New Lower Bounds on the Capacity of Optical Fiber Channels via Optimized Shaping and Detection

Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result, only little progress has been made so far, while the optimal shaping distribution and the ultimate channel capacity remain unknown. In this work, we describe a novel technique to optimize the shaping distribution in a very general setting and high-dimensional space. For a simplified block-memoryless nonlinear optical channel, the capacity lower bound obtained by the proposed technique can be expressed analytically, establishing the conditions for an unbounded growth of capacity with power. In a more realistic scenario, the technique can be implemented by a rejection sampling algorithm driven by a suitable cost function, and the corresponding achievable information rate estimated numerically. The combination of the proposed technique with an improved (non-Gaussian) decoding metric yields a new capacity lower bound for the dual-polarization WDM channel.Comment: Submitted to IEEE Journal of Lightwave Technology on November 30th, 202

A thermodynamic uncertainty relation for a system with memory

We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs typically discussed in the previous years, our observables and the entropy production rate are one-time variables. The bound to the signal-to-noise ratio of such state-dependent observables only in some cases can be mapped to the entropy production rate. For example, this is true in Markovian systems. Hence, the presence of memory in the system complicates the thermodynamic interpretation of the uncertainty relation

When Two Choices Are not Enough: Balancing at Scale in Distributed Stream Processing

Carefully balancing load in distributed stream processing systems has a fundamental impact on execution latency and throughput. Load balancing is challenging because real-world workloads are skewed: some tuples in the stream are associated to keys which are significantly more frequent than others. Skew is remarkably more problematic in large deployments: more workers implies fewer keys per worker, so it becomes harder to "average out" the cost of hot keys with cold keys. We propose a novel load balancing technique that uses a heaving hitter algorithm to efficiently identify the hottest keys in the stream. These hot keys are assigned to $d \geq 2$ choices to ensure a balanced load, where $d$ is tuned automatically to minimize the memory and computation cost of operator replication. The technique works online and does not require the use of routing tables. Our extensive evaluation shows that our technique can balance real-world workloads on large deployments, and improve throughput and latency by $\mathbf{150\%}$ and $\mathbf{60\%}$ respectively over the previous state-of-the-art when deployed on Apache Storm.Comment: 12 pages, 14 Figures, this paper is accepted and will be published at ICDE 201

Information Rates of ASK-Based Molecular Communication in Fluid Media

This paper studies the capacity of molecular communications in fluid media, where the information is encoded in the number of transmitted molecules in a time-slot (amplitude shift keying). The propagation of molecules is governed by random Brownian motion and the communication is in general subject to inter-symbol interference (ISI). We first consider the case where ISI is negligible and analyze the capacity and the capacity per unit cost of the resulting discrete memoryless molecular channel and the effect of possible practical constraints, such as limitations on peak and/or average number of transmitted molecules per transmission. In the case with a constrained peak molecular emission, we show that as the time-slot duration increases, the input distribution achieving the capacity per channel use transitions from binary inputs to a discrete uniform distribution. In this paper, we also analyze the impact of ISI. Crucially, we account for the correlation that ISI induces between channel output symbols. We derive an upper bound and two lower bounds on the capacity in this setting. Using the input distribution obtained by an extended Blahut-Arimoto algorithm, we maximize the lower bounds. Our results show that, over a wide range of parameter values, the bounds are close.Comment: 31 pages, 8 figures, Accepted for publication on IEEE Transactions on Molecular, Biological, and Multi-Scale Communication

On Coding Efficiency for Flash Memories

Recently, flash memories have become a competitive solution for mass storage. The flash memories have rather different properties compared with the rotary hard drives. That is, the writing of flash memories is constrained, and flash memories can endure only limited numbers of erases. Therefore, the design goals for the flash memory systems are quite different from these for other memory systems. In this paper, we consider the problem of coding efficiency. We define the "coding-efficiency" as the amount of information that one flash memory cell can be used to record per cost. Because each flash memory cell can endure a roughly fixed number of erases, the cost of data recording can be well-defined. We define "payload" as the amount of information that one flash memory cell can represent at a particular moment. By using information-theoretic arguments, we prove a coding theorem for achievable coding rates. We prove an upper and lower bound for coding efficiency. We show in this paper that there exists a fundamental trade-off between "payload" and "coding efficiency". The results in this paper may provide useful insights on the design of future flash memory systems.Comment: accepted for publication in the Proceeding of the 35th IEEE Sarnoff Symposium, Newark, New Jersey, May 21-22, 201

Using Hashing to Solve the Dictionary Problem (In External Memory)

We consider the dictionary problem in external memory and improve the update time of the well-known buffer tree by roughly a logarithmic factor. For any \lambda >= max {lg lg n, log_{M/B} (n/B)}, we can support updates in time O(\lambda / B) and queries in sublogarithmic time, O(log_\lambda n). We also present a lower bound in the cell-probe model showing that our data structure is optimal. In the RAM, hash tables have been used to solve the dictionary problem faster than binary search for more than half a century. By contrast, our data structure is the first to beat the comparison barrier in external memory. Ours is also the first data structure to depart convincingly from the indivisibility paradigm