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ICTACT Journal on Communication Technology

CONSTRUCTION OF REGULAR LDPC LIKE CODES BASED ON FULL RANK CODES AND THEIR ITERATIVE DECODING USING A PARITY CHECK TREE

Prashantha Kumar H, Udupi Sripati, Rajesh Shetty K

Published Sep 1, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.21917/ijct.2011.0056

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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.
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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 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
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
This paper proposes a novel code-construction method for constructing (3, k) regular low density parity check (LDPC) codes. Other methods of designing regular LDPC codes suffer from rank-deficiency of H and high encoding complexity. The basic design of the proposed code-construction utilizes deterministic base matrices of information part and parity part in three stages of code-construction to achieve no rank-deficiency of H, no girth of 4-cycles, non-singular parity part (Hpar) and low encoding complexity. It is shown that the proposed (3, k) regular LDPC codes perform better in high code rate application. The result of (3, 42) regular code performs 0.97 dB from Shannon limit at BER 10-6when the value of code rate R = 0.928, code length N = 14364 and encoding complexity of the order of O(1.0225 N).