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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 simple(More)
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. The main feature of this class of permutation codes, called linear programming (LP)-decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is(More)
In this paper, the average coset weight distribution (ACWD) of structured ensembles of low-density parity-check (LDPC) matrices, which are 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(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)
In the present paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, which is referred to hereinafter as interior point decoding, is designed for linear vector channels. The linear vector channels include several practically important channels, such as inter-symbol(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)
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)
Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and(More)