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This paper proposes a coding scheme that derives a multiple-rate code from existing channel codes defined over the composite field and the ground field, where code length is fixed. Formally, from codes C1(k, 1), C2 (k, 2),…, Ck(k, k) defined over GF(q) together with the code C(n,k) over GF(qn), the proposed scheme derives a multiple-rate code with fixed code length. The primary benefit of the proposed...
Error-correcting codes make possible reliable communication over noisy channels. One way to guarantee the correct implementation of error-correcting codes is to use formal verification. This requires in particular the formalization of the mathematical theory of error-correcting codes. This has been made possible by recent advances in the formalization of mathematics using proof-assistants. In this...
The construction of a channel code by using a source code with decoder side information is introduced. For the construction, any pair of encoder and decoder is available for a source code with decoder side information. A constrained-random-number generator, which generates random numbers satisfying a condition specified by a function and its value, is used to construct a stochastic channel encoder...
An application of convolutional codes is the burst error correcting, and the terminated Berlekamp-Preparata convolutional codes are the suboptimal phased burst error correcting codes. This paper presents a decoding method of tail-biting Berlekamp-Preparata convolutional codes that based on tail-biting technology, which can correct the final m block errors without m block termination check data within...
Symbol-pair read channels output overlapping pairs of symbols in storage applications. Pair distance and pair error are used in the channels. In this paper, we discuss the error-trapping decoding for cyclic codes over symbol-pair read channels. By putting some restrictions on the correctable pair error patterns, we discuss a new error-trapping decoding algorithm over the channels and show a circuitry...
This paper presents the new method permuted decoding BCH based on a norm of syndrome. This approach allows correction of the random error and burst error simultaneously. This method is combined with a cyclotomic permutation to reduce the complexity of the decoder. The proposed method reaches the gain coding to 5dB at BER = 10-4 on the flat fading Rayleigh channel compared with the algebraic method.
Instruction set simulators (ISSs) are indispensable tools for developing new architectures and embedded software. Due to the increasing variety of architectures and time-to-market pressure, it is important to efficiently develop fast ISSs based on dynamic binary translation. However, the implementation of such ISSs needs more effort than interpretive ISSs. In this paper, we propose a novel framework...
The susceptibility to Single Event Upset (SEU) is very high for Configuration memory of SRAM based Field Programmable Gate Arrays (FPGA) compared to other FPGA resources. The reduction in feature sizes and core voltages leads to a reduction in the critical charge required to change the state of a memory cell. The SEUs cause failures in the system functionality implemented in FPGA. Fault tolerant techniques...
This paper investigates the performance of the BCH encoder and decoder for different error-correcting capabilities. The focus is on BCH codes of length 255. The motivation for this research is a project where data symbols of this length are transmitted over an error-prone wireless channel. The paper presents a mathematical introduction into encoding for cyclic codes and decoding of the BCH code. The...
We propose a new linear physical-layer network coding and information combining scheme for the K-user fading multiple-access relay network (MARN), which consists of K users, one relay and one destination. The relay and the destination are connected via a rate-constraint backhaul link. In the proposed scheme, the K users transmit signals simultaneously. The relay and the destination receive the superimposed...
This paper proposes a novel method for recovering missing radio frequency identification (RFID) tag identifiers from a group, based on progressive edge-growth (PEG) methods. Extended grouping of RFID tags allows the recovery of missing tag identifiers without external systems such as databases. Motivated by the properties of Tanner graphs, or equivalently, parity check matrices constructed using PEG...
This paper proposes a new approach for 32 bit Arithmetic and Logic Unit for multifunctional processors. The proposed ALU has a novel instruction set including Parity checker, Parity Generator, Binary to Gray converter, gray to binary converter and Manchester encoder decoder along with conventional ALU operations. This extended ALU caters the need of cryptographic processors where an extended security...
Real convolutional lattices over the ring of integers Z are considered in this paper. We study the stability of convolutional lattices under sphere decoding. A new stable family of time-alternating convolutional lattices is proposed. The structure, the parameters, and a performance example are shown for time-alternating convolutional lattices. These lattices can be used as constituent blocks in concatenated...
The Multidimensional Parity Check codes (MDPC) are one of the possible FEC methods of the short information messages. Especially the MDPCs with reduced generator matrix results in codes with block length from few to tens of bits with indispensable code-gain. This paper presents two methods of generation of the MDPC and describe the algorithm for iterative decoding of these codes. The MDPC with short...
Communication technologies are key and standard parts of most of today's integrated as well as field systems. Such technologies have experienced an explosive development during the last decades. More recently, short-distance communication systems have also been discussed as a way to connect embedded electronic systems in industrial applications. As industrial robots are assumed to be real-time and...
The main problems of practical use of pseudorandom codes in modern data transmission systems are considered. The existing methods of generating pseudorandom sequences are analyzed. Physical model of pseudorandom codes in Euclidean space is developed. This model is displayed like carriers of code words in the form of pieces of realization of pseudorandom processes with a limited range.
In this paper, the construction of non binary cyclic One-Step Majority-Logic decoding codes from the dual domain and idempotents is investigated. This had led us to propose a new design algorithm based on Genetic Algorithms, as an extension to previous works on the binary field. With the proposed algorithm, we were able to obtain long new non-binary cyclic OSMLD codes with high coding rates and good...
The compact genetic algorithm cGA is used in this paper to design an efficient soft-decision decoding algorithm, especially for the cyclic codes, because the cGA dramatically reduces the population's size and rapidly converges to the optimal solution compared to classical genetic algorithms. Our main contribution is to exploit the cyclic property of cyclic linear codes to reduce the complexity of...
This work presents a simple study of stochastic arithmetic complex number operators for addition and multiplication. Their usage is demonstrated by design of a sum of product circuit As the stochastic complex number operators need more control random streams than stochastic rational number operators, we optimized the number of random generators used in the real circuit. In the end our sum of product...
We construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes with any length n and dimension k. By sparsest, we mean that each row has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differs by at most one. Codes allowing such encoding schemes are useful in distributed settings where computational load-balancing is critical...
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