Improved bilayer LDPC codes using irregular check node degree distribution

Azmi, Marwan Hadri; Yuan, Jinhong; Ning, Jun; Huynh, H. Q.

doi:10.1109/isit.2008.4594964

Cited by 16 publications

(11 citation statements)

References 14 publications

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“…In this paper, we address the following question: 4 Question 3: Consider the representation of a finite-length binary linear block code by an arbitrary bipartite graph. How simple can such a graphical representation be as a function of the channel model, target block error probability, and code rate (which is below capacity) ? We note that the graphical complexity referred to in this paper measures the total number of edges used for the representation of finite-length codes by bipartite graphs.…”

Section: Introductionmentioning

confidence: 99%

“…For example, [32, Section VI] introduces some capacity-achieving sequences of accumulate-repeat-accumulate code ensembles for the BEC, which also possess a bounded complexity per information bit under BP decoding; they are designed in a way where the degree distributions of the LDPC code ensembles after a proper graph reduction (as explained in [32,Section II]) are self-matched and are both irregular. The irregularity of the parity-check degree distributions in the design of LDPC codes appears to be useful in various cases under BP decoding, e.g., the optimization of finite-length LDPC code ensembles whose transmission takes place over the BEC [1], the heavy-tail Poisson distribution introduced in [24] and [48] which gives rise to capacity-achieving degree distributions for the BEC, the design of bilayer LDPC code ensembles for a degraded relay AWGN channel [4], and the design of LDPC code ensembles for unequal error protection [43].…”

Section: Introductionmentioning

confidence: 99%

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On Universal Properties of Capacity-Approaching LDPC Code Ensembles

Sason

2009

IEEE Trans. Inform. Theory

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This paper is focused on the derivation of some universal properties of capacity-approaching lowdensity parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of informationtheoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Universal Properties of Capacity-Approaching LDPC Code Ensembles

Sason

2009

IEEE Trans. Inform. Theory

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“…codes for the decode-forward (DF) relay channel in half-duplex and full-duplex modes. There is a large body of work focused on designing LDPC codes for the relay channel [8], [9], [10], [11], [12], [13], [14]. These works mostly utilize irregular LDPC codes and use density evolution (or related) techniques to search for optimized irregular LDPC ensembles operating at two different rates.…”

Section: Introductionmentioning

confidence: 99%

Bilayer protograph codes for half-duplex relay channels

Nguyen

Nosratinia

2010

2010 IEEE International Symposium on Information Theory

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Despite encouraging advances in the design of relay codes, several important challenges remain.Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes.

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“…For example, [7, Section VI] introduces some capacity-achieving sequences of accumulate-repeat-accumulate code ensembles for the BEC, which also possess a bounded complexity per information bit under BP decoding; they are designed in a way where the degree distributions of the LDPC code ensembles after a proper graph reduction (as explained in [7,Section II]) are self-matched and are both irregular. The irregularity of the parity-check degree distributions in the design of LDPC codes appears to be useful in various cases under BP decoding (see, e.g., [1], [3], [6], and [10]). …”

Section: Introductionmentioning

confidence: 99%

Linear programming bounds on the degree distributions of LDPC code ensembles

Sason

2009

2009 IEEE International Symposium on Information Theory

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Abstract-This work considers the behavior of the degree distributions of capacity-approaching low-density parity-check (LDPC) code ensembles via linear programming (LP) bounds. These LP bounds are information-theoretic, and they apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. Analytical solutions of these bounds are given in closed form, and the bounds are compared for the BEC with some specific degree distributions of capacity-achieving sequences of LDPC code ensembles. These LP bounds are shown to be informative and are easy to calculate. Due to space limitations, the derivation of the LP bounds is outlined, and the reader is referred to the full paper version [9] for complete proofs and further discussions.Index Terms-Degree distributions, linear programming, lowdensity parity-check (LDPC) codes, memoryless binary-input output-symmetric (MBIOS) channels.

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Improved bilayer LDPC codes using irregular check node degree distribution

Cited by 16 publications

References 14 publications

On Universal Properties of Capacity-Approaching LDPC Code Ensembles

On Universal Properties of Capacity-Approaching LDPC Code Ensembles

Bilayer protograph codes for half-duplex relay channels

Linear programming bounds on the degree distributions of LDPC code ensembles

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