This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes LDPC codes are constructed based on lines and points Euclidean projective geometries over finite fields. Codes these four have good minimum distances their Tanner (1981) graphs girth 6. Finite-geometry can be decoded in various ways, ranging from low high decoding complexity reasonably very performance. They perform well with iterative decoding. Furthermore, they put either...

Error detection incorporated with automatic-repeatrequest (ARQ) is widely used for error control in data communications systems. This method of simple and provides high system reliability. If a properly chosen code detection, virtually error-free transmission can be attained. paper surveys various types ARQ hybrid schemes, using linear block codes.

Quasi-cyclic (QC) low-density parity-check (LDPC) codes form an important subclass of LDPC codes. These have encoding advantage over other types This paper addresses the issue efficient QC-LDPC Two methods are presented to find generator matrices in systematic-circulant (SC) from their matrices, given circulant form. Based on SC matrix a code, various circuits using simple shift registers devised. It is shown that complexity code linearly proportional number parity bits for serial encoding,...

This paper presents two simple and effective criteria for stopping the iteration process in turbo decoding with a negligible degradation of error performance. Both are devised based on cross-entropy (CE) concept. They as efficient CE criterion, but require much less simpler computations.

This letter presents two classes of quasi-cyclic low-density parity-check codes that perform close to the Shannon limit.

The hybrid ARQ scheme with parity retransmission for error control, recently proposed by Lin and Yu [1], [2], is quite robust. This provides both high system throughput reliability. In this paper, a modified Lin-Yu presented. slightly better performance than the original scheme; however, it more flexible in utilizing error-correction power of code. can be incorporated rate 1/2 convolutional code using Viterbi decoding. Furthermore, pure selectiverepeat degenerated case selective mode....

This letter presents an algebraic method for constructing regular low-density parity-check (LDPC) codes based on Reed-Solomon with two information symbols. The construction results in a class of LDPC Gallager's original form. Codes this are free cycles length 4 their Tanner graphs and have good minimum distances. They perform well iterative decoding.

New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction result a class multistep majority-logic decodable and three classes low-density parity-check (LDPC) codes. Decoding the codes, that perform well with iterative decoding spite having many cycles length 4 their Tanner graphs, Most constructed can be either put cyclic or quasi-cyclic form hence encoding implemented linear shift registers.

Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth at least six good minimum distances are presented. These two based on geometry decomposition a masking technique. Numerical results show that the constructed by these perform close to Shannon limit as well random-like LDPC codes. Furthermore, they have low error floors their iterative decoding converges very fast. The technique greatly simplifies designed...

This paper presents a simple and very flexible method for constructing quasi-cyclic (QC) low density paritycheck (LDPC) codes based on finite fields. The code construction is two arbitrary subsets of elements from given field. Some well known constructions QC-LDPC fields combinatorial designs are special cases the proposed construction. in conjunction with technique, as masking, results whose Tanner graphs have girth 8 or larger. Experimental show that constructed using perform error-floors....

A class of cyclic codes is introduced by a polynomial approach that an extension the Mattson-Solomon method and Muller method. This contains several important classes as subclasses, namely, BCH codes, Reed-Solomon generalized primitive Reed-Muller finite geometry codes. Certain fundamental properties this are derived. Some subclasses shown to be majority-logic decodable.

This survey paper provides fundamentals in the design of LDPC codes. To provide a target for code designer, we first summarize EXIT chart technique determining(near-)optimal degree distributions ensembles. We also demonstrate simplicity representing codes by protographs and how this naturally leads to quasi-cyclic The is then extended special case protograph-based Next, present several approaches which incorporate one or more accumulators, including accumulatorbased second half surveys...

It is shown that after a proper simple modification, the soft-output Viterbi algorithm (SOVA) proposed by Hagenauer and Hoeher (1989) becomes equivalent to max-log-maximum posteriori (MAP) decoding algorithm. Consequently, this modified SOVA allows implement max-log-MAP simply adjusting conventional Hence, it provides an attractive solution achieve low-complexity near-optimum soft-input decoding.

It was shown earlier that for a punctured Reed-Muller (RM) code or primitive BCH code, which contains RM of the same minimum distance as large subcode, state complexity minimal trellis diagrams is much greater than an equivalent obtained by proper permutation bit positions. The problem finding positions given minimizes its diagram related to generalized Hamming weight hierarchy and it that, codes, standard binary order optimum at every position with respect using theorem due V.K. Wei (1991)....

This correspondence presents a method for constructing structured regular low-density parity-check (LDPC) codes based on special type of combinatoric designs, known as balance incomplete block designs. Codes constructed by this have girths at least 6 and they perform well with iterative decoding. Furthermore, several classes these are quasi-cyclic hence their encoding can be implemented simple feedback shift registers.

Quasi-cyclic LDPC codes are the most promising class of structured due to their ease implementation and excellent performance over noisy channels when decoded with message-passing algorithms as extensive simulation studies have shown. In this paper, an approach for constructing quasi-cyclic based on Latin squares finite fields is presented. By analyzing parity-check matrices these codes, combinatorial expressions ranks dimensions derived. Experimental results show that, iterative decoding...

This paper is concerned with construction and structural analysis of both cyclic quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists three parts. The first part shows that a code given by matrix in circulant form can be decomposed into descendant codes various lengths rates. Some fundamental properties these are developed, including the characterization roots generator polynomial code. second LDPC derived from finite-geometry using results developed paper....

This paper presents two new large classes of QC-LDPC codes, one binary and non-binary. Codes in these are constructed by array dispersions row-distance constrained matrices formed based on additive subgroups finite fields. Experimental results show that codes perform very well over the AWGN channel with iterative decoding belief propagation. a subclass class have minimum distances comparable to geometry LDPC they offer effective tradeoff between error performance complexity when decoded...

This paper presents two low-complexity reliability-based message-passing algorithms for decoding LDPC codes over non-binary finite fields. These require only field and integer operations they provide effective trade-off between error performance complexity compared to the sum product algorithm. They are particularly constructed based on geometries

A matrix-theoretic approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row column permutations is developed. These put a parity-check in the form of an array circulant matrices into diagonal same size over extension field. The amicable to analysis construction low-density since it takes account specific used decoding with iterative message-passing algorithms. Based this approach, dimension dual can be determined. Several algebraic geometric...