Hamming codes are the first nontrivial family of error-correcting codes that can correct one
error in a block of binary symbols. In this paper we extend the notion of error-correction to …

Motivated by distributed storage applications, we investigate the degree to which capacity
achieving codes can be efficiently updated when a single information symbol changes, and …

Consider the problem of packing Hamming balls of a given relative radius subject to the
constraint that they cover any point of the ambient Hamming space with multiplicity at most …

Developing automatic speech recognition technologies requires transcribed speech so as to
learn the mapping from sound to text. It is traditionally assumed that transcribers need to be …

We study a problem of constructing codes that transform a channel with high bit error rate
(BER) into one with low BER (at the expense of rate). Our focus is on obtaining codes with …

This paper continues the investigation of the combinatorial formulation of the joint source-
channel coding problem. In particular, the connections are drawn to error-reducing codes …

We consider the classic joint source-channel coding problem of transmitting a memoryless
source over a memoryless channel. The focus of this work is on the long-standing open …

A mapping of k-bit strings into n-bit strings is called an (α, β)-map if k-bit strings which are
more than αk apart are mapped to n-bit strings that are more than βn apart in Hamming …

The Chebyshev radius of a set in a metric space is defined to be the radius of the smallest
ball containing the set. This quantity is closely related to the covering radius of the set and, in …

We introduce the notion of information ratio Ir (H/G) between two (simple, undirected) graphs
G and H, defined as the supremum of ratios k/n such that there exists a mapping between …