Irregular Degree Distribution Research Articles

Polar-Slotted ALOHA Over Slot Erasure Channel

To reduce the throughput loss caused by the slot erasure channel (SEC), we propose a polar slotted ALOHA (PSA) framework where the access procedure is decomposed into two-stage and jointly optimized under the slot polarization idea. In the first stage, guided by the slot polarization, a slot subset is constructed at each active user side and the receiver side. With an irregular degree distribution, each active user randomly selects slots from the slot subset to transmit the packet replicas. Subsequently, in the second stage, by using the packet-based polarization transform, the slotted packets are encoded by using a packet-level polar code. Correspondingly, at the receiver side, a packet-oriented successive cancellation (pSC) or pSC list decoding algorithm is performed to overcome the corruption caused by the SEC. And then, the success interference cancellation procedure is executed to recover the packet. Furthermore, for a given average transmission rate, the irregular degree distribution is optimized by searching the maximum within all feasible traffic load thresholds. Then, an upper bound of the polar-code rate for the PSA scheme is derived. Simulation results indicate that the proposed PSA scheme can achieve an improved throughput over the irregular repetition slotted ALOHA scheme for the SEC.

Fast and efficient parallel breadth-first search with power-law graph transformation

In the big data era, graph computing is widely used to exploit the hidden value in real-world graphs in various scenarios such as social networks, knowledge graphs, web searching, and recommendation systems. However, the random memory accesses result in inefficient use of cache and the irregular degree distribution leads to substantial load imbalance. Breadth-First Search (BFS) is frequently utilized as a kernel for many important and complex graph algorithms. In this paper, we describe a preprocessing approach using Reverse Cuthill-Mckee (RCM) algorithm to improve data locality and demonstrate how to achieve an efficient load balancing for BFS. Computations on RCM-reordered graph data are also accelerated with SIMD executions. We evaluate the performance of the graph preprocessing approach on Kronecker graphs of the Graph500 benchmark and real-world graphs. Our BFS implementation on RCM-reordered graph data achieves 326.48 MTEPS/W (mega TEPS per watt) on an ARMv8 system, ranking 2nd on the Green Graph500 list in June 2020 (the 1st rank uses GPU acceleration).

Rate-Loss Mitigation of SC-LDPC Codes Without Performance Degradation

In research on spatially-coupled low-density parity-check (SC-LDPC) codes, rate-loss of SC-LDPC codes is one of the main issues to be addressed. One way to mitigate the rate-loss is to attach additional variable nodes with an irregular degree distribution, where the degree distribution is optimized with a constraint that the belief propagation (BP) threshold should not be degraded by attaching variable nodes. However, it is observed that the degree distribution obtained with the BP threshold constraint induces degradation of the finite-length performance. In order to address the problem, we propose new optimization methods to attach additional variable nodes while minimizing performance degradation. The proposed optimization methods are based on several design techniques including the scaling law, local threshold, expected graph evolution, differential evolution algorithms, the use of a protograph structure, and puncturing codewords. Using the optimized structure for additional variable nodes, the rate-loss of SC-LDPC codes can be reduced by more than 53% without sacrificing the finite-length performance. It is also shown that the rate-loss mitigation can be translated into a performance improvement if the proposed and the conventional SC-LDPC codes are compared at the same code rate.

A Probabilistic Peeling Decoder to Efficiently Analyze Generalized LDPC Codes Over the BEC

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without resorting on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity, but the optimal fraction is strictly smaller than one. We then consider techniques to further reduce the gap to capacity by means of random puncturing, and the inclusion of a certain fraction of generalized variable nodes in the graph.

Fine-grained Locality-aware Parallel Scheme for Anisotropic Mesh Adaptation

In this paper, we provide a fine-grained parallel scheme for anisotropic mesh adaptation on NUMA11Non-Uniform Memory Access architectures.Data dependencies are expressed by a graph for each kernel, and concurrency is extracted through fine-grained graph coloring. Tasks are structured into bulk-synchronous steps to avoid data races and to aggregate shared-data accesses.To ensure performance prediction, time cost and load imbalance are theoretically characterized.The devised scheme was evaluated on a 4 NUMA node (2-socket) machine, and a mean efficiency of 70% was reached on 32 cores for 3 kernels out of 4. The impact of irregular degree distribution and data layout on scalability is highlighted.

Improving the Communication Pattern in Matrix-Vector Operations for Large Scale-Free Graphs by Disaggregation

Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Computations with graphs of this type on parallel distributed-memory computers are challenging. This is due to the fact that scale-free graphs have a degree distribution that follows a power law, and currently available graph partitioners are not efficient for such an irregular degree distribution. The lack of a good partitioning leads to excessive interprocessor communication requirements during every matrix-vector product. We present an approach to alleviate this problem based on embedding the original irregular graph into a more regular one by disaggregating (splitting up) vertices in the original graph. The matrix-vector operations for the original graph are performed via a factored triple matrix-vector product involving the embedding graph. Even though the latter graph is larger, we ...

Lossy Source Compression Using Low-Density Generator Matrix Codes: Analysis and Algorithms

We study the use of low-density generator matrix (LDGM) codes for lossy compression of the Bernoulli symmetric source. First, we establish rigorous upper bounds on the average distortion achieved by check-regular ensemble of LDGM codes under optimal minimum distance source encoding. These bounds establish that the average distortion using such bounded degree families rapidly approaches the Shannon limit as the degrees are increased. Second, we propose a family of message-passing algorithms, ranging from the standard belief propagation algorithm at one extreme to a variant of survey propagation algorithm at the other. When combined with a decimation subroutine and applied to LDGM codes with suitably irregular degree distributions, we show that such a message-passing/decimation algorithm yields distortion very close to the Shannon rate-distortion bound for the binary symmetric source.

UEP Concepts in Modulation and Coding

First unequal error protection (UEP) proposals date back to the 1960's (Masnick and Wolf; 1967), but now with the introduction of scalable video, UEP develops to a key concept for the transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and Turbo codes. For multicarrier modulation, UEP bit-loading together with hierarchical modulation is described allowing for an arbitrary number of classes, arbitrary SNR margins between the classes, and arbitrary number of bits per class. In Turbo coding, pruning, as a counterpart of puncturing is presented for flexible bit-rate adaptations, including tables with optimized pruning patterns. Bit- and/or check-irregular LDPC codes may be designed to provide UEP to its code bits. However, irregular degree distributions alone do not ensure UEP, and other necessary properties of the parity-check matrix for providing UEP are also pointed out. Pruning is also the means for constructing variable-rate LDPC codes for UEP, especially controlling the check-node profile.

Performance and Thresholds for Irregular Tree-LDPC Codes

This paper presents a performance and thresholds for Irregular Tree-LDPC codes. We obtain optimal irregular degree distributions and threshold by the density evolution technique. It is presented that Irregular Tree-LDPC code has performance gain at low SNR.