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Showing 1 to 20 of 20 for “"low-density parity-check (LDPC) codes"”.
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Iterative algorithms for lossy source coding
… embedding. For lossy source coding, we analyze low density parity check (LDPC) codes and low density generator matrix (LDGM) codes for quantization under a Hamming distortion. We prove that LDPC codes can achieve the rate-distortion function. We also show that the variable node degree of any …
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Decoding error-correcting codes via linear programming
Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up …
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Good families of quantum low-density parity-check codes and a geometric framework for the amplitude-damping channel
Classical low-density parity-check (LDPC) codes were first introduced by Robert Gallager in the 1960's and have reemerged as one of the most influential coding schemes. We present new families of quantum low-density parity-check error-correcting codes derived from regular tessellations of Platonic …
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Novel irregular LDPC codes and their application to iterative detection of MIMO systems
Low-density parity-check (LDPC) codes are among the best performing error correction codes currently known. For higher performing irregular LDPC codes, degree distributions have been found which produce codes with optimum performance in the infinite block length case. Significant performance …
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An Information Theoretic Study on Linear Dispersion Codes and Low -Density Parity -Check Codes
… theoretic study of linear dispersion (LD) codes and low-density parity-check (LDPC) codes. For bit-linear LD codes, we find necessary and sufficient conditions on the dispersion matrices for the a posteriori distribution of the information bit vector to be a product distribution. We also …
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Joint Equalization and Decoding via Convex Optimization
… the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the required error rate (after decoding) is too low to be verifiable by simulation, are most important applications of …
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On the construction of some capacity-approaching coding schemes
… bound. The second scheme is based on low-density parity-check (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution from this observation, namely …
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Guessing Random Additive Noise Decoding in Coded Multiple-Input Multiple-Output Systems
… paired with other moderate redundancy linear codes, can yield substantial savings in the range of 0.5 − 2 dB in E_b/N₀ over CA-SCL decoding (list size 16) of CA-Polar codes with the same code parameters, for a block error rate of 10⁻³. We provide extensive benchmarks comparing ORBGRAND to …
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Design and Analysis of Multilevel Coded Modulation for Multi-Node Networks
… The rate penalty due to linearity of component codes is analyzed and to avoid it, a solution is proposed involving the labeling of signal constellations. Simulations show that the proposed architecture together with good point-to-point codes can achieve excellent performance. For the full-duplex …
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Code design for the relay channel
… relaying, we propose dual-rate low-density parity-check (LDPC) codes. In our designs, the source transmission is decoded with the help of side information in the form of additional parity bits from the relay. The key challenge is to discover codes that simultaneously perform well …
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Error Floor Analysis of Quasi-Cyclic LDPC and Spatially Coupled-LDPC Codes and Construction of Codes with Low Error Floor
Forward error-correcting (FEC) codes play an important role in transmitting data with extremely high reliability through modern communication systems. In this thesis, we study the design and analysis of low-density parity-check (LDPC) codes in general and spatially coupled (SC) LDPC codes, in …
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Importance sampling for LDPC codes and turbo-coded CDMA
Low-density parity-check (LDPC) codes have shown capacity-approaching performance with soft iterative decoding algorithms. Simulating LDPC codes at very low error rates normally takes an unacceptably long time. We consider importance sampling (IS) schemes for the error rate estimation of LDPC …
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Data reliability and error correction for NAND Flash Memory System
… widely used for data storage due to its high density, high throughput, and low power. However, as the flash memory scales to smaller process technologies and stores more bits per cell, its reliability is decreasing. The error correction coding can be used to significantly improve the data …
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Spatial Coupling for High-Dimensional Estimation
Many signal processing and statistical problems allow flexibility in the way in which measurements are acquired. For example, in compressed sensing MRI, the sampling frequencies can be chosen to optimize reconstruction performance. This thesis investi- gates spatial coupling, a design technique …
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Unreliable and resource-constrained decoding
… are established. For decoding repetition codes using consensus decoding circuits, the optimal tradeoff between decoding speed and quadratic wiring cost is defined and established. Designing optimal circuits is shown to be NP-complete, but is carried out for small circuit size. The natural …
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Single and joint iterative decoding for higher order modulation schemes
… channel coding techniques, in particular, low-density parity-check (LDPC) codes, iterative decoding on Tanner graphs, and their application on joint iterative receivers based on the turbo principle, previously proposed. The construction of random LDPC codes that fulfil certain desirable …
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On The Design Of Physical Layer Rateless Codes
Codes that are capable of generating any number of encoded symbols from a given number of source symbols are called rateless codes. Luby transform (LT) codes are the first practical realization of rateless codes while Raptor codes are constructed by serially concatenating LT codes with high-rate …
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Trapping Sets of Iterative Decoders for Quantum and Classical Low-Density Parity-Check Codes
… or quantum computation. Error correction codes and their decoders perform this step by adding redundant information that aids the decoder to recover or protect the logical information even in the presence of noise. Low-density parity-check (LDPC) codes have been one of the most popular …
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Efficient Information Reconciliation for Quantum Key Distribution = Reconciliación eficiente de información para la distribución cuántica de claves
… in QKD. Here, we propose the use of low-density parity-check (LDPC) codes, since they are good both in efficiency and throughput. A price to pay, a priori, using LDPC codes is that good efficiency is only attained for very long codes and in a very narrow range of error rates. This …
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Low-density parity-check codes : construction and implementation.
Low-density parity-check (LDPC) codes have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost, time, …