Various local transformations of combinatorial structures (codes, designs, and related structures) that leave the basic parameters unaltered are here unified under the principle of switching. The purpose of the study ...
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Various local transformations of combinatorial structures (codes, designs, and related structures) that leave the basic parameters unaltered are here unified under the principle of switching. The purpose of the study is threefold: presentation of the switching principle, unification of earlier results (including a new result for covering codes), and applying switching exhaustively to some common structures with small parameters. (C) 2011 Elsevier B.V. All rights reserved.
In this correspondence, we give two characterizations of crooked functions: one based on the minimum distance of a Preparata-like code, and the other based on the distance-regularity of a crooked graph.
In this correspondence, we give two characterizations of crooked functions: one based on the minimum distance of a Preparata-like code, and the other based on the distance-regularity of a crooked graph.
The Fibonacci cube Gamma(n) is obtained from the n-cube Q(n) by removing all the vertices that contain two consecutive 1s. It is proved that Gamma(n) admits a perfect code if and only if n <= 3. (C) 2016 Elsevier B...
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The Fibonacci cube Gamma(n) is obtained from the n-cube Q(n) by removing all the vertices that contain two consecutive 1s. It is proved that Gamma(n) admits a perfect code if and only if n <= 3. (C) 2016 Elsevier B.V. All rights reserved.
This brief presents an efficient architecture of the polar decoder that employs the successive-cancellation (SC) decoding algorithm. In the SC decoding algorithm, each bit is decoded successively by recursively calcul...
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This brief presents an efficient architecture of the polar decoder that employs the successive-cancellation (SC) decoding algorithm. In the SC decoding algorithm, each bit is decoded successively by recursively calculating the log likelihood ratio (LLR) based on two kernels. This brief proposes a novel LLR representation scheme so that the kernel processing can be realized in low-complexity and high-speed circuitry. A 1024-bit polar decoder was designed and implemented based on the proposed scheme using a 0.18 mu m CMOS process. Its throughput is 252R Mb/s for the rate-R code, and the gate count is 256K. By the proposed LLR representation scheme, the decoding speed is increased by 18% while the gate count is not increased when compared to the same decoder designed with the signed-magnitude scheme. In terms of the throughput efficiency, the proposed decoder is 1.34 times superior to the previous state-of-the-art decoder.
A novel encoding scheme and a unified encoder and decoder system for Reed-Solomon codes are proposed. The proposed system has a smaller circuit scale than the conventional system for more than 10 correctable errors fo...
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A novel encoding scheme and a unified encoder and decoder system for Reed-Solomon codes are proposed. The proposed system has a smaller circuit scale than the conventional system for more than 10 correctable errors for a short sector of 512 bytes, and more than 15 errors for a long sector of 4096 bytes.
In 1991, C. L. Chen used the inverted construction Y-1 on binary linear codes of minimum Hamming distance five to construct a new [47, 36, 5] code. In this paper, we examine this construction in depth and show that no...
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In 1991, C. L. Chen used the inverted construction Y-1 on binary linear codes of minimum Hamming distance five to construct a new [47, 36, 5] code. In this paper, we examine this construction in depth and show that no such codes are obtained unless the fields GF (8) or GF (32) are used. Using MAGMA, we prove that the binary [11, 4, 5] code and the binary [15, 7, 5] extension found by Chen are the only possible such codes using the held GF(8);indeed, the latter is a Bose-Chaudhuri-Hocquenghem (BCH) code, We prove also that, using the field GF (32), precisely three nonequivalent binary [47, 36, 5] codes arise along with one extension to a [63, 51, 5] code.
Privacy and security concerns are significant barrier for RFID deployment in many applications in modern day world. The implementation of authentication schemes which provide reasonable security under the resource con...
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Privacy and security concerns are significant barrier for RFID deployment in many applications in modern day world. The implementation of authentication schemes which provide reasonable security under the resource constraints of tiny-powered RFID tags are an efficient way to avoid these concerns. In this paper, we present physical unclonable function based unilateral authentication protocol for RFID system. In addition, we use error-correcting code properties to enhance security of the proposed scheme. Use of error-correcting code also reduces computational cost of the proposed scheme drastically. Security and privacy analysis indicates that the proposed scheme resists various attacks. Cost analysis shows that the scheme outshines the existing protocols in terms of storage requirement, computational operations, and communication cost.
Non-volatile memory has many advantages such as high density and low leakage power but it consumes larger writing energy than SRAM. It is quite necessary to reduce writing energy in non-volatile memory design. In this...
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Non-volatile memory has many advantages such as high density and low leakage power but it consumes larger writing energy than SRAM. It is quite necessary to reduce writing energy in non-volatile memory design. In this paper, we propose write-reduction codes based on errorcorrectingcodes and reduce writing energy in non-volatile memory by decreasing the number of writing bits. When a data is written into a memory cell, we do not write it directly but encode it into a codeword. In our write-reduction codes, every data corresponds to an information vector in an error-correcting code and an information vector corresponds not to a single codeword but a set of write-reduction codewords. Given a writing data and current memory bits, we can deterministically select a particular write-reduction codeword corresponding to the data to be written, where the maximum number of flipped bits are theoretically minimized. Then the number of writing bits into memory cells will also be minimized. Experimental results demonstrate that we have achieved writing-bits reduction by an average of 51% and energy reduction by an average of 33% compared to non-encoded memory.
The decoding speed is the biggest problem of random codes based on quasigroups proposed elsewhere. These codes are a combination of cryptographic algorithms and error-correcting codes. In our previous paper we propose...
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The decoding speed is the biggest problem of random codes based on quasigroups proposed elsewhere. These codes are a combination of cryptographic algorithms and error-correcting codes. In our previous paper we proposed Cut-Decoding algorithm which is 4.5 times faster than the original one for code (72,288). In this paper, four new modifications (so-called 4-Sets-Cut-Decoding algorithms) of this algorithm are proposed in order to obtain an improvement of the decoding speed. We present and analyze several experimental results obtained with different algorithms for random codes based on quasigroups. It is shown that using new algorithms, improvement of the efficiency and decoding speed is obtained. Also, we derive the upper bound for packet-error probability obtained with Cut-Decoding and 4-SetsCut-Decoding algorithm. At the end, some methods for reducing the number of unsuccessful decodings in the new proposed algorithms are considered. (C) 2015 Elsevier GmbH. All rights reserved.
Locally recoverable codes are error-correcting codes allowing local recovery of lost encoded data in a codeword. We give a method to construct locally recoverable codes from rational maps between affine spaces, whose ...
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Locally recoverable codes are error-correcting codes allowing local recovery of lost encoded data in a codeword. We give a method to construct locally recoverable codes from rational maps between affine spaces, whose fibres are used as recovery sets. The recovery of erasures is carried out by Lagrangian interpolation in general and simply by one addition in some good cases. We first state the general construction of these codes and study its main properties. Next we apply it to several types of codes, including algebraic geometry codes, Reed-Muller, and other related codes. The existence of several recovering sets for the same coordinate and the possibility of recover more than one erasure at the same time are also treated. (C) 2018 Elsevier Inc. All rights reserved.
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