High Performance Non-Binary Spatially-Coupled Codes for Flash Memories

Modern dense Flash memory devices operate at very low error rates, which require powerful error correcting coding (ECC) techniques. An emerging class of graph-based ECC techniques that has broad applications is the class of spatially-coupled (SC) codes, where a block code is partitioned into components that are then rewired multiple times to construct an SC code. Here, our focus is on SC codes with the underlying circulant-based structure. In this paper, we present a three-stage approach for the design of high performance non-binary SC (NB-SC) codes optimized for practical Flash channels; we aim at minimizing the number of detrimental general absorbing sets of type two (GASTs) in the graph of the designed NB-SC code. In the first stage, we deploy a novel partitioning mechanism, called the optimal overlap partitioning, which acts on the protograph of the SC code to produce optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental GASTs. In the third stage, we use the weight consistency matrix framework to manipulate edge weights to eliminate as many as possible of the GASTs that remain in the NB-SC code after the first two stages (that operate on the unlabeled graph of the code). Simulation results reveal that NB-SC codes designed using our approach outperform state-of-the-art NB-SC codes when used over Flash channels.Comment: 8 pages (double column), 5 figures, the short version was accepted at the IEEE Information Theory Worksho

Exact Reconstruction from Insertions in Synchronization Codes

This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes. These sequences have been corrupted by a fixed number of symbol insertions (larger than the minimum edit distance of the code), yielding a number of distinct traces to be used for reconstruction. We wish to know the minimum number of traces needed for exact reconstruction. This is a general version of a problem tackled by Levenshtein for uncoded sequences. We introduce an exact formula for the maximum number of common supersequences shared by sequences at a certain edit distance, yielding an upper bound on the number of distinct traces necessary to guarantee exact reconstruction. Without specific knowledge of the codewords, this upper bound is tight. We apply our results to the famous single deletion/insertion-correcting Varshamov-Tenengolts (VT) codes and show that a significant number of VT codeword pairs achieve the worst-case number of outputs needed for exact reconstruction. We also consider extensions to other channels, such as adversarial deletion and insertion/deletion channels and probabilistic channels.Comment: 18 pages, 3 figures. Accepted to IEEE Transactions on Information Theor

Transient Effects at Power-Supply System of the Czech Railways from EMC Viewpoint

The paper deals with the behavior of the traction power-supply system 25 kV, 50 Hz at the Czech Railways. Electrical conditions on a contact line affect electrical conditions in a feeding station. This relation represents galvanic coupling from EMC viewpoint. Explanation of transient effects during short-circuits at the contact line can be considered as the main problem. These effects can arise during a failure in a traction circuit. Therefore, the attention is turned to an adjustment protection design of the traction circuit. Simulation diagrams were created. The design can be utilizable for a feeding station with Filter-Compensation Equipment, which is designed for the EMI reduction