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Concatenated error correction code
About: Concatenated error correction code is a research topic. Over the lifetime, 14582 publications have been published within this topic receiving 377390 citations.
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01 Jan 1963TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
11,592 citations
Book•
01 Jan 1977
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Abstract: Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, Designs and Perfect Codes. Cyclic Codes. Cyclic Codes: Idempotents and Mattson-Solomon Polynomials. BCH Codes. Reed-Solomon and Justesen Codes. MDS Codes. Alternant, Goppa and Other Generalized BCH Codes. Reed-Muller Codes. First-Order Reed-Muller Codes. Second-Order Reed-Muller, Kerdock and Preparata Codes. Quadratic-Residue Codes. Bounds on the Size of a Code. Methods for Combining Codes. Self-dual Codes and Invariant Theory. The Golay Codes. Association Schemes. Appendix A. Tables of the Best Codes Known. Appendix B. Finite Geometries. Bibliography. Index.
10,083 citations
TL;DR: In this paper, the authors consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas and derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective.
Abstract: We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders.
7,105 citations
TL;DR: The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.
Abstract: The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above R_{0} , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.
6,804 citations
Journal Article•
6,667 citations