6,609 research outputs found
Weighted nonbinary repeat-accumulate codes
No full textRepeat-accumulate (RA) codes are random-like codes having remarkably good performance over an additive white Gaussian noise (AWGN) channel, like turbo and low-density parity-check (LDPC) codes. In this correspondence, we introduce an ensemble of random codes called "weighted nonbinary repeat-accumulate (WNRA) codes" whose encoder consists of a nonbinary repeater, a weighter, a pseudorandom symbol interleaver, and an accumulator over a finite field GF (q). They can be decoded in a simple way by applying the sum-product algorithm to their factor graphs over GF (q). Simulation results show that WNRA codes with proper weighting values over GF (4) or GF (8) are superior to binary RA codes on AWGN channels.X117sciescopu
Space-time codes with full antenna, diversity using weighted nonbinary repeat-accumulate codes
No full textLike turbo codes, repeat-accumulate codes have remarkably good performance when r greater than or equal to 3, where r is the number of repetition times. In this letter, we present space-time codes with full antenna diversity using "weighted" nonbinary repeat-accumulate codes. Compared with the space-time turbo codes in Liu et al. and So et al., the main advantage of this new scheme is to construct space-time codes with full diversity for any m less than or equal to r and any length of frame without searching for interleavers, where m is the number of transmit antennas. These space-time codes have rate m/r and so, have full rate when m = r. Furthermore, they have an efficient decoding based on the message passing algorithm.X113sciescopu
A combining method of quasi-cyclic LDPC codes by the chinese remainder theorem
No full textIn this paper we propose a method of constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of large length by combining QC-LDPC codes of small length as their component codes, via the Chinese Remainder Theorem. The girth of the QC-LDPC codes obtained by the proposed method is always larger than or equal to that of each component code. By applying the method to array codes, we present a family of high-rate regular QC-LDPC codes with no 4-cycles. Simulation results show that they have almost the same performance as random regular LDPC codes.X1132sciescopu
Balanced shrinking generators
No full textThe shrinking generator is a keystream generator which is good for stream ciphers in wireless mobile communications, because it has simple structure and generates a keystream faster than other generators. Nevertheless, it has a serious disadvantage that its keystream is not balanced if they use primitive polynomials as their feedback polynomials. In this paper, we present a method to construct balanced shrinking generators by modifying the structure of the shrinking generator and analyze their cryptographical properties including period, balancedness, linear complexity, and probability distribution. Experimental results show that the keystreams of these generators have larger linear complexity than that of the shrinking generator, provided that-the sizes of LFSRs are fixed.X11sciescopu
ON THE TRUE MINIMUM DISTANCE OF HERMITIAN CODES
No full textA class of geometric Goppa codes based on Hermitian curves was introduced by Stichtenoth [3]. These codes are parametrized by an integer m that governs both dimension and minimum distance of the code. In that paper, the exact minimum distance is given in the range that 0 less-than-or-equal-to m less-than-or-equal-to q3 - q2 or m = 0 (mod q) with m < q3. In this paper we determine the exact minimum distance of these codes for any m with m greater-than-or-equal-to q3 - q2. Taken together the two results give the exact minimum distance of Hermitian codes for all values of the parameter m.X1149sci
ON THE GENERALIZED HAMMING WEIGHTS OF PRODUCT CODES
No full textThe rth generalized Hamming weight of a linear code is the minimum support size of any r-dimensional subcode. It has been found useful in the studies of cryptography and trellis coding. We derive several results on expressing the generalized Hamming weights of a product code in terms of those of its component codes. We also formulate a general conjecture.X1170sciescopu
On the minimum distance of array codes as LDPC codes
No full textFor a prime q and an integer j less than or equal to q, the code C(q, j) is a class of low-density parity-check (LDPC) codes from array codes which has a nice algebraic structure. In this correspondence, we investigate the minimum distance d(q, j) of the code in an algebraic way. We first prove that the code is invariant under a doubly transitive group of "affine" permutations. Then, we show that d(5, 4) = 8, d(7, 4) = 8, and d(q, 4) greater than or equal to 10 for any prime q > 7. In addition, we also analyze the codewords of weight 6 in the case of j 3 and the codewords of weight 8 in C(5, 4) and C(7, 4).X1155sciescopu
Autocorrelation properties of resilient functions and three-valued almost-optimal functions satisfying PC(p)
No full textThe absolute indicator and the sum-of-squares indicator are used as a measure of global avalanche criterion (GAC) to evaluate the propagation characteristics of Boolean functions in a global manner. In this paper, we derive a new lower bound on the absolute indicator of resilient functions and three-valued almost-optimal functions satisfying the propagation criterion of degree p (or PC(p)).X11sciescopu
ON THE WEIGHT HIERARCHY OF GOETHALS CODES OVER Z(4)
No full textThe rth generalized Hamming weight d(r)(m,j) of the Goethals code g(m)(j) of length 2(m) over Z(4) is considered in this correspondence. Zn the case that m greater than or equal to 3 is an odd integer, d(r)(m,j) is exactly determined for r = 0.51 1, 1.5, 2, 2.5, and 3.0. For a composite m, we give an upper bound d(r)(m,j) using the lifting technique.X115sciescopu
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