Low-density parity-check (LDPC) codes and convolutional Turbo codes are two of the most powerful error correcting codes that are widely used in modern communication systems. In a multi-mode baseband receiver, both LDPC and Turbo decoders may be required. However, the different decoding approaches for LDPC and Turbo codes usually lead to different hardware architectures. In this paper we propose...

Multi-Edge type Low-Density Parity-Check codes (METLDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we dri...

In this paper, we present a construction method of terminated non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an expansion of Felstrom and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary LDPC convolutional codes is also discussed. The proposed ratecompatible code is designed from one single ...

Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct -codes whose T...

Quantum low-density parity check (LDPC) codes such as generalized toric codes with finite rate suggested by Tillich and Zémor offer an alternative route for quantum computation. Here, we study LDPC codes and show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, has a finite error threshold. Based on that, we conclude that quantu...

Hamming code-based LDPC (H-LDPC) block codes are obtained by replacing the single parity-check constituent codes in Gallager’s LDPC codes with Hamming codes. This paper investigates the asymptotic performance of ensembles of random H-LDPC codes, used over the binary symmetric channel and decoded with a low-complexity hard-decision iterative decoding algorithm. It is shown that there exist H-LDP...

If the degree distribution is chosen carefully, the irregular LDPC codes can outperform the regular ones. In this paper, we proposed an LDPC coded BICM scheme in image transmission system to improve both efficiency and reliability. Simulation results show that LDPC codes are good coding schemes over fading channel in image communication with lower system complexity. Simultaneously, irregular co...

In this study, a new method for constructing low-density parity-check (LDPC) codes is presented. This construction is based on permutation matrices which come from a finite abstract group and hence the codes constructed in this manner are called group permutation low-density parity-check (GP-LDPC) codes. A necessary and sufficient condition under which a GP-LDPC code has a cycle, is given and s...

In this paper we investigate the minimum code distance of QC LDPC codes [1], [2], [3]. These codes form an important subclass of LDPC codes [4], [5]. These codes also are a subclass of protograph-based LDPC codes [6]. QC LDPC codes can be easily stored as their parity-check matrices can be easily described. Besides such codes have efficient encoding [7] and decoding [8] algorithms. All of these...

AhtractOrthogonal Frequency Division Multiplexing (OFDM) is a very attractive technique for high-hit-rate data transmission in multipath environments. Many error-correcting codes have been applied to OFDM, convolutional codes, Reed-Solomon codes, Turbo codes, and so on. Recently, low-density parity-check (LDPC) codes have attracted much attention particularly in the tield of coding theory. LDPC...