Binary low-density parity-check (LDPC) codes have recently emerged as a promising alternative to turbo codes and have been shown to achieve excellent coding gains in AWGN channels. Non-binary LDPC codes have demonstrated improved performance over binary LDPC codes but their decoding is computationally intensive. Fourier transform decoding can reduce the decoding complexity but has a number of p...

The introduction of turbo codes and the rediscovery of low-density parity-check (LDPC) codes have revolutionized coding theory and practice. Such modern codes offer outstanding coding gain over traditional (e.g., algebraic or convolutional) codes – more than 3 dB in many cases. While good modern codes have been demonstrated for most operational scenarios of interest, no one simple code structur...

Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived – one based on nonprimitive narrow-sense BCH codes and the other directly based on cyclotomic cosets. The constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard itera...

Strong rate-compatible codes is important to achieve high throughput in hybrid automatic repeat request with forward error correction (ARQ/FEC) systems in packet data transmission. This paper focuses on the construction of efficient rate-compatible low density parity check (RC-LDPC) codes over a wide rate range. The conventional approach of puncturing is first studied. Analysis on the code ense...

Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexibl...

A forward-error correction )FEC) scheme based on low-density parity check (LDPC) codes and iterative decoding using belief propagation in code graphs is presented in this paper. We show that LDPC codes provide a significant system performance improvement with respect to the state-of-the-art FEC schemes employed in optical communications systems. We present a class of structured codes based on m...

In this paper the broadband wireless access system, provided by the IEEE 802.16 wireless MAN air interface with its amendment to mobile users (IEEE 802.16e), is being analyzed. We provide performance results for the most important forward error correcting (FEC) schemes intended for IEEE 802.16e – convolutional turbo codes (CTC) and Low Density Parity Check (LDPC) codes.

Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, whi...

Supporting a great diversity of multi-rate H-matrices for multiple communication protocols requires a large amount of non-volatile memory, which may consume a large silicon area or logic elements and constrain the implementation of an overall decoder. Therefore, schemes for memory reduction are necessary to make the paritycheck storage more compact. This study proposes a specific set of quasi-c...