In this paper, we consider coding schemes for computationally bounded
channels, which can introduce an arbitrary set of errors as long as (a) the
fraction of errors is bounded with high probability by a parameter p and (b)
the process which adds the errors can be described by a sufficiently "simple"
circuit.
For three classes of channels, we provide explicit, efficiently
encodable/decodable codes of optimal rate where only inefficiently decodable
codes were previously known. In each case, we provide one encoder/decoder that
works for every channel in the class.
Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals.
For every p in (0,1/2), we give an explicit construction of binary codes of
rate approaching "capacity" 1-H(p) that enable reliable communication in the
presence of worst-case additive errors}, caused by a channel oblivious to the
codeword (but not necessarily the message).