Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beating the Gilbert-Varshamov Bound for Online Channels   In the online channel coding model, a sender wishes to communicate a message
to a receiver by transmitting a codeword x =(x_1,...,x_n) in {0,1}^n bit by bit
via a channel limited to at most pn corruptions. The channel is online in the
sense that at the ith step the channel decides whether to flip the ith bit or
not and its decision is based only on the bits transmitted so far, i.e.,
(x_1,...,x_i). This is in contrast to the classical adversarial channel in
which the corruption is chosen by a channel that has full knowledge on the sent
codeword x. The best known lower bound on the capacity of both the online
channel and the classical adversarial channel is the well-known
Gilbert-Varshamov bound. In this paper we prove a lower bound on the capacity
of the online channel which beats the Gilbert-Varshamov bound for any positive
p such that H(2p) < 0.5 (where H is the binary entropy function). To do so, we
prove that for any such p, a code chosen at random combined with the nearest
neighbor decoder achieves with high probability a rate strictly higher than the
Gilbert-Varshamov bound (for the online channel).

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas