The 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 computation of the minimum distance of the LDPC codes. The EI method is successfully applied to sub-...

42 JANUARY 2004 1053-5888/04/$20.00©2004IEEE e consider the problem of designing unoriented bipartite graphs with large girth. These graphs are the Tanner graphs associated with the parity-check matrix H of low density parity-check (LDPC) codes or Gallager codes. Larger girth improves the computational and bit error rate (BER) performance of these codes. The article overviews several existing m...

Using group theory, we analyze cycle GF(2) codes that use Cayley graphs as their associated graphs. First, we show that through row and column permutations the parity check matrix H can be put in a concatenation form of row-permuted block-diagonal matrices. Encoding utilizing this form can be performed in linear time and in parallel. Second, we derive a rule to determine the nonzero entries of ...

For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even Min-Sum (MS) variants computationally expensive. To alleviate it, we present a class of hybrid schemes by concatenating a parallel bit flipping (BF) variant with an Min-Sum (MS) variant. In most SNR region of interest, without compromising performance or conv...

Both constant and variable Forward Error Correcting (FEC) coding is provided by the DVB-S2 system. Variable FEC can be used for different levels of error protection according to different applications. DVB-S2 system [15] is intended to provide interactive services, which are mainly point-to-point or point-to multipoint, where variable FEC may be combined with the use of return channels, to achi...

Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

A code is said to be a Locally Recoverable Code (LRC) with availability if every coordinate can be recovered from multiple disjoint sets of other coordinates called recovering sets. The vector of sizes of recovering sets of a coordinate is called its recovery profile. In this work, we consider LRCs with availability under two different settings: (1) irregular recovery: non-constant recovery pro...

We study sets of lines of AG(n, q) and PG(n, q) with the property that no three lines form a triangle. As a result the associated point-line incidence graph contains no 6-cycles and necessarily has girth at least 8. One can then use the associated incidence matrices to form binary linear codes which can be considered as LDPC codes. The relatively high girth allows for efficient implementation o...

We report a result of perturbation analysis on decoding error of the belief propagation decoder for Gallager codes. The analysis is based on information geometry, and it shows that the principal term of decoding error at equilibrium comes from the m-embedding curvature of the log-linear submanifold spanned by the estimated pseudoposteriors, one for the full marginal, and K for partial posterior...

A simple design method using dynamic programming is proposed for good LDPC codes with relatively low code-rate. By applying a dynamic programming optimization to the construction of the portion fixed for easy encoding in the parity-check matrix, we can maximize the girth associated with columns contained in that portion of the matrix. Simulation results show performance improvement over the con...