nordstrom-robinson (NR) code is an optimum nonlinear code of length 16, which is employed in Digital Terrestrial / Television Multimedia Broadcasting (DTMB) standard of China. In this paper a new soft-in-soft-out (SIS...
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(纸本)9780769532783
nordstrom-robinson (NR) code is an optimum nonlinear code of length 16, which is employed in Digital Terrestrial / Television Multimedia Broadcasting (DTMB) standard of China. In this paper a new soft-in-soft-out (SISO) decoder for the NR code is presented. The decoding process is carried out in two steps. Firstly, an algorithm is performed to find out the most valuable codewords (MVC) set to reduce calculation complexity. Then, approximate soft information is computed based on the MVC set. Theoretical analysis and simulation results both show that the performance of the decoder is very close to ideal algorithm.
We present two new binary codes: a (25, 384, 9) code and a (49, 393216, 13) code. These codes are better than the currently known binary codes with the same length and minimum distance.
We present two new binary codes: a (25, 384, 9) code and a (49, 393216, 13) code. These codes are better than the currently known binary codes with the same length and minimum distance.
The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's, Recently, there has been an increased interest in the study of...
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The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's, Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the nordstrom-robinson code is the image under the Gray mapping of an algebraic geometric code over Z/4Z.
We show that the nordstrom-robinson code may he represented as the union of binary images of two isomorphic linear (4,2,3) codes over GF(4). Certain symmetries of the unique quaternary (4, 2, 3) quadracode are discuss...
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We show that the nordstrom-robinson code may he represented as the union of binary images of two isomorphic linear (4,2,3) codes over GF(4). Certain symmetries of the unique quaternary (4, 2, 3) quadracode are discussed. It is shown how the properties of the nordstrom-robinson code itself, such as weight distribution, distance invariance, and the well-known representation as the union of eight cosets of the (16,5,8) Reed-Muller code, may be easily rederived from these symmetries. In addition we introduce a decoding algorithm for the nordstrom-robinson code which involves projecting its codewords onto the codewores of the quadracode. The algorithm is simple enough to enable hard-decision decoding of the nordstrom-robinson code by hand. Furthermore we present an algorithm for maximum-likelihood soft-decision decoding of the nordstrom-robinson code based on its representation over GF(4). The complexity of the proposed algorithm is at most 205 real operations. This is, to the best of our knowledge, less than the complexity of any existing decoder, and twice as efficient as the fast maximum-likelihood decoder of Adoul. We also investigate several related topics, such as bounded-distance decoding, sphere-packings, and the (20, 2048, 6) code.
Conway and Sloane have developed an efficient approach to the maximum-likelihood decoding of a linear block code based on the partitioning of the code into a subcode and its cosets. This procedure works for certain no...
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Conway and Sloane have developed an efficient approach to the maximum-likelihood decoding of a linear block code based on the partitioning of the code into a subcode and its cosets. This procedure works for certain nonlinear codes as well, and we apply it in this paper to the development of several decoding algorithms for the extended nordstrom-robinson code used in conjunction with both BPSK and QPSK modulations. The small operation counts and the highly regular structures of many of these algorithms make them particularly well-suited to VLSI implementation. We describe one such implementation in this paper.
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