2,689 research outputs found
Decoding of Block Codes by using Genetic Algorithms and Permutations Set
Recently Genetic algorithms are successfully used for decoding some classes of error correcting codes. For decoding a linear block code C, these genetic algorithms computes a permutation p of the code generator matrix depending of the received word. Our main contribution in this paper is to choose the permutation p from the automorphism group of C. This choice allows reducing the complexity of re-encoding in the decoding steps when C is cyclic and also to generalize the proposed genetic decoding algorithm for binary nonlinear block codes like the Kerdock codes. In this paper, an efficient stop criterion is proposed and it reduces considerably the decoding complexity of our algorithm. The simulation results of the proposed decoder, over the AWGN channel, show that it reaches the error correcting performances of its competitors. The study of the complexity shows that the proposed decoder is less complex than its competitors that are based also on genetic algorithms
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as , where is the number of source symbols.Comment: 6 pages, ISITA1
Enhanced Recursive Reed-Muller Erasure Decoding
Recent work have shown that Reed-Muller (RM) codes achieve the erasure
channel capacity. However, this performance is obtained with maximum-likelihood
decoding which can be costly for practical applications. In this paper, we
propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure
channel based on Plotkin construction. We present several improvements over the
generic decoding. They allow, for a light cost, to compete with
maximum-likelihood decoding performance, especially on high-rate codes, while
significantly outperforming it in terms of speed
Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers
We transfer the concept of linear feed-back shift registers to quantum
circuits. It is shown how to use these quantum linear shift registers for
encoding and decoding cyclic quantum error-correcting codes.Comment: 18 pages, 15 figures, submitted to Proc. R. Soc.
Cyclic Low-Density MDS Array Codes
We construct two infinite families of low density MDS array codes which are also cyclic. One of these families includes the first such sub-family with redundancy parameter r > 2. The two constructions have different algebraic formulations, though they both have the same indirect structure. First MDS codes that are not cyclic are constructed and then by applying a certain mapping to their parity check matrices, non-equivalent cyclic codes with the same distance and density properties are obtained. Using the same proof techniques, a third infinite family of quasi-cyclic codes can be constructed
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