A bit on one side

One-Bit ExpanderSketch for One-Bit Compressed Sensing

Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h ∈ H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called onebit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain th...

One Bit of Advi

One Bit of Advice

The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP/1) if and only if the Polynomial Hierarchy (PH) collapses to D, the second level of the Boolean Hierarchy (BH). Previous work showed that BH ⊆ D =⇒ coNP ⊆ NP/poly. The stronger assumption that PH ⊆ D in the new result allows the length of the advice function to be reduced to a single bit and also makes ...

On the Power of One Bit of a #P Function

We introduce the class MP of languages L which can be solved in polynomial time with an oracle for one selected bit of the value f (y) of a #P function f on a selected argument y. This extends the much-studied language classes P and PP, which correspond to the power of the least and most signiicant bits, respectively. We show that MP is captured by the power of the middle bit; namely: a languag...

A Further Result on the ICA One-Bit-Matching Conjecture

The one-bit-matching conjecture for independent component analysis (ICA) has been widely believed in the ICA community. Theoretically, it has been proved that under the assumption of zero skewness for the model probability density functions, the global maximum of a cost function derived from the typical objective function on the ICA problem with the one-bit-matching condition corresponds to a f...