Short Code

About: Short Code is a research topic. Over the lifetime, 395 publications have been published within this topic receiving 6153 citations.

Product Quantization for Nearest Neighbor Search

Abstract: This paper introduces a product quantization-based approach for approximate nearest neighbor search. The idea is to decompose the space into a Cartesian product of low-dimensional subspaces and to quantize each subspace separately. A vector is represented by a short code composed of its subspace quantization indices. The euclidean distance between two vectors can be efficiently estimated from their codes. An asymmetric version increases precision, as it computes the approximate distance between a vector and a code. Experimental results show that our approach searches for nearest neighbors efficiently, in particular in combination with an inverted file system. Results for SIFT and GIST image descriptors show excellent search accuracy, outperforming three state-of-the-art approaches. The scalability of our approach is validated on a data set of two billion vectors.

Jump-oriented programming: a new class of code-reuse attack

Abstract: Return-oriented programming is an effective code-reuse attack in which short code sequences ending in a ret instruction are found within existing binaries and executed in arbitrary order by taking control of the stack. This allows for Turing-complete behavior in the target program without the need for injecting attack code, thus significantly negating current code injection defense efforts (e.g., W⊕X). On the other hand, its inherent characteristics, such as the reliance on the stack and the consecutive execution of return-oriented gadgets, have prompted a variety of defenses to detect or prevent it from happening.In this paper, we introduce a new class of code-reuse attack, called jump-oriented programming. This new attack eliminates the reliance on the stack and ret instructions (including ret-like instructions such as pop+jmp) seen in return-oriented programming without sacrificing expressive power. This attack still builds and chains functional gadgets, each performing certain primitive operations, except these gadgets end in an indirect branch rather than ret. Without the convenience of using ret to unify them, the attack relies on a dispatcher gadget to dispatch and execute the functional gadgets. We have successfully identified the availability of these jump-oriented gadgets in the GNU libc library. Our experience with an example shellcode attack demonstrates the practicality and effectiveness of this technique.

Composite Quantization for Approximate Nearest Neighbor Search

Abstract: This paper presents a novel compact coding approach, composite quantization, for approximate nearest neighbor search. The idea is to use the composition of several elements selected from the dictionaries to accurately approximate a vector and to represent the vector by a short code composed of the indices of the selected elements. To efficiently compute the approximate distance of a query to a database vector using the short code, we introduce an extra constraint, constant inter-dictionary-element-product, resulting in that approximating the distance only using the distance of the query to each selected element is enough for nearest neighbor search. Experimental comparisonwith state-of-the-art algorithms over several benchmark datasets demonstrates the efficacy of the proposed approach.

Hypercontractivity, sum-of-squares proofs, and their applications

Abstract: We study the computational complexity of approximating the 2-to-q norm of linear operators (defined as |A|2->q = maxv≠ 0|Av|q/|v|2) for q > 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot's Unique Games Conjecture (UGC). We show the following: For any constant even integer q ≥ 4, a graph G is a small-set expander if and only if the projector into the span of the top eigenvectors of G's adjacency matrix has bounded 2->q norm. As a corollary, a good approximation to the 2->q norm will refute the Small-Set Expansion Conjecture --- a close variant of the UGC. We also show that such a good approximation can be obtained in exp(n2/q) time, thus obtaining a different proof of the known subexponential algorithm for Small-Set-Expansion. Constant rounds of the "Sum of Squares" semidefinite programing hierarchy certify an upper bound on the 2->4 norm of the projector to low degree polynomials over the Boolean cube, as well certify the unsatisfiability of the "noisy cube" and "short code" based instances of Unique-Games considered by prior works. This improves on the previous upper bound of exp(logO(1) n) rounds (for the "short code"), as well as separates the "Sum of Squares"/"Lasserre" hierarchy from weaker hierarchies that were known to require ω(1) rounds. We show reductions between computing the 2->4 norm and computing the injective tensor norm of a tensor, a problem with connections to quantum information theory. Three corollaries are: (i) the 2->4 norm is NP-hard to approximate to precision inverse-polynomial in the dimension, (ii) the 2->4 norm does not have a good approximation (in the sense above) unless 3-SAT can be solved in time exp(√n poly log(n)), and (iii) known algorithms for the quantum separability problem imply a non-trivial additive approximation for the 2->4 norm.

A matrix-algebraic approach to successive interference cancellation in CDMA

Abstract: In this paper, we describe linear successive interference cancellation (SIC) based on matrix-algebra. We show that linear SIC schemes (single stage and multistage) correspond to linear matrix filtering that can be performed directly on the received chip-matched filtered signal vector without explicitly performing the interference cancellation. This leads to an analytical expression for calculating the resulting bit-error rate which is of particular use for short code systems. Convergence issues are discussed, and the concept of /spl epsiv/-convergence is introduced to determine the number of stages required for practical convergence for both short and long codes.