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In this paper, we introduce two new methods of mitigating decoder error propagation for low-latency sliding window decoding (SWD) of spatially coupled low density parity check (SC-LDPC) codes. Building on the recently introduced idea of check node (CN) doping of regular SC-LDPC codes, here we employ variable node (VN) doping to fix (set to a known value) a subset of variable nodes in the coupling chain. Both of these doping methods have the effect of allowing SWD to recover from error propagation, at a cost of a slight rate loss. Experimental results show that, similar to CN doping, VN doping improves performance by up to two orders of magnitude compared to undoped SC-LDPC codes in the typical signal-to-noise ratio operating range. Further, compared to CN doping, VN doping has the advantage of not requiring any changes to the decoding process.In addition, a log-likelihood-ratio based window extension algorithm is proposed to reduce the effect of error propagation. Using this approach, we show that decoding latency can be reduced by up to a significant fraction without suffering any loss in performance 

Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as {\em efficient} encoding and decoding algorithms. In many applications, polynomial running time may still be prohibitively expensive, which has motivated the study of codes with {\em super-efficient} decoding algorithms. These have led to the well-studied notions of Locally Decodable Codes (LDCs) and Locally Correctable Codes (LCCs). Inspired by these notions, Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015) generalized Hamming LDCs to insertions and deletions. To the best of our knowledge, these are the only known results that study the analogues of Hamming LDCs in channels performing insertions and deletions. Here we continue the study of insdel codes that admit local algorithms. Specifically, we reprove the results of Ostrovsky and Paskin-Cherniavsky for insdel LDCs using a different set of techniques. We also observe that the techniques extend to constructions of LCCs. Specifically, we obtain insdel LDCs and LCCs from their Hamming LDCs and LCCs analogues, respectively. The rate and error-correction capability blow up only by a constant factor, while the query complexity blows up by a poly log factor in the block length. Since insdel locally decodable/correctble codes are scarcely studied in the literature, we believe our results and techniques may lead to further research. In particular, we conjecture that constant-query insdel LDCs/LCCs do not exist. 

This paper presents the software design for three interactive simulations on the subject of Earth and Environmental science in grades 5, 6 and 7. These simulations together with some programming activities have been successfully integrated into a series of instructional modules for local New Jersey elementary and middle schools. The goal of these modules was for the students to explore the steerable parameters of the simulations and develop their computational and mathematical thinking. In this paper, we present three simulations we developed, discuss their design and examine student assessment results that were collected and analyzed using statistical inferences. Our findings illustrate the effectiveness of such enticing exploratory learning processes for developing students’ reasoning of Earth and Environmental science, computational thinking and mathematics.