6,377 research outputs found
Capacity Upper Bounds for Deletion-Type Channels
We develop a systematic approach, based on convex programming and real
analysis, for obtaining upper bounds on the capacity of the binary deletion
channel and, more generally, channels with i.i.d. insertions and deletions.
Other than the classical deletion channel, we give a special attention to the
Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions
on Information Theory, 2006). Our framework can be applied to obtain capacity
upper bounds for any repetition distribution (the deletion and Poisson-repeat
channels corresponding to the special cases of Bernoulli and Poisson
distributions). Our techniques essentially reduce the task of proving capacity
upper bounds to maximizing a univariate, real-valued, and often concave
function over a bounded interval. We show the following:
1. The capacity of the binary deletion channel with deletion probability
is at most for , and, assuming the capacity
function is convex, is at most for , where
is the golden ratio. This is the first nontrivial
capacity upper bound for any value of outside the limiting case
that is fully explicit and proved without computer assistance.
2. We derive the first set of capacity upper bounds for the Poisson-repeat
channel.
3. We derive several novel upper bounds on the capacity of the deletion
channel. All upper bounds are maximums of efficiently computable, and concave,
univariate real functions over a bounded domain. In turn, we upper bound these
functions in terms of explicit elementary and standard special functions, whose
maximums can be found even more efficiently (and sometimes, analytically, for
example for ).
Along the way, we develop several new techniques of potentially independent
interest in information theory, probability, and mathematical analysis.Comment: Minor edits, In Proceedings of 50th Annual ACM SIGACT Symposium on
the Theory of Computing (STOC), 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
Secrecy Through Synchronization Errors
In this paper, we propose a transmission scheme that achieves information
theoretic security, without making assumptions on the eavesdropper's channel.
This is achieved by a transmitter that deliberately introduces synchronization
errors (insertions and/or deletions) based on a shared source of randomness.
The intended receiver, having access to the same shared source of randomness as
the transmitter, can resynchronize the received sequence. On the other hand,
the eavesdropper's channel remains a synchronization error channel. We prove a
secrecy capacity theorem, provide a lower bound on the secrecy capacity, and
propose numerical methods to evaluate it.Comment: 5 pages, 6 figures, submitted to ISIT 201
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