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International Conference on Intelligent and Advanced Systems

(5, k) regular LDPC codes using novel code-construction

Silvia Anggraeni, V Jeoti

Published Jun 1, 2010• 0 citations
Publisher

Abstract

This paper is a continuation of the work in [15] wherein a novel code-construction method was proposed for constructing (3, k) regular LDPC codes. In this paper, the (3, k) construction technique is generalized to construct (5, k) regular code. The basic design of the proposed code-construction utilizes deterministic base matrices for 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. A typical performance of proposed (5, k) regular LDPC codes has been shown.

DOI
10.1109/icias.2010.5716198

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This paper is a continuation of the work in [15] wherein a novel code-construction method was proposed for constructing (3, k) regular LDPC codes. In this paper, the (3, k) construction technique is generalized to construct (5, k) regular code. The basic design of the proposed code-construction utilizes deterministic base matrices for 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. A typical performance of proposed (5, k) regular LDPC codes has been shown.
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).
A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes
Abstract Recent breakthroughs in forward error correction, in the form of low-density parity-check(LDPC) and turbo codes, have seen the promise of near Shannon limit information trans-mission realised. The deterministic construction of good codes, for LDPC codes in par-ticular, is currently the subject of intense interest in the research and development com-munity. This thesis adds to this field, developing methods and supporting theory for thedesign of algebraic LDPC codes using incidence structures from combinatorial designs.The benefits of this approach are guaranteed code properties, parameter flexibility, easeof implementation and reduced encoding complexity.In the first part of this thesis Steiner 2-designs and partial geometries are used toprovide systematic constructions of regular LDPC codes with Tanner graphs free of 4-cyclesandwithdeterministiccodeproperties. Drawingextensivelyfromexistingincidencestructures we present new families of algebraic LDPC codes with benefits over traditionalrandomly constructed regular codes, particularly where small-to-medium length codes areconcerned. We focus in particular on exploring the effect of different design propertieson the code parameters by deriving the rate, minimum distance, girth, and stopping setdistribution of LDPC codes from designs.In the second part of this thesis resolvable designs are employed to create regularLDPC codes free of 4-cycles with the parameter flexibility and decoding performance ofrandomly constructed regular LDPC codes. Employing resolvability greatly extends theclass of LDPC codes that can be algebraically constructed. These codes can offer sig-nificant implementation advantages due to the deterministic structure of their resolutionclasses and in some cases their simple encoding.A shortcoming of LDPC codes is their potentially high encoding complexity, whichis generally quadratic in the code length. Finding computationally efficient encodersis therefore critical for LDPC codes to be considered as serious contenders for futuregenerations of forward error correction devices. As a result the purpose of the last part ofthis thesis is to design codes which have the graph-based properties necessary to performwell with sum-product decoding but which are also cyclic or quasi-cyclic and so can beencoded simply. The main focus is regular codes but we also extend our constructionof quasi-cyclic codes to produce irregular LDPC codes with simple linear-time encodingcircuits.
A new combinatorial technique for constructing girth-6 structured binary regular low-density parity-check (LDPC) codes based on special types of t-designs is given. A very large number of well-known t-designs can be used by this method for code construction. Based on this method, a t-(v,k,λ) design D=(X,B) can be exploited for code construction if it satisfies the following three conditions: 1) |B1 ∩ B2|≤ t for any two blocks B1,B2∈ B and B1≠ B2; 2) λ>1; and 3) k>t. Though the technique works for any t-design satisfying these conditions, we focus only on the utilization of simple triple systems, super-simple BIBDs, Steiner systems, and large sets (LSs) of t-designs. We also construct binary and non-binary girth-6 QC-LDPC codes from the t-designs satisfying these conditions by using matrix dispersion method. Experimental results show that the constructed non-binary QC-LDPC codes can provide good practical performance under iterative decoding using the fast Fourier transform based q-ary sum-product algorithm (FFT-QSPA) and they can achieve acceptable coding gains over random-like codes of comparable parameters decoded with sum-product algorithm (SPA).
In this paper, we construct regular and irregular LDPC codes using (n, {k1,k2}, 1)block design. The problem of designing regular and irregular structured LDPC codes that have good overall error performance for wide range of code rates and block sizes with attractive storage requirements is attempted. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Further we analyze the constructed codes based on number of short cycles of the corresponding Tanner graph. The analysis shows that codes having small number of short cycles and a cycle structure which is not overly regular in their Tanner graph perform better. The presented codes are well structured and unlike random codes can lend themselves to a very low-complexity encoder and decoder implementation.