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— A novel class of bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are called gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. Based on gradient descent formulation, the proposed algorithms are naturally derived from a(More)
In this paper, the average coset weight distribution (ACWD) of struc-tured ensembles of LDPC (Low-density Parity-Check) matrix, which is called combined ensembles, is discussed. A combined ensemble is composed of a set of simpler ensembles such as a regular bipartite ensemble. Two classes of combined ensembles have prime importance; a stacked ensemble and a(More)
— In this paper, the minimum span of stopping sets of regular LDPC codes are defined and analyzed. The minimum span of an LDPC code is closely related to immunity to burst erasures when an LDPC code is decoded with belief propagation (BP) for erasure channels. The minimum span of stopping sets is the smallest span of a non-empty stopping set. If a single(More)
— A set of linearly constrained permutation matrices are proposed for constructing permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a soft-decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. An efficient LP solver based on simplex methods or interior(More)
In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with linearly dependent rows. These linearly dependent rows (redundant rows) significantly reduce the number of stopping sets(More)
In this paper, we will present an analysis on the fault erasure BP decoders based on the density evolution. In the fault BP decoder, messages exchanged in a BP process are stochastically corrupted due to unreliable logic gates and flip-flops; i.e., we assume circuit components with transient faults. We derived a set of the density evolution equations for(More)
—We use the replica method of statistical mechanics to examine a typical performance of correctly reconstructing N-dimensional sparse vector x = (xi) from its linear transformation y = F x of P dimensions on the basis of minimization of the Lp-norm ||x||p = limǫ→+0 N i=1 |xi| p+ǫ. We characterize the reconstruction performance by the critical relation of(More)