15 research outputs found
An Upper Bound on the Capacity of non-Binary Deletion Channels
We derive an upper bound on the capacity of non-binary deletion channels.
Although binary deletion channels have received significant attention over the
years, and many upper and lower bounds on their capacity have been derived,
such studies for the non-binary case are largely missing. The state of the art
is the following: as a trivial upper bound, capacity of an erasure channel with
the same input alphabet as the deletion channel can be used, and as a lower
bound the results by Diggavi and Grossglauser are available. In this paper, we
derive the first non-trivial non-binary deletion channel capacity upper bound
and reduce the gap with the existing achievable rates. To derive the results we
first prove an inequality between the capacity of a 2K-ary deletion channel
with deletion probability , denoted by , and the capacity of the
binary deletion channel with the same deletion probability, , that is,
. Then by employing some existing upper
bounds on the capacity of the binary deletion channel, we obtain upper bounds
on the capacity of the 2K-ary deletion channel. We illustrate via examples the
use of the new bounds and discuss their asymptotic behavior as .Comment: accepted for presentation in ISIT 201
A Note on the Deletion Channel Capacity
Memoryless channels with deletion errors as defined by a stochastic channel
matrix allowing for bit drop outs are considered in which transmitted bits are
either independently deleted with probability or unchanged with probability
. Such channels are information stable, hence their Shannon capacity
exists. However, computation of the channel capacity is formidable, and only
some upper and lower bounds on the capacity exist. In this paper, we first show
a simple result that the parallel concatenation of two different independent
deletion channels with deletion probabilities and , in which every
input bit is either transmitted over the first channel with probability of
or over the second one with probability of , is nothing
but another deletion channel with deletion probability of . We then provide an upper bound on the concatenated
deletion channel capacity in terms of the weighted average of ,
and the parameters of the three channels. An interesting consequence
of this bound is that which
enables us to provide an improved upper bound on the capacity of the i.i.d.
deletion channels, i.e., for . This
generalizes the asymptotic result by Dalai as it remains valid for all . Using the same approach we are also able to improve upon existing upper
bounds on the capacity of the deletion/substitution channel.Comment: Submitted to the IEEE Transactions on Information Theor
Write Channel Model for Bit-Patterned Media Recording
We propose a new write channel model for bit-patterned media recording that
reflects the data dependence of write synchronization errors. It is shown that
this model accommodates both substitution-like errors and insertion-deletion
errors whose statistics are determined by an underlying channel state process.
We study information theoretic properties of the write channel model, including
the capacity, symmetric information rate, Markov-1 rate and the zero-error
capacity.Comment: 11 pages, 12 figures, journa
Bounds on the Capacity of Random Insertion and Deletion-Additive Noise Channels
We develop several analytical lower bounds on the capacity of binary
insertion and deletion channels by considering independent uniformly
distributed (i.u.d.) inputs and computing lower bounds on the mutual
information between the input and output sequences. For the deletion channel,
we consider two different models: independent and identically distributed
(i.i.d.) deletion-substitution channel and i.i.d. deletion channel with
additive white Gaussian noise (AWGN). These two models are considered to
incorporate effects of the channel noise along with the synchronization errors.
For the insertion channel case we consider the Gallager's model in which the
transmitted bits are replaced with two random bits and uniform over the four
possibilities independently of any other insertion events. The general approach
taken is similar in all cases, however the specific computations differ.
Furthermore, the approach yields a useful lower bound on the capacity for a
wide range of deletion probabilities for the deletion channels, while it
provides a beneficial bound only for small insertion probabilities (less than
0.25) for the insertion model adopted. We emphasize the importance of these
results by noting that 1) our results are the first analytical bounds on the
capacity of deletion-AWGN channels, 2) the results developed are the best
available analytical lower bounds on the deletion-substitution case, 3) for the
Gallager insertion channel model, the new lower bound improves the existing
results for small insertion probabilities.Comment: Accepted for publication in IEEE Transactions on Information Theor
Directly Lower Bounding the Information Capacity for Channels with I.I.D. Deletions and Duplications
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