Information Theory and Reliable Communication

We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.

Regular and irregular progressive edge-growth tanner graphs

In this correspondence, the construction of low-density parity-check (LDPC) codes from circulant permutation matrices is investigated. It is shown that such codes cannot have a Tanner graph representation with girth larger than 12, and a relatively mild necessary and sufficient condition for the code to have a girth of 6, 8,10, or 12 is derived. These results suggest that families of LDPC codes with such girth values are relatively easy to obtain and, consequently, additional parameters such as the minimum distance or the number of redundant check sums should be considered. To this end, a necessary condition for the codes investigated to reach their maximum possible minimum Hamming distance is proposed.

/pdf/quasicyclic-low-density-parity-check-codes-from-circulant-4x8uyibr4c.pdf

Quasicyclic low-density parity-check codes from circulant permutation matrices

Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.

Reduced-complexity decoding of LDPC codes

Some years ago quantum hacking became popular: devices implementing the unbreakable quantum cryptography were shown to have imperfections which could be exploited by attackers. Security has been thoroughly enhanced, as a consequence of both theoretical and experimental advances. This review gives both sides of the story, with the current best theory of quantum security, and an extensive survey of what makes quantum cryptosystem safe in practice.

Secure quantum key distribution with realistic devices

We propose a general method for constructing Tanner (1981) graphs with large girth by progressively establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction. Lower bounds on the girth and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms or parameters of the graphs. Encoding of LDPC codes based on the PEG principle is also investigated. We show how to exploit the PEG graph construction to obtain LDPC codes that allow linear time encoding. The advantages of PEG Tanner graphs over randomly constructed graphs are demonstrated by extensive simulation results on code performance.

Progressive edge-growth Tanner graphs

Efficient implementations of the sum-product algorithm (SPA) are presented for decoding low-density parity-check (LDPC) codes using log-likelihood ratios (LLR) as messages between symbol and parity-check nodes. Various reduced-complexity derivatives of the LLR-SPA are proposed. Both serial and parallel implementations are investigated, leading to trellis and tree topologies, respectively. Furthermore, by exploiting the inherent robustness of LLRs, it is shown, via simulations, that coarse quantization tables are sufficient to implement complex core operations with negligible or no loss in performance. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency and computational complexity perspective.

/pdf/efficient-implementations-of-the-sum-product-algorithm-for-uq5qugxsgz.pdf

Efficient implementations of the sum-product algorithm for decoding LDPC codes

Write amplification is a critical factor limiting the random write performance and write endurance in storage devices based on NAND-flash memories such as solid-state drives (SSD). The impact of garbage collection on write amplification is influenced by the level of over-provisioning and the choice of reclaiming policy. In this paper, we present a novel probabilistic model of write amplification for log-structured flash-based SSDs. Specifically, we quantify the impact of over-provisioning on write amplification analytically and by simulation assuming workloads of uniformly-distributed random short writes. Moreover, we propose modified versions of the greedy garbage-collection reclaiming policy and compare their performance. Finally, we analytically evaluate the benefits of separating static and dynamic data in reducing write amplification, and how to address endurance with proper wear leveling.

/pdf/write-amplification-analysis-in-flash-based-solid-state-29qqajkwed.pdf

Xiao-Yu Hu

Papers

Regular and irregular progressive edge-growth tanner graphs

Reduced-complexity decoding of LDPC codes

Progressive edge-growth Tanner graphs

Efficient implementations of the sum-product algorithm for decoding LDPC codes

Write amplification analysis in flash-based solid state drives