data. We present several approaches towards dealing with these problems, aiming to improve the robustness of current methods and to improve the autonomy in training. We applied our novel word and line text recognition approaches on nine data sets differing in time period, language, and difficulty: three locally collected historical Latin-based data sets from Naturalis, Leiden; four public Latin-based benchmark data sets for comparability with other approaches; and two Arabic data sets. Using ensemble voting of just five neural networks, a level of accuracy was achieved which required hundreds of neural networks in earlier studies. Moreover, we increased the speed of evaluation of each training epoch without the need of labeled data

An efficient minimum-distance decoding algorithm for convolutional error-correcting codes

Minimum-distance decoding of convolutional codes has generally been considered impractical for other than relatively short constraint length codes, because of the exponential growth in complexity with increasing constraint length. The minimum-distance decoding algorithm proposed in the paper, however, uses a sequential decoding approach to avoid an exponential growth in complexity with increasing constraint length, and also utilises the distance and structural properties of convolutional codes to considerably reduce the amount of tree searching needed to find the minimum-distance path. In this way the algorithm achieves a complexity that does not grow exponentially with increasing constraint length, and is efficient for both long and short constraint length codes. The algorithm consists of two main processes. Firstly, a direct-mapping scheme, which automatically finds the minimum-distance path in a single mapping operation, is used to eliminate the need for all short back-up tree searches. Secondly, when a longer back-up search is required, an efficient tree-searching scheme is used to minimise the required search effort. The paper describes the complete algorithm and its theoretical basis, and examples of its operation are given