152 research outputs found
Permutation Fixed Points With Application to Estimation of Minimum Distance of Turbo Codes
No full textIn this paper we present a systematic technique for obtaining all the input sequences that are mapped by a given permutation either to themselves or to shifted versions of themselves (generically called permutation fixed points). Such sequences or their subsets, represent the primary candidates for examination in connection with obtaining estimates of the minimum distance of parallel concatenated codes, specially for interleaver lengths for which the determination of the actual minimum distance may be very difficult. Subsequently, we present a new class of permutations that nearly achieve the lower bound on the number of possible fixed points associated with a given permutation of prime length . Preliminary experimental evidence suggests that certain permutations of this class lead to turbo codes with large minimum distances for short interleaver lengths
Generalized fixed points of permutations with application to estimation of minimum distance of turbo codes
No full textIn this paper we present a systematic technique for obtaining all the input sequences that are mapped by a given permutation either to themselves or to shifted versions of themselves (generically called permutation fixed points). Subsequently, we present a new class of permutations that nearly achieve the lowerbound on the number of possible fixed points associated with a given permutation of prime length p
An Algorithm for the Estimation of the Minimum Distance of LDPC Codes
No full textThe evaluation of the minimum distance of Low- Density Parity-Check (LDPC) codes remains an open problem due to the rather large dimension of the parity check matrix H associated with any practical code. In this article, we propose an effective modification of the Error Impulse (EI) technique for estimation of the minimum distance of the LDPCs. The EI method is successfully applied to sub-optimum decoding algorithms such as the iterative MAP decoding algorithm for Turbo Codes. We present novel modifications and extensions of this method to the suboptimum iterative sum-product algorithm for LDPCs. Simulation results validate the functionality of the proposed technique. Simulations focus on a particular class of LDPC codes, but our approach is general and applies to any LDPC code
Optimized Prunable Single Cycle Interleavers for Turbo Codes
No full textThis paper is aimed at the problem of designing optimized interleavers for parallel concatenated convolutional codes (PCCC) that satisfy several requirements simultaneously: 1) designing interleavers tailored to the constituent codes of the PCCC; 2) improving the distance spectra of the resulting turbo codes which dominate their asymptotic performance; 3) constructing optimized interleavers recursively so that they are implicitly prunable; and 4) completely avoiding short permutation cycles in order to reduce the risk of having strong correlations between the extrinsic information during iterative decoding. To this end, we present two theorems that lead to a modification of a previously developed iterative interleaver growth algorithm (IGA) that can be used to design optimized variable-length interleavers, whereby at every length the optimized permutation implemented by the interleaver is a single-cycle permutation. Two more modifications of the IGA are presented to improve the performance of the optimized interleavers at a reduced complexity. The optimization is achieved via constrained minimization of a cost function closely related to the asymptotic bit-error rate or frame-error rate of the code
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