Beating the Gilbert-Varshamov Bound for Online Channels

Details Beating the Gilbert-Varshamov Bound for Online Channels Beating the Gilbert-Varshamov Bound for Online Channels

2011-01-05

arxiv.org/abs/1101.1045v1

Computer Science

Information Theory

14 pages, 1 figure

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Beating the Gilbert-Varshamov Bound for Online Channels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Beating the Gilbert-Varshamov Bound for Online Channels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Beating the Gilbert-Varshamov Bound for Online Channels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267558