Belief propagation (BP) is a soft-decision (SD) decoder that is commonly used to obtain near-optimal decoding performance for linear codes defined over sparse parity-check matrix. Nevertheless, the BP yields poor perf...
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Belief propagation (BP) is a soft-decision (SD) decoder that is commonly used to obtain near-optimal decoding performance for linear codes defined over sparse parity-check matrix. Nevertheless, the BP yields poor performance when used in the decoding of algebraic block codes, usually described by a dense parity-checkmatrix. Hence, enhanced BP decoders transform the paritycheckmatrix of such codes at each iteration for efficient decoding. In this article, the performance of the transformed parity-checkmatrix of the iterative SD decoder is analysed for the class of binary cyclic codes using a perfect knowledge model (PKM). The PKM computes a list of candidate matrices and selects a baseline parity-checkmatrix according to a distance metric. The selected matrix is optimal since it minimizes the probability of error over various choices in the list. Results show that, for a given channel condition, the conventional transformed matrix obtained by Gaussian elimination is sub-optimal and does not necessarily contain unitary weighted columns at corresponding columns of the unreliable bits. Moreover, PKM can be used to verify the performances of newly developed iterative SD decoders for binary cyclic codes based on parity-check equations instead of maximum-likelihood decoding.
In non-cooperative communications, blind identification of the widely used LDPC codes is an emerging research hot spot. This is different from and more difficult than blind identification of channel coding in cooperat...
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In non-cooperative communications, blind identification of the widely used LDPC codes is an emerging research hot spot. This is different from and more difficult than blind identification of channel coding in cooperative communications. Common disadvantages of the existing algorithms are poor fault tolerance, high number of iterations, and only being applicable to short codes. Our proposed algorithm is based on the idea presented by Sicot et al. (2009) for binary phase-shift keying (BPSK) signals over the additive white Gaussian noise (AWGN) channel. Firstly, to sort the codewords according to a proper threshold, we present a threshold function and derive its zero point, which is verified to be the optimal threshold through experiments. This threshold improves the fault tolerance of our algorithm. Secondly, an operation called bidirectional Gaussian column elimination (BGCE) is proposed to replace Gaussian column elimination (GCE). This operation speeds up the process of deriving parity-checks, and considerably reduces the number of iterations. Thirdly, we use an existing technique for finding low-weight codewords as proposed by Canteaut and Chabaud (1998) to make the linearly independent parity-checks sparse, thereby realizing reconstruction of the sparse parity-check matrix of the LDPC code. The results of comparative experiments demonstrate that our algorithm outperforms existing algorithms.
In this paper we present three optimization techniques of improving the performance of some irregular low-density parity-check ensemble with determinate structure and finite block length. Firstly, it is permutation ma...
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ISBN:
(纸本)9781424453023
In this paper we present three optimization techniques of improving the performance of some irregular low-density parity-check ensemble with determinate structure and finite block length. Firstly, it is permutation matrix optimization. We present a new random permutation matrix called as the Q-matrix. We substituted Q-matrix for identity matrix in base matrix array which can be expanded into R-matrix of the irregular QC-LDPC codes recommended in IEEE 802.16e standard draft and can make the performance of this QC-LDPC codes improve about 0.4dB. Secondly, it is large girth optimization technique. We design H-matrix of the irregular LDPC ensemble and make it at least not include 8-cycle. Thirdly, it is column weight optimization technique in H-matrix of the irregular LDPC ensemble. For the presented irregular LDPC ensemble, it is not such case that the larger the column weight is and the better the performance is, but the column weight should be a moderate value(1).
It is well-established "folk knowledge" that in order to be iteratively decodable, a code should have a sparse parity-check matrix. But exactly how sparse does it need to be and why? We provide some qualitat...
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ISBN:
(纸本)0780382803
It is well-established "folk knowledge" that in order to be iteratively decodable, a code should have a sparse parity-check matrix. But exactly how sparse does it need to be and why? We provide some qualitative and quantitative answers to this question, for finite-length codes.
A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the enco...
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A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparseparitycheckmatrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.
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