We investigate algebraic constructions for a class of iteratively encodable low-density parity-check codes suitable for high rate applications. The iterative encoding technique, which is based upon the graphical representation of the code, allows the decoder circuit to be also used for encoding, thus saving circuit area. A method for constructing a (3,6)-regular class of such codes is already k...

This paper presents a new class of q-ary erasure-correcting codes based on Latin and Sudoku squares of order q, and an iterative decoding algorithm similar to the one used for the Low Density Parity Check code. The algorithm works by assigning binary variables to the q-ary values, and by generalizing the definition of parity check operation to represent the constraints that define the Latin and...

Symbol flipping-based hard decision decoding for non-binary low-density parity check (LDPC) codes has attracted much attention due to low decoding complexity even though the error performance of the symbol flipping decoder is inferior to that of the soft decision decoders. Standard symbol flipping decoding involves two steps, selection of the symbol position to be flipped and selection of the f...

In this paper, we propose a normalized a posteriori probability (APP) based algorithm for the decoding of low-density parity check (LDPC) codes. The normalized APP-based algorithm utilizes normalization to improve the accuracy of the soft values delivered by the simplified APP-based algorithm from one iteration to another during the iterative decoding, and can achieve very good tradeoff between...

A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform. A decoding technique for such codes is proposed. Index Terms – finite field Fourier transform, number theoretic transform, eigensequences, linear block codes.

In general, encoding for LDPC codes can be difficult to realize efficiently. This paper presents techniques and architectures for LDPC encoding that are efficient and practical for a particular class of codes. These codes are the irregular partitioned permutation LDPC codes recently introduced by the author at ICC’03, [4]. Since these codes are quasi-cyclic, it is known that a simpler encoding ...