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A general construction for perfect integer codes is provided, which allows to efficiently compute such codes. The method is applied to investigate in detail the special error set {plusmn1, plusmna, plusmnb, plusmnc,} interesting for single error correction of peak shifts and codes defined on lattices
Maximum rank distance codes are the equivalent in rank-metric of Reed-Solomon codes whose subcodes have been widely studied. In this paper we characterize subspace subcodes of MRD codes and we show that it is possible to construct efficient polynomial-time encoding-decoding procedures for these subcodes. In a second part we show that subfield subcodes of maximum rank distance codes can be represented...
The basis for designing error-correcting codes for two dimensional signal sets is considered in this paper. Both, algebraic and graph-theoretical approaches are employed in this research for establishing the fundamentals of these codes. We give a solution to the t-dominating set problem in a subfamily of degree four circulant graphs which directly provides perfect codes over the Gaussian integers...
For q-ary n-sequences, we develop the concept of similarity functions that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence between two q-ary n-sequences. Codes based on similarity functions are called DNA codes. DNA codes are important components in biomolecular computing and other biotechnical...
A new class of DC-free codes of odd length is presented. The new codes, related to polarity-switch (PS) codes, make use of a redefinition of the running digital sum. The spectral efficiency of the new codes is determined, and it is shown that they provide better power suppression in the low-frequency region than classical PS codes
We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [42N, 24N, 3]2. While it is known that the product construction...
Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal F4-linear and F2-linear convolutional codes, respectively. These quantum convolutional codes have higher rate than comparable quantum block codes or previous quantum convolutional codes, and are simple to decode. A block single-error-correcting [9,3,3] tail-biting...
This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the algorithm approaches maximum a-posteriori decoding. We also demonstrate a stochastic approximations to the alternative update rule successive relaxation. Stochastic...
An algorithm that performs joint equalization and decoding for channels with nonlinear two-dimensional intersymbol interference is presented. The algorithm performs sum-product message-passing on a factor graph that represents the underlying system. The two-dimensional optical storage (Two-DOS) technology is an example of a system with nonlinear two-dimensional intersymbol interference. Simulations...
We design codes to transmit information over a network, some subset of which is controlled by a malicious adversary. The computationally unbounded, hidden adversary knows the message to be transmitted, and can observe and change information over the part of the network being controlled. The network nodes do not share resources such as shared randomness or a private key. We first consider a unicast...
This paper introduces a type-I hybrid ARQ scheme for the Z-channel, based on a class of codes which can correct t asymmetric errors and further detect d (d > t) more. The specific parameters of the ARQ schemes are considered and an upper bound on the probability of undetected error is derived. We give a couple of detailed examples based on classic inner error correcting codes. They show good behavior...
The complexity-rate tradeoff for error-correcting codes below the Shannon limit is a central question in coding theory. This paper makes progress in this area by presenting a joint numerical optimization of rate and decoding complexity for low-density parity-check codes. The focus of this paper is on the binary symmetric channel and on a class of decoding algorithms for which an exact extrinsic information...
Practical implementation of random binning is one of the key challenges in achieving the largest available rate regions for many multiuser channels. This paper explores the use of low-density parity-check (LDPC) like codes for a particular kind of deterministic broadcast channel called the Blackwell channel and illustrates that random linear codes can be used to construct practical binning schemes...
We present a method to combine error-correction coding and spectral-efficient modulation for transmission over the additive white Gaussian noise (AWGN) channel. The code employs signal shaping which can provide a so-called shaping gain. The code belongs to the family of sparse graph codes for which efficient decoding algorithms can be derived. Simulation results show that the performance of the code...
Current-mode circuits are presented for implementing analog min-sum (MS) iterative decoders. Proposed circuits are devised based on current mirrors. Therefore, in any fabrication technology that accurate current mirrors can be designed, analog MS decoders can be implemented. The functionality of the proposed modules was verified by implementing an analog MS decoder for a (32,8,10) regular LDPC code...
In this paper we propose an information theoretic framework for studying coding and throughput optimization for multi-layered packet transmission systems. Our approach assumes that the system is divided into two separate layers: One code word forms a packet at the physical layer and the code at the network layer spans over these packets. At the receiver, the network layer assumes that the decoded...
Binary primitive triple-error-correcting BCH codes have been the object of intensive studies for several decades. In the 1970s their covering radius were determined in a series of papers to be 5. However, one problem for these codes that has been open up to now is to find their coset distribution. In this paper we solve this problem and thus determine the number of cosets of each weight in binary...
Error-correcting signature code is proposed. An n/2-decodable signature code with code length n - 1 and cardinality n - 1 is developed from an Hadamard matrix of order n. The code is used to identify users through the multiple-access adder channel, even in the presence of channel noise
The only known construction of error-correcting codes in rank metric was proposed in 1985. These were codes with fast decoding algorithm. We present a new construction of rank codes, which defines new codes and includes known codes. This is a generalization of E.M. Gabidulin, 1985. Though the new codes seem to be very similar to subcodes of known rank codes, we argue that these are different codes...
Spotty byte error control codes are very effective for correcting/ detecting errors in semiconductor memory systems using recent high-density RAM chips with wide I/O data, e.g., 8, 16, or 32 bits I/O data. A spotty byte error is defined as random t-bit errors within a byte of length b-bit, where t les b, and also m-spotty byte errors as multiple spotty byte errors in a byte. In semiconductor memory...
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