12 research outputs found
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
An Efficient Algorithm for Counting Cycles in QC and APM LDPC Codes
In this paper, a new method is given for counting cycles in the Tanner graph
of a (Type-I) quasi-cyclic (QC) low-density parity-check (LDPC) code which the
complexity mainly is dependent on the base matrix, independent from the
CPM-size of the constructed code. Interestingly, for large CPM-sizes, in
comparison of the existing methods, this algorithm is the first approach which
efficiently counts the cycles in the Tanner graphs of QC-LDPC codes. In fact,
the algorithm recursively counts the cycles in the parity-check matrix
column-by-column by finding all non-isomorph tailless backtrackless closed
(TBC) walks in the base graph and enumerating theoretically their corresponding
cycles in the same equivalent class. Moreover, this approach can be modified in
few steps to find the cycle distributions of a class of LDPC codes based on
Affine permutation matrices (APM-LDPC codes). Interestingly, unlike the
existing methods which count the cycles up to , where is the girth,
the proposed algorithm can be used to enumerate the cycles of arbitrary length
in the Tanner graph. Moreover, the proposed cycle searching algorithm improves
upon various previously known methods, in terms of computational complexity and
memory requirements.Comment: 18 pages, 4 figure
Topologically Driven Methods for Construction Of Multi-Edge Type (Multigraph with nodes puncturing) Quasi-Cyclic Low-density Parity-check Codes for Wireless Channel, WDM Long-Haul and Archival Holographic Memory
In this Phd thesis discusses modern methods for constructing MET QC-LDPC
codes with a given error correction ("waterfall, error-floor") and complexity
(parallelism level according circulant size plus scheduler orthogonality of
checks) profiles: 1. weight enumerators optimization, protograph construction
using Density Evolution, MI (P/Exit-chart) and it approximation: Gaussian
Approximation, Reciprocal-channel approximation and etc; 2. Covariance
evolution and it approximation; 3. Lifting methods for QC codes
construction:PEG, Guest-and-Test, Hill-Climbing with girth, EMD, ACE
optimization; 4. Upper and lower bounds on code distance estimation and its
parallel implementation using CPU/GPU; 5. Brouwer-Zimmerman and Number Geometry
code distance estimation methods; 6. Importance Sampling for error-floor
estimation; 7. Length and rate adaption methods for QC codes based on cyclic
group decomposition; 8. Methods for interaction screening which allow to
improve performance (decorrelate variables) under BP and it's approximation. We
proposed several state-of-the-art methods: Simulated Annealing lifting for MET
QC-LDPC codes construction; fast EMD and code distance estimation; floor scale
modular lifting for lenght adaption; fast finite-length covariance evolution
rate penalty from threshold for code construction and it hardware friendly
compression for fast decoder's LLRs unbiasing due SNR's estimation error. We
found topology reason's of efficient of such methods using topology thickening
(homotopy of continuous and discrete curvature) under matched metric space
which allow to generalize this idea to a class of nonlinear codes for Signal
Processing and Machine Learning. Using the proposed algorithms several
generations of WDM Long-Haul error-correction codes were built. It was applied
for "5G eMBB" 3GPP TS38.212 and other applications like Flash storage,
Compressed sensing measurement matrix.Comment: Phd Thesis, 176 pages, in Russian, 62 pictures, 13 tables, 5 appendix
including links to binary and source code
On the girth of quasi cyclic protograph LDPC codes
In this paper, we study the relationships between the girth of the Tanner graph of a quasi cyclic (QC) protograph low-density parity-check (LDPC) code, on one hand, and the lifting degree and the size and the structure of the base graph, on the other hand. As a result, for a given base graph and a given lifting degree, we derive an upper bound on the girth of the resulting lifted graphs (codes). The upper bounds derived here are generally tighter than the existing bounds. The results presented in this work can be used to select an appropriate lifting degree for a given base graph, in order to have a desired girth, or to provide some insight in designing good base graphs, or to properly select the base graph's edge permutations