In this paper, we propose to leverage the simple and explicit parity checks inherent in low-density parity-check (LDPC) codes to realize dominant error events detection without code rate penalty. This is enabled by enforcing a very weak constraint on LDPC code parity check matrix structure. Such a constraint can be readily satisfied by most structured LDPC codes ever studied in the open literat...

In [4], starting from an automorphism θ of a finite field Fq and a skew polynomial ring R = Fq[X; θ], module θ-codes are defined as left R-submodules of R/Rf where f ∈ R. In [4] it is conjectured that an Euclidean self-dual module θ-code is a θ-constacyclic code and a proof is given in the special case when the order of θ divides the length of the code. In this paper we prove that this conjectu...

An important code of length n is obtained by taking centralizer of a square matrix over a finite field Fq. Twisted centralizer codes, twisted by an element a ∈ Fq, are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer...

The AWGNC, BSC, and max-fractional pseudocodeword redundancy ρ(C) of a code C is defined as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of C. This paper provides new results on the AWGNC, BSC, and max-fractional pseudocodeword redundancies of codes. The pseudocodeword redundancies for all codes of...

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.

Abstract—In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the correspondence between code subtrellises in the tailbiting code-trellis and error subtrellises in the tailbiting error-trellis. Also, we present a construction ...

In this paper, we consider a class of column-weight two quasi-cyclic low-density parity check 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 convolutio...

Low Density Parity Check (LDPC) codes are specified by the parity check matrix H. Smaller girths in the Tanner graphs of LDPC codes prevent the sum-product algorithm from converging, i.e., short cycles in H-matrix degrade the performance of LDPC decoder. In this paper, we present an algorithm for constructing LDPC codes without short cycles. The H-matrix must be sufficiently sparse to increase ...

The Tanner graph associated with an extended parity-check (EPC) matrix of a cyclic code is shown to be useful in effectively implementing soft decision iterativedecoding procedures based on belief propagation. Decoding with an EPC matrix has the advantage that is universal, in the sense that it does not depend on the specific family of cyclic codes being used. It is shown that there is no need ...