For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of la...

Low-density parity-check (LDPC) code, have become most popular, promising near-optimal error correction code (ECC). Trade off between the performance and complexity of LDPC decoders is of paramount interest to communication engineers and researchers. The VLSI implementation of LDPC decoder is a big challenge. VLSI implementations has many difficulties to achieve as lower error floors, reduced i...

We design multilevel coding (MLC) with a semi bitinterleaved coded modulation (BICM) scheme based on low density parity check (LDPC) codes. Different from traditional designs, we joint the MLC and BICM together by using the Gray mapping, which is suitable to transmit the data over several equivalent channels with different code rates. To perform well at signal-to-noise ratio (SNR) very close to...

A turbo block code (TBC) technique for improving the performance of a multi-carrier code division multiple access (MC-CDMA) system in terms of bit error rate (BER) is proposed in this paper. The objective of this work is to develop a coding scheme that generates low BER code-words. By implementing a time domain TBC, designed using powerful low density parity check (LDPC) code, the BER performan...

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...

A numerical method has recently been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we extend this technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimized irregular LDPC codes ...

Low-density parity-check (LDPC) coded optical orthogonal frequency division multiplexing (OFDM) is shown to significantly outperform LDPC coded on-off keying (OOK) over the atmospheric turbulence channel in terms of both coding gain and spectral efficiency. In the regime of strong turbulence at a bit-error rate of 10(-5), the coding gain improvement of the LDPC coded single-side band unclipped-...

The design of LDPC codes based on a class of expander graphs is investigated. Graph products, such as the zig-zag product [9], of smaller expander graphs have been shown to yield larger expanders. LDPC codes are designed based on the zigzag product graph of two component Cayley graphs. The results for specific cases simulated reveal that the resulting LDPC codes compare well with other random L...

Low-Density Parity-Check (LDPC) code is one kind of prominent error correcting codes (ECC) being considered in next generation industry standards. The decoder implementation complexity has been the bottleneck of its application. This paper presents a new kind of high-throughput and memory efficient LDPC decoder architecture. In general, more than fifty percent of memory can be saved over conven...

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-...