Readings

Inverted World [Christopher Priest]. A science-fiction novel, but of a piece with a writer like M. John Harrison — there’s a kind of disconnect and a focus on the conceptual world building rather than the nitty-gritty you get with Iain M. Banks. To avoid spoilers, I’ll just say it’s set in a city which moves through the world, always trying to be at a place called optimum. The city is on rails — it constantly builds fresh tracks ahead of it and winches itself forward a tenth of a mile per day. The city is run by a guild system of track layers, traction experts, bridge builders, surveyors, and the like. The protagonist, Helward Mann, takes an oath and joins a guild as an apprentice. The book follows his progress as he learns, and we learn, more about the strange world through which the city moves. Recommended if you like heady, somewhat retro, post-apocalyptic conceptual fiction.

Luka and the Fire of Life [Salman Rushdie]. A re-read for me, this didn’t hold up as well the second time around. I much prefer Haroun and the Sea of Stories, which I can read over and over again.

Boxers and Saints [Gene Luen Yang]. A great two-part graphic novel about the Boxer Rebellion in China. Chances are you don’t know much about this history. You won’t necessarily get a history lesson from this book, but you will want to learn more about it.

The Adventures of Augie March [Saul Bellow]. After leaving Chicago I have decided to read more books set in Chicago so that I can miss it more. I had read this book before but it was a rushed job. This time I let myself longer a bit more over Bellow’s language. It’s epic and scope and gave me a view of Chicago and the Great Depression that I hadn’t had before. Indeed, given our current economic woes, it was an interesting comparison to see the similarities (the rich are still pretty rich, and if you can get employed by them, you may do ok) and the dissimilarities.

The Idea Factory: Bell Labs and the Great Age of American Innovation [John Gertner]. A history of Bell Labs and a must-read for researchers who work on anything related to computing, communications, or applied physics and chemistry. It’s not all rah-rah, and while Gertner takes the “profiles of the personalities” approaches to writing about the place, I am sure there will be things in there that would surprise even the die-hard Shannonistas who may read this blog…

SPCOM 2014: some more talks (and a plenary)

I did catch Greg Wornell’s plenary at SPCOM, which was called When Bits Absolutely, Positively, Have to be There as Soon as Possible, a riff on this FedEx commercial, which is older than I am. The talk was on link-aware PHY-layer design– basically looking at how ARQ enables incremental redundancy, and how to do a sort of layered superposition + incremental redundancy scheme in the sequential setting as well as a “multi-path” setting where blocks can arrive out of order. This was really digging into the signal issues in a way that a lot of non-communication engineering information theorists may get squeamish about. The nice thing is that I think the engineering problem is approachable without knowing a lot of heavy-duty math, but still requires some careful analysis.

Communication and Compression Via Sparse Linear Regression
Ramji Venkataramanan
This was on building codewords and codebooks out of a lower-complexity code dictionary A \in \mathbb{R}^{n \times ML} where each codeword is a superposition of L columns, one each from groups of size M. Thus encoding is A \beta where \beta is a sparse vector. I saw a talk by Barron and Joseph from a previous ISIT about this, but the framework extends to rate distortion (achieving the rate distortion function), and channel coding. The main point is to lower the complexity of the code at the expense of the gap to optimal rate — encoding and decoding are polynomial time but the rate gap for rate-distortion goes to zero as 1/\log n. Ramji gave a really nice and clear talk on this — I hope he puts the slides up!

An Optimal Varentropy Bound for Log-Concave Distributions
Mokshay Madiman; Liyao Wang
Mokshay’s talk was also really clear and excellent. For a distribution f(X) on \mathbb{R}^n, we can define \tilde{h}(X) = - \log f(X). The entropy is the expectation of this random variable, and the varentropy is the variance. Their main result is a upper bound on the varentropu of log concave distributions f(X). To wit, \mathrm{Var}(\tilde{h}) \le n. This bound doesn’t depend on the distribution and is sharp if f is a product of exponentials. They then use this to prove a universal bound on the deviation of \tilde{h} from its expectation, which gives a AEP that doesn’t really assume anything about the joint distribution of the variables except for log-concavity. There was more in the talk, but I eagerly await the paper.

Event-triggered Sampling and Reconstruction of Sparse Real-valued Trigonometric Polynomials
Neeraj Sharma; Thippur V. Sreenivas
This was on non-uniform sampling where the sampler tries to detect level crossings of the analog signal and samples at that point — the rate may not be uniform enough to use existing nonuniform sampling techniques. They come up with a method for reconstructing signals which are real-valued trigonometric polynomials with a few nonzero coefficients (e.g. sparse) and it seems to work pretty decently in experiments.

Removing Sampling Bias in Networked Stochastic Approximation
Vivek Borkar; Raaz Dwivedi
In networked stochastic approximation, the intermittent communication between nodes may mean that the system tracks a different ODE than the one we want. By modifying the method to account for “local clocks” on each edge, we can correct for this, but we end up with new conditions on the step size to make things work. I am pretty excited about this paper, but as usual, my notes were not quite up to getting the juicy bits. That’s what paper reading is for.

On Asymmetric Insertion and Deletion Errors
Ankur A. Kulkarni
The insertion/deletion channel model is notoriously hard. Ankur proposed a new model where 0‘s are “indestructible” — they cannot be inserted or deleted. This asymmetric model leads to new asymptotic bounds on the capacity. I don’t really work on this channel model so I can’t get the finer points of the results, but once nice takeaway was that asymptotically, each indestructible 0 in the codeword lets us correct around 1/2 a deletion more.

A teaser for ITAVision 2015

As part of ITAVision 2015 we are soliciting individuals and groups to submit videos documenting their love of information theory and/or its applications. During ISIT we put together a little example with our volunteers (it sounded better in rehearsal than at the banquet, alas). The song was Entropy is Awesome based on this, obviously. If you want to sing along, here is the Karaoke version:

The lyrics (so far) are:

Entropy is awesome!
Entropy is sum minus p log p
Entropy is awesome!
When you work on I.T.

Blockwise error vanishes as n gets bigger
Maximize I X Y
Polarize forever
Let’s party forever

I.I.D.
I get you, you get me
Communicating at capacity

Entropy is awesome…

This iteration of the lyrics is due to a number of contributors — truly a group effort. If you want to help flesh out the rest of the song, please feel free to email me and we’ll get a group effort going.

More details on the contest will be forthcoming!

SPCOM 2014: some talks

Relevance Singular Vector Machine for Low-­rank Matrix Sensing
Martin Sundin; Saikat Chatterjee; Magnus Jansson; Cristian Rojas
This talk was on designing Bayesian priors for sparse-PCA problems — the key is to find a prior which induces a low-rank structure on the matrix. The model was something like y = A \mathrm{vec}(X) + n where X is a low-rank matrix and n is noise. The previous state of the art is by Babacan et al., a paper which I obviously haven’t read, but the method they propose here (which involved some heavy algebra/matrix factorizations) appears to be competitive in several regimes. Probably more of interest to those working on Bayesian methods…

Non-Convex Sparse Estimation for Signal Processing
David Wipf
More Bayesian methods! Although David (who I met at ICML) was not trying to say that the priors are particularly “correct,” but rather that the penalty functions that they induce on the problems he is studying actually make sense. More of an algorithmist’s approach, you might say. He set up the problem a bit more generally, to minimize problems of the form
\min_{X_i} \sum_{i} \alpha_i \mathrm{rank}[X_i] \ \ \ \ \ \ \ Y = \sum_{i} A_i(X_i)
where A_i are some operators. He made the case that convex relaxations of many of these problems, while analytically beautiful, have restrictions which are not satisfied in practice, and indeed they often have poor performance. His approach is via Empirical Bayes, but this leads to non-convex problems. What he can show is that the algorithm he proposes is competitive with any method that tries to separate the error from the “low-rank” constraint, and that the new optimization is “smoother.” I’m sure more details are in his various papers, for those who are interested.

PCA-HDR: A Robust PCA Based Solution to HDR Imaging
Adit Bhardwaj; Shanmuganathan Raman
My apologies for taking fewer notes on this one, but I don’t know much about HDR imaging, so this was mostly me learning about HDR image processing. There are several different ways of doing HDR, from multiple exposures to flash/no-flash, and so on. The idea is that artifacts introduced by the camera can be modeled using the robust PCA framework and that denoting in HDR imaging may be better using robust PCA. I think that looking at some of the approaches David mentioned may be good in this domain, since it seems unlikely to me that these images will satisfy the conditions necessary for convex relaxations to work…

On Communication Requirements for Secure Computation
Vinod M Prabhakaran
Vinod showed some information theoretic approaches to understanding how much communication is needed for secure computation protocols like remote oblivious transfer: Xavier has \{X_0, X_1\}, Yvonne has Y \in \{0,1\} and Zelda wants Z = X_Y, but nobody should be able to infer each other’s values. Feige, Killian, and Naor have a protocol for this, which Vinod and Co. can show is communication-optimal. There were several ingredients here, including cut-set bounds, distribution switching, data processing inequalities, and special bounds for 3-party protocols. More details in his CRYPTO paper (and others).

Artificial Noise Revisited: When Eve Has More Antennas Than Alice
Shuiyin Liu; Yi Hong; Emanuele Viterbo
In a MIMO wiretap setting, if the receiver has more antennas than the transmitter, then the transmitter can send noise in the nullspace of the channel matrix of the direct channel — as long as the eavesdropper has fewer antennas than the transmitter then secure transmission is possible. In this paper they show that positive secrecy capacity is possible even when the eavesdropper has more antennas, but as the number of eavesdropper antennas grows, the achievable rate goes to 0. Perhaps a little bit of a surprise here!

SPCOM 2014: tutorials

I just attended SPCOM 2014 at the Indian Institute of Science in Bangalore — many thanks to the organizers for the invitation! SPCOM 2014 happens every two years and is a mix of invited and submitted papers (much like Allerton). This year they mixed the invited talks with the regular talks which I thought was a great idea — since invited papers were not for specific sessions, it makes a lot more sense to do it that way, plus it avoids a sort of “two-tier” system.

I arrived early enough to catch the tutorials on the first day. There was a 3 hour session in the morning and another on the in afternoon. For the morning I decided to expand my horizons by attending Manoj Gopalkrishnan‘s tutorial on the physics of computation. Manoj focused on the question of how much energy it takes to erase or copy a bit of information. He started with some historical context via von Neumann, Szilard, and Landauer to build a correspondence between familiar information theoretic concepts and their physical counterparts. So in this correspondence, relative entropy is the same as free energy. He then turned to look at what one might call “finite time” thermodynamics. Suppose that you have to apply a control that operates in finite time in order to change a bit. One way to look at this is through controlling the transition probabilities in a two-state Markov chain representing the value of the bit you want to fix. You want to drive the resting state (with stationary distribution (1/2,1/2) to something like (\epsilon, 1 - \epsilon) within time T. At this level I more or less understood what was going on, but since my physics background is pretty poor, I think I missed out on how the physical intuition/constraints impact what control strategies you can choose.

Prasad Santhanam gave the other tutorial, which was a bit more solid ground for me. This was not quite a tutorial on large-alphabet probability estimation, but more directly on universal compression and redundancy calculations. The basic setup is that you have a family of distributions \mathcal{P} and you don’t know which distribution p \in \mathcal{P} will generate your data. Based on the data sample you want to do something: estimate some property of the distribution, compress the sample to a size close to its entropy, etc. A class can be weakly or strongly compressible, or insurable (which means being able to estimate quantiles), and so on. These problems turn out to be a bit different from each other depending on some topological features of the class. One interesting thing to consider for the machine learners out there this stopping time that you need in some analyses. As you are going along, observing the data and doing your task (estimation, compression, etc) can you tell from the data that you are doing well? This has major implications for whether or not an online algorithm can even work the way we want it to, and is something Prasad calls “data-driven compressible.”

I’ll try to write another post or two about the talks I saw as well!

ISIT 2014: a few more talks

Identification via the Broadcast Channel
Annina Bracher (ETH Zurich, Switzerland); Amos Lapidoth (ETHZ, Switzerland)
The title pretty much describes it — there are two receivers which are both looking out for a particular message. This is the identification problem, in which the receiver only cares about a particular message (but we don’t know which one) and we have to design a code such that they can detect the message. The number of messages is 2^{2^{nC}} where C is the Shannon capacity of the DMC. In the broadcast setting we run into the problem that the errors for the two receivers are entangled. However, their message sets are disjoint. The way out is to look at the average error for each (averaged over the other user’s message). The main result is that the rates only depend on the conditional marginals, and they have a strong converse.

Efficient compression of monotone and m-modal distributions
Jayadev Acharya (University of California, San Diego, USA); Ashkan Jafarpour (University of California, San Diego, USA); Alon Orlitsky (University of California, San Diego, USA); Ananda Theertha Suresh (University of California, San Diego, USA)
A monotone distribution is a distribution on \mathbb{N} such that the probabilities are non-increasing. The redundancy for this class is infinite, alas, so they restrict the support to size k (where k can be large). They propose a two-step compression scheme in which the first step is to approximate the true distribution with a piecewise constant step distribution, and then use a compression scheme for step distributions.

Writing on a Dirty Paper in the Presence of Jamming
Amitalok J Budkuley (Indian Institute of Technology, Bombay, India); Bikash K Dey (Indian Institute of Technology Bombay, India); Vinod M Prabhakaran (Tata Institute of Fundamental Research, India)
Ahh, jamming. A topic near and dear to my heart. This paper takes a game-theoretic approach to jamming in a DPC setup: “the capacity of the channel in the presence of the jammer is the unique Nash equilibrium utility of the zero sum communication game between the user and the jammer.” This is a mutual information game, and they show that i.i.d. Gaussian jamming and dirty paper coding are a Nash equilibrium. I looked at an AVC version of this problem in my thesis, and the structure is quite a bit different, so this was an interesting different take on the same problem — how can we use the state information to render adversarial interference as harmless as noise?

Stable Grassmann Manifold Embedding via Gaussian Random Matrices
Hailong Shi (Tsinghua University & Department of Electronic Engineering, P.R. China); Hao Zhang (TsinghuaUniversity, P.R. China); Gang Li (Tsinghua University, P.R. China); Xiqin Wang (Tsinghua University, P.R. China)
This was in the session I was chairing. The idea is that you are given a subspace (e.g., a point on the Grassman manifold) and you want to see what happens when you randomly project this into a lower-dimensional subspace using an i.i.d. Gaussian matrix a la Johnson-Lindenstrauss. The JL Lemma says that projections are length-preserving. Are they also volume-preserving? It turns out that they are (no surprise). The main tools are measure concentration results together with a union bound over a covering set.

Is “Shannon capacity of noisy computing” zero?
Pulkit Grover (Carnegie Mellon University, USA)
Yes. I think. Maybe? Pulkit set up a physical model for computation and used a cut-set argument to show that the total energy expenditure is high. I started looking at the paper in the proceedings and realized that it’s significantly different than the talk though, so I’m not sure I really understood the argument. I should read the paper more carefully. You should too, probably.

ISIT 2014: two more plenaries

As I wrote before, I took pretty woeful notes during ISIT this year, so I don’t have much to write about. Andrea Goldsmith’s plenary was about how we always say IT/Comm is dead, but she thinks we should be more sanguine about it. She presented a glimpse of some recent work with Stefano Rini on a unified approach for providing achievable results for single-hop networks using a graph to represent superposition coding and binning operations among the auxiliary variables. If it is actually as easy to use as advertised, it might save over the 23+ rate inequalities defining some achievable rate regions. The moral of the story is that it’s sometimes better to clean up our existing results a bit. I think the El-Gamal and Kim book did a great job of this for basic multiterminal IT, for example.

Vijay Kumar’s plenary was on codes for distributed storage and repair-bandwidth tradeoffs, focusing on extensions of the model. There was a lot of discussion of other code constructions, and how asking for certain properties (such as “locality”) can cost you something in the tradeoff. This is important when you can’t repair a code from arbitrary nodes in the network/data center — because there’s an underlying network which supplies the data for repair, codes should probably respect that network. At least that was the moral I took from this talk. Since I don’t work on coding, some things were a little over my head, but I thought he did an excellent job of keeping it accessible with nice concrete examples.