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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)
— 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)
We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated by its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0 ≤ ρ ≤ 1). Problems of this type can be solved by minimizing a cost function with respect to the L p-norm ||x|| p = lim(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)
— In this paper, an idea of the cutting plane method is employed to improve the fractional distance of a given binary parity check matrix. The fractional distance is the minimum weight (with respect to 1-distance) of vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity check matrix and it plays a key(More)