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A REVIEW OF CONSTRUCTION METHODS FOR REGULAR LDPC CODES

Nisha Sarwade

Published Jan 1, 2012• 8 citations
OpenAlex

Abstract

Low-Density parity-check (LDPC) codes are one of the most powerful error correcting codes available today. Their Shannon capacity approaching performance and lower decoding complexity have made them the best choice for many wired and wireless applications. This paper gives an overview about LDPC codes and compares the Gallager’s method, Reed-Solomon based algebraic method and the Progressive edge growth (PEG) combinatorial method for the construction of regular LDPC codes.

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Low-Density parity-check (LDPC) codes are one of the most powerful error correcting codes available today. Their Shannon capacity approaching performance and lower decoding complexity have made them the best choice for many wired and wireless applications. This paper gives an overview about LDPC codes and compares the Gallager’s method, Reed-Solomon based algebraic method and the Progressive edge growth (PEG) combinatorial method for the construction of regular LDPC codes.
Low Density Parity Check (LDPC) codes are one of the most powerful error correction codes available today. Its Shannon capability that closely matches performance and lower decoding complexity has made them the best choice for many wired and wireless applications. This Paper provides an overview of the LDPC codes and compares the Gallager method, the Reed-Solomon-based algebraic method, and the combinatorial Progressive Growth (PEG) method for constructing regular LDPC codes and also Overlapped and Modified overlapped message passing algorithm for Non-Quasi Cyclic(NQC) LDPC codes.
Low density parity check (LDPC) codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical Shannon limit for a memory less channel. LDPC codes are finding increasing use in applications like LTE-Networks, digital television, high density data storage systems, deep space communication systems etc. Several algebraic and combinatorial methods are available for constructing LDPC codes. In this paper we discuss a novel low complexity algebraic method for constructing regular LDPC like codes derived from full rank codes. We demonstrate that by employing these codes over AWGN channels, coding gains in excess of 2dB over un-coded systems can be realized when soft iterative decoding using a parity check tree is employed.
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 10-6. This is while the decoding complexity is still quite manageable even for dimensions of a few thousands
In this paper, we present three construction methods of systematic regular LDPC-CCs based on randomly or algebraically structured sparse matrices. We provide an overview of LDPC-CCs and compares between Gallager’s, Mackay-Neal and Quasi-Cyclic (QC) construction methods, which are a good choice for many wireless applications due to their errors correction efficiency and low decoding complexity. At a rate-1/2, for the same size of the parity matrix to obtain the same encoding and decoding complexity, and using the Bit Flipping (BF) decoding algorithm over Additive White Gaussian Noise (AWGN) channel, we simulated the BER performance of a (3,6) regular LDPC convolutional codes, where the results showed that Gallager’s construction method (random) outperforms Mackay-Neal and QC ones.
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes