A new algorithm to construct good low-density parity-check (LDPC) codes with large stopping sets is presented. Since the minimum stopping set characterizes an LDPC code, searching for stopping sets in LDPC codes is an important issue. Large minimum stopping sets avoid the LDPC code to get trapped in cycles specially on the binary erasure channel. Dealing with stopping sets is not an easy task s...

The LDPC codes are codes that approach optimal decoding performances, with an acceptable decoding computational cost ([1, 2, 3]). In this paper we present a class of quasi-cyclic LDPC codes and we show that we are able to guarantee some relevant properties of the codes. Experimentally, their decoding performance is comparable with the performance obtained by random LDPC codes. Traditionally, co...

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding threshold...

We show the great potential of nonbinary LDPC convolutional codes (NB-LDPC-CC) with low-latency windowed decoding. It is experimentally demonstrated that NB-LDPC-CC can offer a performance improvement of up to 5 dB compared with binary coding.

In this paper, we propose a novel method for constructing quasi-cyclic low-density parity check (QC-LDPC) codes based row division method which can guarantee a concentrated node degree distribution with large girth. The main advantage is that large girth QC-LDPC codes can be easily constructed with a variety of block lengths and rates. Simulation results show that the proposed codes perform sig...

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding threshold...

The most powerful channel coding schemes, namely those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper presents a 2048-bit, rate-1/2 soft decision decoder for a new class of codes known as Turbo Gallager Codes. These...

Abstract: Two different ways of obtaining generalized low-density parity-check codes are considered. Lower bounds on the minimum distance, stopping distance, and pseudodistance are derived for these codes using graph based analysis. These bounds are generalizations of Tanner’s bit-oriented and parity-oriented bound for simple LDPC codes. The new bounds are useful in predicting the performance o...

Abstract. We study a class of quasi-cyclic LDPC codes. We provide both a Gröbner basis approach, which leads to precise conditions on the code dimension, and a graph theoretic prospective, that lets us guarantee high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a significant achievement for algebra...

Low-Density Parity-Check (LDPC) codes have gained lots of popularity due to their capacity achieving/approaching property. This work studies the iterative decoding also known as message-passing algorithms applied to LDPC codes. Belief propagation (BP) algorithm and its approximations, most notably min-sum (MS), are popular iterative decoding algorithms used for LDPC and turbo codes. The thesis ...