New sequences of capacity achieving LDPC code ensembles over the binary erasure channel

Saeedi, Hamid; Banihashemi, Amir H.

doi:10.1109/isit.2008.4595096

Cited by 18 publications

(45 citation statements)

References 16 publications

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“…In [12]- [14], the authors proposed new sequences of capacity achieving LDPC code ensembles over the BEC which contained Shokrollahi's sequences as a special case. Unlike Shokrollahi's sequences in which all variable node degrees from 2 to have to be present, the sequences of [12]- [14] only contain variable node degrees from 2 to < and degree , where is a strictly increasing function of (and ultimately a function of ( ) and ). 3 For a given ensemble ( , ) within the sequences proposed in [12]- [14], we have:…”

Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

“…In the method proposed in [12]- [14], the values of are computed based on the following principle: Starting from = 2, and by sequentially going through the values of ≥ 2, set the value of to a maximum value˜such that the ensemble remains convergent for sufficiently large . For the BEC, this process results in˜= * [13], [14].…”

Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

“…For the BEC, this process results in˜= * [13], [14]. Intuitively, the method of [12]- [14] works since based on (1), maximizing the rate is equivalent to maximizing −1 , which in turn implies that one should assign higher percentages to the lower degree coefficients as far as the constructed ensemble remains convergent.…”

Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

“…In [3]- [5], Shokrollahi et al proposed a scheme to design sequences of LDPC code ensembles over the BEC, whose performance is proved to achieve the capacity for sufficiently large average check and variable node degrees. A more general category of capacity achieving sequences over the BEC were proposed in [12]- [14]. Construction and analysis of capacity achieving ensemble sequences of codes defined on graphs have also been studied in [6]- [9] for the BEC.…”

Section: Introductionmentioning

confidence: 99%

“…We then provide some evidence suggesting that the designed sequences could in fact be universally capacity achieving. Starting from the unpunctured case, we extend some of the properties of capacity achieving sequences over the BEC [12], [13], to BIOSM channels. Among such properties, only the stability condition [10] has been shown to be extendable to BIOSM channels other than the BEC.…”

Section: Introductionmentioning

confidence: 99%

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Successive Maximization for Systematic Design of Universally Capacity Approaching Rate-Compatible Sequences of LDPC Code Ensembles over Binary-Input Output-Symmetric Memoryless Channels

Saeedi

Pishro-Nik

Banihashemi

2011

IEEE Trans. Commun.

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Abstract-A systematic construction of capacity achieving lowdensity parity-check(LDPC) code ensemble sequences over the Binary Erasure Channel (BEC) has been proposed by Saeedi et al. based on a method, here referred to as Successive Maximization (SM). In SM, the fraction of degree-nodes are successively maximized starting from = 2 with the constraint that the ensemble remains convergent over the channel. In this paper, we propose SM to design universally capacity approaching rate-compatible LDPC code ensemble sequences over the general class of Binary-Input Output-Symmetric Memoryless (BIOSM) channels. This is achieved by first generalizing the SM method to other BIOSM channels to design a sequence of capacity approaching ensembles called the parent sequence. The SM principle is then applied to each ensemble within the parent sequence, this time to design rate-compatible puncturing schemes. As part of our results, we extend the stability condition which was previously derived for degree-2 variable nodes to other variable node degrees as well as to the case of ratecompatible codes. Consequently, we prove that using the SM principle, one is able to design universally capacity achieving rate-compatible LDPC code ensemble sequences over the BEC. Unlike the previous results in the literature, the proposed SM approach is naturally extendable to other BIOSM channels. The performance of the rate-compatible schemes designed based on our method is comparable to those designed by optimization.

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Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

Section: Capacity Achieving Sequences and The Principle Of Succementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Successive Maximization for Systematic Design of Universally Capacity Approaching Rate-Compatible Sequences of LDPC Code Ensembles over Binary-Input Output-Symmetric Memoryless Channels

Saeedi

Pishro-Nik

Banihashemi

2011

IEEE Trans. Commun.

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Construction of quasi‐cyclic low‐density parity‐check codes with low encoding complexity

2012

Int J Communication

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Low encoding complexity is very important for quasi-cyclic low-density parity-check (QC-LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC-LDPC codes with low encoding complexity. This scheme is called two-stage particle swarm optimization (TS-PSO) algorithm, in which both the threshold and girth distribution of QC-LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC-LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC-LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity-check matrix of the QC-LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC-LDPC codes constructed by proposed scheme, the QC-LDPC code in 802.16e standard, and the QC-LDPC code in Tam's study. Simulation results show that the QC-LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC-LDPC codes with low encoding complexity. leads to the lowest error rate. Optimization of the degree distribution pairs of irregular LDPC codes has already been considered on additive white Gaussian noise (AWGN) channels [9, 13], Rayleigh channels [11], binary erasure channels [14,15], and so on. In addition to the threshold, girth is another important parameter used to construct the LDPC codes [7]. Girth refers to the shortest cycles in the parity-check matrix or Tanner graph of LDPC codes [7,8]. The typical construction method based on girth is the progressive edge-growth (PEG) algorithm, which aims to construct the quasi-cyclic LDPC (QC-LDPC) codes by maximizing the girth of the Tanner graph of LDPC codes [16][17][18].From a practical point of view, the algebraic construction method is a good choice. The QC-LDPC code is a very important subclass of algebraic construction LDPC codes for its structured paritycheck matrix. The parity-check matrix of QC-LDPC codes is formed by the circulant permutation matrix or zero matrix, which may be easily implemented by the shift register. Consequently, QC-LDPC codes have been employed in several advanced communication standards such as 802.16e and 802.11n because of their hardware-friendly structures [1-3].The extrinsic information transfer (EXIT) chart method is another widely used method in the design of irregular LDPC codes because of its simplicity and accuracy [19,20]. However, the conventional EXIT chart method cannot be applied in the multi-edge type and protograph-based LDPC codes. To evaluate the performance of protograph LDPC codes [21], ...

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Cospectral Bipartite Graphs with the Same Degree Sequences but with Different Number of Large Cycles

Dehghan

Banihashemi

2019

Graphs and Combinatorics

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Finding the multiplicity of cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. Recently, Blake and Lin computed the number of shortest cycles (g-cycles, where g is the girth of the graph) in a bi-regular bipartite graph, in terms of the degree sequences and the spectrum (eigenvalues of the adjacency matrix) of the graph [IEEE Trans. Inform. Theory 64 (10): [6526][6527][6528][6529][6530][6531][6532][6533][6534][6535] 2018]. This result was subsequently extended in [IEEE Trans. Inform. Theory, accepted for publication, Dec. 2018] to cycles of length g + 2, . . . , 2g − 2, in bi-regular bipartite graphs, as well as 4-cycles and 6-cycles in irregular and halfregular bipartite graphs, with g ≥ 4 and g ≥ 6, respectively. In this paper, we complement these positive results with negative results demonstrating that the information of the degree sequences and the spectrum of a bipartite graph is, in general, insufficient to count (a) the i-cycles, i ≥ 2g, in bi-regular graphs, (b) the i-cycles for any i > g, regardless of the value of g, and g-cycles for g ≥ 6, in irregular graphs, and (c) the i-cycles for any i > g, regardless of the value of g, and g-cycles for g ≥ 8, in half-regular graphs. To obtain these results, we construct counter-examples using the Godsil-McKay switching.

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New sequences of capacity achieving LDPC code ensembles over the binary erasure channel

Cited by 18 publications

References 16 publications

Successive Maximization for Systematic Design of Universally Capacity Approaching Rate-Compatible Sequences of LDPC Code Ensembles over Binary-Input Output-Symmetric Memoryless Channels

Successive Maximization for Systematic Design of Universally Capacity Approaching Rate-Compatible Sequences of LDPC Code Ensembles over Binary-Input Output-Symmetric Memoryless Channels

Construction of quasi‐cyclic low‐density parity‐check codes with low encoding complexity

Cospectral Bipartite Graphs with the Same Degree Sequences but with Different Number of Large Cycles

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