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This paper addresses to design an R-S (Reed-Solomon) encoder and R-S decoder and verify its functionality on FPGA. An RTL (register transfer logic) code was developed for an R-S encoder that takes a 32-bit input data and produces a 48-bit output. The logic synthesis and optimization of the code was carried out using Quartus II tool. Also, an R-S decoder was developed that decodes the transmitted data.
We construct 2D codewords by using 2D finite field Fourier transform. The components of the codeword in the transformed domain are from an extension field GF(2m) and are linked by a conjugacy constraint. We provide encoding and decoding schemes in the transformed domain.
Low density lattice codes (LDLC) can be decoded efficiently using iterative decoding, and approach the capacity of the AWGN channel. In the iterative LDLC decoder the messages are Gaussian mixtures. In any implementation, the Gaussian mixtures must be approximated. This work describes a three/two Gaussian parametric LDLC decoder. Internally at the variable node the periodic Gaussian mixtures are approximated...
We present an efficient decoding algorithm for constant rate quantum hyper graph-product LDPC codes which provably corrects adversarial errors of weight proportional to the code minimum distance, or equivalently to the square-root of the block length. The algorithm runs in time linear in the number of qubits, which makes its performance the strongest to date for linear-time decoding of quantum codes...
BCH (Bose-Chaudhuri-Hocquenghem) coding is very useful to detect and correct the errors in communication system and also on-chip (computer) memory systems. This paper presents a High-speed BCH decoder that corrects double-adjacent and single-bit errors in parallel and serially corrects multiple-bit errors instead of double-adjacent errors. Its operation is based on extending an existing decoder that...
A new design to provide unequal error protection (UEP) using Raptor codes over erasure channels, named Intermediate Symbols Expanding Window Raptor (ISEW Raptor) codes using windowing techniques, is developed and discussed. ISEW Raptor encodes intermediate symbols with EWF approach, possessing UEP property while keeping systematic code characteristics. ISEW Raptor is improved based on standard Raptor...
In large storage systems, erasure codes is a primary technique to provide high reliability with low monetary cost. Among various erasure codes, a major category called XORbased codes uses purely XOR operations to generate redundant data and offer low computational complexity. These codes are conventionally implemented via matrix based method or several specialized non-matrix based methods. However,...
We introduce a low-latency stochastic decoding algorithm, called conditional stochastic decoding, to implement iterative Low-Density Parity-Check (LDPC) decoders. The conditional stochastic decoder, which utilizes reliable messages in the decoding process and the channel receiving probability to generate stochastic streams, improves error rate performance and decreases decoding latency. Compared to...
In this paper, we propose a novel network coded non-binary low-density generator matrix (LDGM) code structure for a multi-access relay system, where multiple sources transmit lattice signals to a destination with the help of a relay. Specifically, we first develop a network coded non-binary LDGM code structure by jointly considering lattice-signal transmissions at the sources and the relay. Then we...
Skew polynomials are elements of a noncommutative ring that, in recent years, have found applications in coding theory and cryptography. Skew polynomials have a well-defined evaluation map. This map leads to the definition of a class of codes called Generalized Skew-Evaluation codes that contains Gabidulin codes as a special case as well as other related codes with additional desirable properties...
We report the first 25Gb/s 3-level modulated BM-RX employing a ¼-rate linear BM APD-TIA and a custom decoder IC. We successfully demonstrated burst-mode sensitivity of −20.4dBm with 18dB dynamic burst-to-burst for 25Gb/s upstream links.
As the rapid growth of data, many storage systems have used erasure codes instead of replication to reduce the storage cost under the same level of reliability. Maximum-Distance- Separable (MDS) codes have been the most widely adopted, due to their optimal storage efficiency. It is well understood that the application of codes in storage systems, where the data is less frequently accessed. For the...
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding algorithm for the codes that finds a close codeword to a given random word. We provide both theoretical analysis of the performance and stability of the decoding algorithm,...
Recently, a new type of product-like codes, known as half-product codes, have been studied for OTN applications. Motivated by these codes, new classes of symmetry-invariant subproduct codes are proposed and investigated under iterative hard-decision decoding. A subset of the new class of quarter product codes has lower error floors than comparable half-product codes in terms of length, rate and performance.
In this paper, we study a construction of binary switch codes. A switch code is a code such that a multi-set request of information symbols can be simultaneously recovered from disjoint sets of codeword symbols. Our construction is optimal in the sense that it has the smallest codeword length given its average encoding degree, which is logarithmic in the code dimension. Moreover, the number of queries...
Fire codes are cyclic codes generated by the product of two polynomials: a binomial that characterizes the code's guaranteed burst correcting capability and an irreducible polynomial that characterizes the code length. However, the true burst correcting capability of a Fire code may exceed its guaranteed burst correcting capability. The true burst correcting capability of primitive Fire codes, in...
The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We show that the column sum rank parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several column distance properties and introduce a new family of convolutional codes that maximize the column...
Consider the problem of reliable multicast over a network in the presence of adversarial errors. In contrast to traditional network error correction codes designed for a given network capacity and a given number of errors, we study an arguably more realistic setting that prior knowledge on the network and adversary parameters is not available. For this setting we propose efficient and throughput-optimal...
An interpolation-based list decoding algorithm for ℓ-quasi-cyclic codes over finite fields is developed and its guaranteed decoding radius for ℓ-phased burst errors is proven. It is also shown that for this error model and for certain parameter ranges, this new approach is advantageous over existing schemes.
This paper presents a hybrid multimode Bose Chaudhuri Hocquenghem (BCH) encoder for reducing the input length of Syndrome calculation (SC) based on re-encoding approach. In previous re-encoding approaches, a conventional BCH encoder with long generator polynomials is used as a remainder operator to reduce the input length of SC. However, the input length is still large since long polynomial is used...
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