On Ordinary Words of Standard Reed–Solomon Codes over Finite Fields

Reed–Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm. Usually we use the maximum likelihood decoding (MLD) algorithm in the decoding process of Reed–Solomon codes. MLD algorithm relies on determining the error distance of received word. Dür, Guruswami, Wan, Li, Hong, Wu, Yue and Zhu et al. got some results on the error distance. For the Reed–Solomon code [Formula: see text], the received word [Formula: see text] is called an ordinary word of [Formula: see text] if the error distance [Formula: see text] with [Formula: see text] being the Lagrange interpolation polynomial of [Formula: see text]. We introduce a new method of studying the ordinary words. In fact, we make use of the result obtained by Y.C. Xu and S.F. Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed–Solomon codes over the finite field of [Formula: see text] elements. This completely answers an open problem raised by Li and Wan in [On the subset sum problem over finite fields, Finite Fields Appl. 14 (2008) 911–929].

Reduced-Complexity LDPC Decoding for Next-Generation IoT Networks

Low-density parity-check (LDPC) codes have become the focal choice for next-generation Internet of things (IoT) networks. This correspondence proposes an efficient decoding algorithm, dual min-sum (DMS), to estimate the first two minima from a set of variable nodes for check-node update (CNU) operation of min-sum (MS) LDPC decoder. The proposed architecture entirely eliminates the large-sized multiplexing system of sorting-based architecture which results in a prominent decrement in hardware complexity and critical delay. Specifically, the DMS architecture eliminates a large number of comparators and multiplexors while keeping the critical delay equal to the most delay-efficient tree-based architecture. Based on experimental results, if the number of inputs is equal to 64, the proposed architecture saves 69%, 68%, and 52% area over the sorting-based, the tree-based, and the low-complexity tree-based architectures, respectively. Furthermore, the simulation results show that the proposed approach provides an excellent error-correction performance in terms of bit error rate (BER) and block error rate (BLER) over an additive white Gaussian noise (AWGN) channel.

ISTDECO: In Situ Transcriptomics Decoding by Deconvolution

In Situ Transcriptomics (IST) is a set of image-based transcriptomics approaches that enables localisation of gene expression directly in tissue samples. IST techniques produce multiplexed image series in which fluorescent spots are either present or absent across imaging rounds and colour channels. A spot’s presence and absence form a type of barcoded pattern that labels a particular type of mRNA. Therefore, the expression of a gene can be determined by localising the fluorescent spots and decode the barcode that they form. Existing IST algorithms usually do this in two separate steps: spot localisation and barcode decoding. Although these algorithms are efficient, they are limited by strictly separating the localisation and decoding steps. This limitation becomes apparent in regions with low signal-to-noise ratio or high spot densities. We argue that an improved gene expression decoding can be obtained by combining these two steps into a single algorithm. This allows for an efficient decoding that is less sensitive to noise and optical crowding.We present IST Decoding by Deconvolution (ISTDECO), a principled decoding approach combining spectral and spatial deconvolution into a single algorithm. We evaluate ISTDECO on simulated data, as well as on two real IST datasets, and compare with state-of-the-art. ISTDECO achieves state-of-the-art performance despite high spot densities and low signal-to-noise ratios. It is easily implemented and runs efficiently using a GPU.ISTDECO implementation, datasets and demos are available online at:github.com/axanderssonuu/istdeco

A Novel Niederreiter-like cryptosystem based on the (u|u + υ)-construction codes

In this paper, we present a new variant of the Niederreiter Public Key Encryption (PKE) scheme which is resistant against recent attacks. The security is based on the hardness of the Rank Syndrome Decoding (RSD) problem and it presents a (u|u + υ)-construction code using two different types of codes: Ideal Low Rank Parity Check (ILRPC) codes and λ-Gabidulin codes. The proposed encryption scheme benefits are a larger minimum distance, a new efficient decoding algorithm and a smaller ciphertext and public key size compared to the Loidreau’s variants and to its IND-CCA secure version.

Design and Implementation of RS(450, 406) Decoder

Nowadays, in the field of data transmission between receiver and transmitter, the Reed Solomon code is used very frequently. FEC codes have two foremost and influential operations: (1) calculating parity symbols at the encoder side and (2) transmitting message symbols with parity symbols and decoding the received codeword at the second side by using the decoding algorithms. Gigabit automotive ethernet is used in the automotive car to provide better bandwidth for every kind of applications to connect functional components of the vehicles. This error correction technique is used in the gigabit automotive ethernet to reduce the channel noise during data transmission. RS (450, 406) is a powerful error correction techniques used in automotive ethernet. This paper focused only on the analysis of Reed Solomon decoding. Reed Solomon decoding is more efficient decoding techniques for correcting both burst and random errors. The critical steps of the Reed Solomon decoding are to solve the error evaluator and error calculator polynomial, which is also known as KES solver.