Showing papers on "BCH code published in 1977"
Book•
01 Jan 1977TL;DR: In this paper, the authors present a survey of advanced topics for part I and a survey for part II of a survey on the Gaussian channel and the source coding theorem, including linear codes, BCH Goppa codes, and variable-length source coding.
Abstract: 1. Entropy and mutual information 2. Discrete memoryless channels and their capacity-cost functions 3. Discrete memoryless sources and their rate-distortion functions 4. The Gaussian channel and source 5. The source-channel coding theorem 6. Survey of advanced topics for part I 7. Linear codes 8. BCH Goppa, and related codes 9. Convolutional codes 10. Variable-length source coding 11. Survey of advanced topics for part II.
673 citations
TL;DR: It is shown that i) erasures-and-errors decoding of Goppa codes can be done using O(n \log^{2} n) arithmetic operations, ii) long primitive binary Bose-Chaudhuri-Hocquenghem (BCH) codesCan be decoded using O-log n arithmetic Operations, and iii) Justesen's asymptotically good codes can been decoded use O( n^{2}) bit operations.
Abstract: It is shown that i) erasures-and-errors decoding of Goppa codes can be done using O(n \log^{2} n) arithmetic operations, ii) long primitive binary Bose-Chaudhuri-Hocquenghem (BCH) codes can be decoded using O(n \log n) arithmetic operations, and iii) Justesen's asymptotically good codes can be decoded using O(n^{2}) bit operations. These results are based on the application of efficient computational techniques to the decoding algorithms recently discovered by Sugiyama, Kasahara, Hirasawa, and Namekawa.
36 citations
TL;DR: It is shown that the only modification of the Berlekamp algorithm required to decode the class of alternant codes consists of a linear transformation of the syndromes prior to the application of the algorithm.
Abstract: It is shown that the only modification of the Berlekamp algorithm required to decode the class of alternant codes consists of a linear transformation of the syndromes prior to the application of the algorithm. Since alternant codes include all Bose-Chaudhuri-Hocquenghem (BCH) and Goppa codes, the Chien-Choy generalized BCH codes, and the generalized Srivastava codes, all of these can be decoded with no increase in complexity over BCH decoding.
10 citations
15 Dec 1977
TL;DR: In this article, techniques of combinational algebra and computer simulation are combined to determine the number of weight 22 codewords in the (128,64) BCH code which is being studied for use on future deep-space missions.
Abstract: Techniques of combinational algebra and computer simulation are combined to determine the number of weight 22 codewords in the (128,64) BCH code which is being studied for use on future deep-space missions
3 citations
TL;DR: A new random-error-correction code is presented, which corrects two errors and uses a Viterbi decoder, and is decodable with a one-step majority logic.
Abstract: A new random-error-correction code presented here is one of the most efficient two-error-correction codes. The new code can correct 2-bit random errors within twelve (12) consecutive bits while (15,7) BCH code [1] corrects two errors within fifteen (15) bits and Hagelbarger's code [2] corrects two errors within fourteen (14) bits. Although Peterson and Weldon's double-error-correcting (12,6) code [1] and Massey's two-error-correcting convolutional code [3] also correct two errors within twelve (12) bits, both codes propagate errors. The (12,6) Viterbi code [1], [4] corrects two errors and uses a Viterbi decoder, while the new code is decodable with a one-step majority logic. Error propagation in the feedback majority logic decoder is discussed, and it is proved empirically that the new code presented here does not propagate errors.
2 citations