2,072 research outputs found
Achievable Rates for Noisy Channels with Synchronization Errors
Cataloged from PDF version of article.We develop several lower bounds on the capacity of binary input symmetric output channels with synchronization errors, which also suffer from other types of impairments such as substitutions, erasures, additive white Gaussian noise (AWGN), etc. More precisely, we show that if a channel suffering from synchronization errors as well as other type of impairments can be decomposed into a cascade of two component channels where the first one is another channel with synchronization errors and the second one is a memoryless channel (with no synchronization errors), a lower bound on the capacity of the original channel in terms of the capacity of the component synchronization error channel can be derived. A primary application of our results is that we can employ any lower bound derived on the capacity of the component synchronization error channel to find lower bounds on the capacity of the (original) noisy channel with synchronization errors. We apply the general ideas to several specific classes of channels such as synchronization error channels with erasures and substitutions, with symmetric q-ary outputs and with AWGN explicitly, and obtain easy-to-compute bounds. We illustrate that, with our approach, it is possible to derive tighter capacity lower bounds compared to the currently available bounds in the literature for certain classes of channels, e.g., deletion/substitution channels and deletion/AWGN channels (for certain signal-to-noise ratio (SNR) ranges). © 2014 IEEE
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
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
Upper bounds on the capacity of deletion channels using channel fragmentation
Cataloged from PDF version of article.We study memoryless channels with synchronization
errors as defined by a stochastic channel matrix allowing for
symbol drop-outs or symbol insertions with particular emphasis
on the binary and non-binary deletion channels. We offer
a different look at these channels by considering equivalent
models by fragmenting the input sequence where different
subsequences travel through different channels. The resulting
output symbols are combined appropriately to come up with an
equivalent input–output representation of the original channel
which allows for derivation of new upper bounds on the channel
capacity. We consider both random and deterministic types
of fragmentation processes applied to binary and nonbinary
deletion channels. With two specific applications of this idea,
a random fragmentation applied to a binary deletion channel
and a deterministic fragmentation process applied to a nonbinary
deletion channel, we prove certain inequality relations among the
capacities of the original channels and those of the introduced
subchannels. The resulting inequalities prove useful in deriving
tighter capacity upper bounds for: 1) independent identically
distributed (i.i.d.) deletion channels when the deletion probability
exceeds 0.65 and 2) nonbinary deletion channels. Some extensions
of these results, for instance, to the case of deletion/substitution
channels are also explored
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
Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound
We introduce synchronization strings as a novel way of efficiently dealing
with synchronization errors, i.e., insertions and deletions. Synchronization
errors are strictly more general and much harder to deal with than commonly
considered half-errors, i.e., symbol corruptions and erasures. For every
, synchronization strings allow to index a sequence with an
size alphabet such that one can efficiently transform
synchronization errors into half-errors. This powerful new
technique has many applications. In this paper, we focus on designing insdel
codes, i.e., error correcting block codes (ECCs) for insertion deletion
channels.
While ECCs for both half-errors and synchronization errors have been
intensely studied, the later has largely resisted progress. Indeed, it took
until 1999 for the first insdel codes with constant rate, constant distance,
and constant alphabet size to be constructed by Schulman and Zuckerman. Insdel
codes for asymptotically large or small noise rates were given in 2016 by
Guruswami et al. but these codes are still polynomially far from the optimal
rate-distance tradeoff. This makes the understanding of insdel codes up to this
work equivalent to what was known for regular ECCs after Forney introduced
concatenated codes in his doctoral thesis 50 years ago.
A direct application of our synchronization strings based indexing method
gives a simple black-box construction which transforms any ECC into an equally
efficient insdel code with a slightly larger alphabet size. This instantly
transfers much of the highly developed understanding for regular ECCs over
large constant alphabets into the realm of insdel codes. Most notably, we
obtain efficient insdel codes which get arbitrarily close to the optimal
rate-distance tradeoff given by the Singleton bound for the complete noise
spectrum
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