A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N ≥ 2) nonoverlapping components with the same size. Then, these components are combined together to form the parity-check matrix of a longer code, according to a given N×N Latin square....

In this paper we propose the construction of Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes using a Quasi-Cyclic (QC) algorithm. The QC based approach is optimized to obtain memory efficiency in storing the parity-check matrix in the decoders. A hardware model of the parity-check storage units has been designed for Xilinx FPGA to compare the logic and memory requirements for various...

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finitelength analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding minimum pseudoweight equals its minimum Hamming distance. By using the value assignment of Chen and Kløve we present new results on the pseudo...

We study a modification method for constructing lowdensity parity-check (LDPC) codes for solid burst erasures. Our proposed modification method is based on a column permutation technique for a parity-check matrix of the original LDPC codes. It can change the burst erasure correction capabilities without degradation in the performance over random erasure channels. We show by simulation results t...

Performance of low-density parity-check (LDPC) codes with maximum likelihood decoding (MLD) for solid burst erasures is discussed. The columns of the paritycheck matrix of LDPC codes are permuted to increase the distance between elements (DBEs) which are defined as a number of symbol positions between elements 1 at each row of the parity-check matrix. The column permutation method can change th...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

Abstract. As a generalization of cyclic codes of length p over Fpa , we study n-dimensional cyclic codes of length p1 ×· · ·×pn over Fpa generated by a single “monomial”. Namely, we study multi-variable cyclic codes of the form 〈(x1 − 1) i1 · · · (xn − 1) n〉 ⊂ Fq [x1,...,xn] 〈x ps1 1 −1,...,x psn n −1〉 . We call such codes monomial-like codes. We show that these codes arise from the product of ...

Let C be a Z2Z4-additive code of length n > 3. We prove that if the binary Gray image of C, C = Φ(C), is a 1-perfect nonlinear code, then C cannot be a Z2Z4-cyclic code except for one case of length n = 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z2Z4-additive 1-perfect code gives an extended 1-perfect code. We also prove that an...

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2m ), where m > 0 cyclic low-density paritycheck codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to in...