Systematic recursive construction of LDPC codes

This letter presents a systematic and recursive method to construct good low-density parity-check (LDPC) codes, especially those with high rate. The proposed method uses a parity check matrix of a quasi-cyclic LDPC code with given row and column weights as a core upon which the larger code is recursively constructed with extensive use of pseudorandom permutation matrices. This construction preserves the minimum distance and girth properties of the core matrix and can generate either regular, or irregular LDPC codes. The method provides a unique representation of the code in compact notation.     

Finite field construction for quasi-cyclic LDPC convolutional codes with cyclic 2-D MDS codes

The parity-check matrices for quasi-cyclic low-density parity-check convolutional (QC-LDPC-C) codes have different characteristics of time-varying periodicity and need to realize fast encoding. The finite field construction method for QC-LDPC-C codes with cyclic two-dimensional maximum distance separable (2-D MDS) codes is proposed using the base matrix framework and matrix unwrapping, thus the constructed parity-check matrices are free of length-4 cycles. The unwrapped matrices are constructed respectively based on different cyclic 2-D MDS codes for the case of matrix period less than or greater than constraint block length, and construction examples are given. LDPC-C codes with different periodicity characteristics are compared with QC-LDPC-C codes constructed with the proposed method. Experimental results show that QC-LDPC-C codes with the proposed method outperform the other codes and have lower encoding and decoding complexity.

     

A lattice-based systematic recursive construction of quasi-cyclic LDPC codes

This paper presents a low-complexity recursive and systematic method to construct good well-structured low-density parity-check (LDPC) codes. The method is based on a recursive application of a partial Kronecker product operation on a given gamma x q, q ges 3 a prime, integer lattice L(gamma x q). The (n - 1)- fold product of L(gamma x q) by itself, denoted Lⁿ(gamma x q), represents a regular quasi-cyclic (QC) LDPC code, denoted (see PDF), of high rate and girth 6. The minimum distance of (see PDF) is equal to that of the core code (see PDF) introduced by L(gamma x q). The support of the minimum weight codewords in (see PDF) are characterized by the support of the same type of codewords in (see PDF). From performance perspective the constructed codes compete with the pseudorandom LDPC codes.     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

Improved progressive-edge-growth (PEG) construction of irregular LDPC codes

Progressive-edge-growth (PEG) algorithm is known to construct low-density parity-check codes at finite block lengths with very good performance. In this letter, we propose a very simple modification to PEG construction for irregular codes, which considerably improves the performance at high signal-to-noise (SNR) ratios with no sacrifice in low-SNR performance.     

Explicit construction of optimal constant-weight codes foridentification via channels

The identification coding theorems of R. Ahlswede and G. Dueck (1981) have shown that for any nonzero probabilities of missed and false identification, it is possible to transmit exp(exp(nR)) messages with n uses of a noisy channel, where R is as close as desired to the Shannon capacity of the channel. That capability is achieved by the identification codes explicitly constructed with a three-layer concatenated constant-weight code used in conjunction with a channel transmission code of rate R     

Flexible construction of irregular partitioned permutation LDPC codes with low, error floors

Irregular partitioned permutation (IPP) low-density parity-check (LDPC) codes have been recently introduced to facilitate hardware implementation of belief propagation (BP) decoders. In this letter, we present a new method to construct IPP LDPC codes with great flexibility in the selection of code parameters. Meanwhile, small stopping sets are avoided in the code construction, thus good error floor performance can be achieved.     

A new construction method of LDPC codes for optical transmission systems

Based on the construction method of systematically constructed Gallager (SCG)(4,k) code,a new improved construction method of low density parity check (LDPC) code is proposed.Compared with the construc...     

Girth conditioning for construction of short block length irregular LDPC codes

A girth conditioning scheme for construction of short block length low-density parity-check (LDPC) codes is presented. The parity-check matrix is generated in a column-by-column fashion under the condition that a newly added column is chosen, among a number of trial columns, to maximise the average girth of variable nodes. The girth-conditioned LDPC codes are found to give a large performance gain especially at high SNRs.     

Low-complexity decoding of LDPC codes

The offset BP-based algorithm is a reduced-complexity derivative of the belief-propagation algorithm for decoding of low-density parity- check codes. It uses a constant offset term to simplify decoding, but at the cost of performance. A method to obtain a 'variable' offset parameter is presented here, to improve the performance of the algorithm.     

卫星激光通信中LDPC码构造方法的研究进展

激光因其单色性好、功率密度大等特性被提出应用于卫星通信系统中以应对未来通信业务需求,但激光通信在传输过程中受大气等因素影响会造成其传输可靠性降低.而低密度奇偶校验(Low-Density Parity-Check,LDPC)码因其灵活的构造方法、较低的编译码复杂度、纠错能力强等优点已被证明适用于卫星激光通信.本文从LD...     

LDPC codes and convolutional codes with equal structural delay: a comparison

We compare convolutional codes and LDPC codes with respect to their decoding performance and their structural delay, which is the inevitable delay solely depending on the structural properties of the coding scheme. Besides the decoding performance, the data delay caused by the channel code is of great importance as this is a crucial factor for many applications. Convolutional codes are known to show a good performance while imposing only a very low latency on the data. LDPC codes yield superior decoding performance but impose a larger delay due to the block structure. The results obtained by comparison will also be related to theoretical limits obtained from random coding and the sphere packing bound. It will be shown that convolutional codes are still the first choice for applications for which a very low data delay is required and the bit error rate is the considered performance criterion. However, if one focuses on a low signal-to-noise ratio or if the obtained frame error rate is the base for comparison, LDPC codes compare favorably.     

The rate of regular LDPC codes

We find the rate of a typical code from the regular low-density parity-check (LDPC) ensemble. We then show that the rate of a code from the ensemble converges to the design rate in quadratic mean and almost surely.     

低差错平底特性的非规则LDPC码的设计

介绍了非规则LDPC码的发展并给出了其优势及缺点，重点论述用ACE算法来构造非规则LDPC码从而降低其差错平底特性。对降低非规则LDPC码的差错平底特性的其它方法提出了展望。     

Several properties of short LDPC codes

In this paper, we present several properties on minimum distance(d/sub min/) and girth(G/sub min/) in Tanner graphs for low-density parity-check (LDPC) codes with small left degrees. We show that the distance growth of (2, 4) LDPC codes is too slow to achieve the desired performance. We further give a tight upper bound on the maximum possible girth. The numerical results show that codes with large G/sub min/ could outperform the average performance of regular ensembles of the LDPC codes over binary symmetric channels. The same codes perform about 1.5 dB away from the sphere-packing bound on additive white Gaussian noise channels.     

Implementation aspects of LDPC convolutional codes

Potentially large storage requirements and long initial decoding delays are two practical issues related to the decoding of low-density parity-check (LDPC) convolutional codes using a continuous pipeline decoder architecture. In this paper, we propose several reduced complexity decoding strategies to lessen the storage requirements and the initial decoding delay without significant loss in performance. We also provide bit error rate comparisons of LDPC block and LDPC convolutional codes under equal processor (hardware) complexity and equal decoding delay assumptions. A partial syndrome encoder realization for LDPC convolutional codes is also proposed and analyzed. We construct terminated LDPC convolutional codes that are suitable for block transmission over a wide range of frame lengths. Simulation results show that, for terminated LDPC convolutional codes of sufficiently large memory, performance can be improved by increasing the density of the syndrome former matrix.     

Memory-efficient sum-product decoding of LDPC codes

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.     

Computationally efficient decoding of LDPC codes

A computationally efficient algorithm for the decoding of low-density parity check codes is introduced. Instead of updating all bit and check nodes at each decoding iteration, the developed algorithm only updates unreliable check and bit nodes. A simple reliability criteria is developed to determine the active bit and check nodes per decoding iteration. Based on the developed technique, significant computation reductions are achieved with very little or no loss in the BER performance of the LDPC codes. The proposed method can be implemented with a slight modification to the sum-product algorithm with negligible additional hardware complexity.     

Surrogate-channel design of universal LDPC codes

A universal code is a code that may be used across a number of different channel types or conditions with little degradation relative to a good single-channel code. The explicit design of universal codes, which simultaneously seeks to solve a multitude of optimization problems, is a daunting task. This letter shows that a single channel may be used as a surrogate for an entire set of channels to produce good universal LDPC codes. This result suggests that sometimes a channel for which LDPC code design is simple may be used as a surrogate for a channel for which LDPC code design is complex. We explore here the universality of LDPC codes over the BEC, AWGN, and flat Rayleigh fading channels in terms of decoding threshold performance. Using excess mutual information as a performance metric, we present design results which support the contention that an LDPC code designed for a single channel can be universally good across the three channels.