Low Density Parity Check Codes Codes Research Articles

Gradient projection decoding of LDPC codes and algorithmic variations

The current study proposes decoding algorithms for low density parity check codes (LDPC), which offer competitive performance-complexity trade-offs relative to some of the most efficient existing decoding techniques. Unlike existing low-complexity algorithms, which are essentially reduced complexity variations of the classical belief propagation algorithm, starting point in the developed algorithms is the gradient projections (GP) decoding technique, proposed by Kasparis and Evans (2007). The first part of this paper is concerned with the GP algorithm itself, and specifically with determining bounds on the step-size parameter, over which convergence is guaranteed. Consequently, the GP algorithm is reformulated as a message passing routine on a Tanner graph and this new formulation allows development of new low-complexity decoding routines. Simulation evaluations, performed mainly for geometry-based LDPC constructions, show that the new variations achieve similar performances and complexities per iteration to the state-of-the-art algorithms. However, the developed algorithms offer the implementation advantages that the memory-storage requirement is significantly reduced, and also that the performance and convergence speed can be finely traded-off by tuning the step-size parameter.

A good puncturing scheme for rate compatible low-density parity-check codes

We consider the challenges of finding good puncturing patterns for rate-compatible low-density parity-check code (LDPC) codes over additive white Gaussian noise (AWGN) channels. Puncturing is a scheme to obtain a series of higher rate codes from a lower rate mother code. It is widely used in channel coding but it causes performance is lost compared to non-punctured LDPC codes at the same rate. Previous work, considered the role of survived check nodes in puncturing patterns. Limitations, such as single survived check node assumption and simulation-based verification, were examined. This paper analyzes the performance according to the role of multiple survived check nodes and multiple dead check nodes. Based on these analyses, we propose new algorithm to find a good puncturing pattern for LDPC codes over AWGN channels.

Implementation of a Flexible LDPC Decoder

Low-density parity-check codes (LDPC) are among the most powerful error correcting tools today available. For this reason they became very popular in several applications such as the digital satellite broadcasting system (DVB-S2), wireless local area network (IEEE 802.11n) and metropolitan area network (802.16e). Whereas several code-specific decoders have been proposed in the literature, the implementation of a high performance yet flexible LDPC decoder still is a challenging topic. This work presents a novel formulation of the decoding algorithm that strongly simplifies internal communication requirements and enables the development of decoders supporting generally defined LDPC codes. The resulting architecture is tailored to decode both IEEE 802.11n and IEEE 802.16e LDPC codes, as well as any other code of comparable complexity. The implementation cost deriving from the full flexibility offered by the proposed approach is also evaluated.

Low-Density Parity-Check Lattices: Construction and Decoding Analysis

Low-density parity-check codes (LDPC) can have an impressive performance under iterative decoding algorithms. In this paper we introduce a method to construct high coding gain lattices with low decoding complexity based on LDPC codes. To construct such lattices we apply Construction D', due to Bos, Conway, and Sloane, to a set of parity checks defining a family of nested LDPC codes. For the decoding algorithm, we generalize the application of max-sum algorithm to the Tanner graph of lattices. Bounds on the decoding complexity are derived and our analysis shows that using LDPC codes results in low decoding complexity for the proposed lattices. The progressive edge growth (PEG) algorithm is then extended to construct a class of nested regular LDPC codes which are in turn used to generate low density parity check lattices. Using this approach, a class of two-level lattices is constructed. The performance of this class improves when the dimension increases and is within 3 dB of the Shannon limit for error probabilities of about 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> . This is while the decoding complexity is still quite manageable even for dimensions of a few thousands

Construction of well-structured quasi-cyclic low-density parity check codes

Two classes of well-structured binary low-density parity check codes (LDPC) are described. The first class is based on a branch of combinatorial mathematics, known as the balanced incomplete block design (BIBD). Construction of three types of codes derived from BIBD designs is illustrated in addition to a family of LDPC codes constructed by decomposition of incidence matrices of the proposed BIBD designs. The decomposition technique reduces the density of the parity check matrix and hence reduces the number of short cycles, which generally lead to better performing LDPC codes. The second class of well-structured LDPC codes, Vandermonde or array LDPC codes, are defined by a small number of parameters and cover a large set of code lengths and rates with different column weights. The presented LDPC codes are quasi-cyclic with no cycles of length four; hence simple encoding while maintaining good performance is achieved. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs. It is shown that well-structured LDPC codes perform very similar to the known random LDPC codes.

Irregular low-density parity-check codes: construction and performance on perpendicular magnetic recording channels

In this paper, we propose an algorithm to design an irregular low-density parity-check code (LDPC), with a given degree distribution pair, from a random regular LDPC code. The proposed algorithm splits columns and rows of the regular code in order to achieve the desired degree distribution pair. Kou, Lin, and Fossorier have used column splitting to increase code rate. However, we use the splitting technique to achieve a given degree distribution pair in the bipartite graph of the resultant irregular code. The bit-error rate (BER) performance of high-rate irregular LDPC codes, constructed using this algorithm, were simulated on equalized perpendicular magnetic recording channels. In addition, this paper compares the performance of these irregular codes with that of random regular LDPC codes.

Low-density parity check codes for long-haul optical communication systems

Forward error correction (FEC) scheme based on low density parity check codes (LDPC) codes is presented in this paper. We show that LDPC codes provide a significant system performance enhancement with respect to the state-of-the-art FEC schemes employed in optical communication systems.