22,769 research outputs found
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
On Asynchronous Communication Systems: Capacity Bounds and Relaying Schemes
abstract: Practical communication systems are subject to errors due to imperfect time alignment among the communicating nodes. Timing errors can occur in different forms depending on the underlying communication scenario. This doctoral study considers two different classes of asynchronous systems; point-to-point (P2P) communication systems with synchronization errors, and asynchronous cooperative systems. In particular, the focus is on an information theoretic analysis for P2P systems with synchronization errors and developing new signaling solutions for several asynchronous cooperative communication systems. The first part of the dissertation presents several bounds on the capacity of the P2P systems with synchronization errors. First, binary insertion and deletion channels are considered where lower bounds on the mutual information between the input and output sequences are computed for independent uniformly distributed (i.u.d.) inputs. Then, a channel suffering from both synchronization errors and additive noise is considered as a serial concatenation of a synchronization error-only channel and an additive noise channel. It is proved that the capacity of the original channel is lower bounded in terms of the synchronization error-only channel capacity and the parameters of both channels. On a different front, to better characterize the deletion channel capacity, the capacity of three independent deletion channels with different deletion probabilities are related through an inequality resulting in the tightest upper bound on the deletion channel capacity for deletion probabilities larger than 0.65. Furthermore, the first non-trivial upper bound on the 2K-ary input deletion channel capacity is provided by relating the 2K-ary input deletion channel capacity with the binary deletion channel capacity through an inequality. The second part of the dissertation develops two new relaying schemes to alleviate asynchronism issues in cooperative communications. The first one is a single carrier (SC)-based scheme providing a spectrally efficient Alamouti code structure at the receiver under flat fading channel conditions by reducing the overhead needed to overcome the asynchronism and obtain spatial diversity. The second one is an orthogonal frequency division multiplexing (OFDM)-based approach useful for asynchronous cooperative systems experiencing excessive relative delays among the relays under frequency-selective channel conditions to achieve a delay diversity structure at the receiver and extract spatial diversity.Dissertation/ThesisPh.D. Electrical Engineering 201
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
Models and information-theoretic bounds for nanopore sequencing
Nanopore sequencing is an emerging new technology for sequencing DNA, which
can read long fragments of DNA (~50,000 bases) in contrast to most current
short-read sequencing technologies which can only read hundreds of bases. While
nanopore sequencers can acquire long reads, the high error rates (20%-30%) pose
a technical challenge. In a nanopore sequencer, a DNA is migrated through a
nanopore and current variations are measured. The DNA sequence is inferred from
this observed current pattern using an algorithm called a base-caller. In this
paper, we propose a mathematical model for the "channel" from the input DNA
sequence to the observed current, and calculate bounds on the information
extraction capacity of the nanopore sequencer. This model incorporates
impairments like (non-linear) inter-symbol interference, deletions, as well as
random response. These information bounds have two-fold application: (1) The
decoding rate with a uniform input distribution can be used to calculate the
average size of the plausible list of DNA sequences given an observed current
trace. This bound can be used to benchmark existing base-calling algorithms, as
well as serving a performance objective to design better nanopores. (2) When
the nanopore sequencer is used as a reader in a DNA storage system, the storage
capacity is quantified by our bounds
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
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