Modern storage engines and key-value stores have come to rely on the log-structured merge-tree (LSM-tree) as their core data structure. LSM-tree operates by gradually merge-sorting data across levels of exponentially increasing capacities in storage. A crucial design dimension of LSM-tree is its compaction granularity. Some designs perform Full Merge , whereby entire levels get compacted at once. Others perform Partial Merge , whereby smaller groups of files with overlapping key ranges are compacted independently. This paper shows that both strategies exhibit serious flaws. With Full Merge, space-amplification is exorbitant. The reason is that while compacting the LSM-tree's largest level, there must be at least twice as much storage space as data to store both the original and new files until the compaction is finished. On the other hand, Partial Merge exhibits excessive write-amplification. The reason is twofold. (1) The files getting compacted typically do not have perfectly overlapping key ranges, and so some non-overlapping data is superfluously rewritten in each compaction. (2) Files with different lifetimes become interspersed within the SSD leading to high SSD garbage-collection overheads. As the data size grows, these problems grow in magnitude. We introduce Spooky, a novel compaction granulation method to address these problems. Spooky partitions data at the largest level into equally sized files, and it partitions data at smaller levels based on the file boundaries at the largest level. This allows merging one group of perfectly overlapping files at a time to limit space-amplification and compaction overheads. At the same time, Spooky writes larger though fewer files simultaneously so that files with different lifetimes do not become as interspersed within the SSD. This cheapens garbage-collection. We show empirically that Spooky achieves >2x lower space-amplification than Full Merge and >2x lower write-amplification than Partial Merge at the same time.

Modern key-value stores typically rely on an LSM-tree in storage (SSD) to handle writes and Bloom filters in memory (DRAM) to optimize reads. With ongoing advances in SSD technology shrinking the performance gap between storage and memory devices, the Bloom filters are now emerging as a performance bottleneck.

With the end of Moore's Law, database architects are turning to hardware accelerators to offload computationally intensive tasks from the CPU. In this paper, we show that accelerators can facilitate far more than just computation: they enable algorithms and data structures that lavishly expand computation in order to optimize for disparate cost metrics. We introduce the Pliops Extreme Data Processor (XDP), a novel storage engine implemented from the ground up using customized hardware. At its core, XDP consists of an accelerated hash table to index the data in storage using less memory and fewer storage accesses for queries than the best alternative. XDP also employs an accelerated compressor, a capacitor, and a lock-free RAID sub-system to minimize storage space and recovery time while minimizing performance penalties. As a result, XDP overcomes cost contentions that have so far been inescapable.

The performance of maximum-likelihood (ML) decoded binary linear block codes over the additive white Gaussian noise (AWGN) channel is addressed via the tangential sphere bound (TSB) and two of its recent improved versions. The correspondence is focused on the derivation of the error exponents of these bounds. Although it was shown that some recent improvements of the TSB tighten this bound for finite-length codes, it is demonstrated in this correspondence that their error exponents coincide. For an arbitrary ensemble of binary linear block codes, the common value of these error exponents is explicitly expressed in terms of the asymptotic growth rate of the average distance spectrum

The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and output-symmetric communication channel, and their effectiveness is exemplified for various ensembles of turbo-like codes over the additive white Gaussian noise (AWGN) channel. An expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds.

The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and output-symmetric communication channel. The effectiveness of these bounds is exemplified for ensembles of turbo-like codes