In this paper, we directly lower bound the information capacity for channels with independent identically distributed (i.i.d.) deletions and duplications. Our approach differs from previous work in that we focus on the information capacity using ideas from renewal theory, rather than focusing on the transmission capacity by analyzing the error probability of some randomly generated code using a combinatorial argument. Of course, the transmission and information capacities are equal, but our change of perspective allows for a much simpler analysis that gives more general theoretical results. We then apply these results to the binary deletion channel to improve existing lower bounds on its capacity.

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of mu messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Theta(mu) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations.

We directly lower bound the information capacity for channels with i.i.d. deletions and duplications. Our approach differs from previous work in that we focus on the information capacity using ideas from renewal theory, rather than focusing on the transmission capacity by analyzing the error probability of some randomly generated code using a combinatorial argument. Of course, the transmission and information capacities are equal, but our change of perspective allows for a much simpler analysis that gives more general theoretical results. We then apply these results to the binary deletion channel to improve existing lower bounds on its capacity.

This paper considers the capacity of binary deletion channels, where bits are deleted independently with probability d. It improves significantly upon the best previous framework used to obtain provable lower bounds on this capacity by utilizing a stronger definition of a typical output from the channel. The new results give the best known provable bounds on the capacity for all values of d. Moreover, the techniques presented here extend to yield lower bounds for channels with certain types of random insertions, namely, duplications, or combinations of duplications and deletions. To demonstrate these techniques in this context, two binary channels are analyzed: a channel where each transmitted bit is copied with probability nu and a channel where each transmitted bit is copied a geometrically distributed number of times.

This correspondence considers binary deletion channels, where bits are deleted independently with probability d; it improves upon the framework used to analyze the capacity of binary deletion channels established by Diggavi and Grossglauser, improving on their lower bounds. Diggavi and Grossglauser considered codebooks with codewords generated by a first-order Markov chain. They only consider typical outputs, where an output is typical if an N bit input gives an N(1-d)(1-epsi) bit output. The improvements in this correspondence arise from two considerations. First, a stronger notion of a typical output from the channel is used, which yields better bounds even for the codebooks studied by Diggavi and Grossglauser. Second, codewords generated by more general processes than first-order Markov chains are considered

We present a simple proof that the capacity of the binary independent and identically distributed (i.i.d.) deletion channel, where each bit is deleted independently with probability d, is at least (1-d)/9, by developing a correspondence between the deletion channel and an insertion/deletion channel that we call a Poisson-repeat channel

We consider binary deletion channels, where bits are deleted independently with probability d. We extend the framework used to analyze the capacity of binary deletion channels established by Diggavi and Grossglauser [2001], improving on their lower bounds. In Diggavi and Grossglauser, the codewords are generated by a first order Markov chain. Our improvements arise from two considerations. First, Diggavi and Grossglauser consider typical outputs, where an output is typical if an N bit input produces an output of at least N(1-d)(1-/spl epsi/) bits. We provide a stronger notion of a typical output that yields better bounds even for the cases studied in Diggavi and Grossglauser. Second, we consider codewords generated by more general processes than first order Markov chains.