Abstract-This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1 2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10 5 at 0.9 dB and 1.4 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders.

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PurposeGlaucoma is the main cause of irreversible blindness worldwide. However, the diagnosis and treatment of glaucoma remain difficult because of the lack of an effective glaucoma grading measure. In this study, we aimed to propose an artificial intelligence system to provide adequate assessment of glaucoma patients.MethodsA total of 16,356 visual fields (VFs) measured by Octopus perimeters and Humphrey Field Analyzer (HFA) were collected, from three hospitals in China and the public Harvard database. We developed a fine-grained grading deep learning system, named FGGDL, to evaluate the VF loss, compared to ophthalmologists. Subsequently, we discuss the relationship between structural and functional damage for the comprehensive evaluation of glaucoma level. In addition, we developed an interactive interface and performed a cross-validation study to test its auxiliary ability. The performance was valued by F1 score, overall accuracy and area under the curve (AUC).ResultsThe FGGDL achieved a high accuracy of 85 and 90%, and AUC of 0.93 and 0.90 for HFA and Octopus data, respectively. It was significantly superior (p < 0.01) to that of medical students and nearly equal (p = 0.614) to that of ophthalmic clinicians. For the cross-validation study, the diagnosis accuracy was almost improved (p < 0.05).ConclusionWe proposed a deep learning system to grade VF of glaucoma with a high detection accuracy, for effective and adequate assessment for glaucoma patients. Besides, with the convenient and credible interface, this system can promote telemedicine and be used as a self-assessment tool for patients with long-duration diseases.

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