2,202 research outputs found
Conditions for a Monotonic Channel Capacity
Motivated by results in optical communications, where the performance can
degrade dramatically if the transmit power is sufficiently increased, the
channel capacity is characterized for various kinds of memoryless vector
channels. It is proved that for all static point-to-point channels, the channel
capacity is a nondecreasing function of power. As a consequence, maximizing the
mutual information over all input distributions with a certain power is for
such channels equivalent to maximizing it over the larger set of input
distributions with upperbounded power. For interference channels such as
optical wavelength-division multiplexing systems, the primary channel capacity
is always nondecreasing with power if all interferers transmit with identical
distributions as the primary user. Also, if all input distributions in an
interference channel are optimized jointly, then the achievable sum-rate
capacity is again nondecreasing. The results generalizes to the channel
capacity as a function of a wide class of costs, not only power.Comment: This is an updated and expanded version of arXiv:1108.039
On the Construction of Polar Codes for Achieving the Capacity of Marginal Channels
Achieving security against adversaries with unlimited computational power is
of great interest in a communication scenario. Since polar codes are capacity
achieving codes with low encoding-decoding complexity and they can approach
perfect secrecy rates for binary-input degraded wiretap channels in symmetric
settings, they are investigated extensively in the literature recently. In this
paper, a polar coding scheme to achieve secrecy capacity in non-symmetric
binary input channels is proposed. The proposed scheme satisfies security and
reliability conditions. The wiretap channel is assumed to be stochastically
degraded with respect to the legitimate channel and message distribution is
uniform. The information set is sent over channels that are good for Bob and
bad for Eve. Random bits are sent over channels that are good for both Bob and
Eve. A frozen vector is chosen randomly and is sent over channels bad for both.
We prove that there exists a frozen vector for which the coding scheme
satisfies reliability and security conditions and approaches the secrecy
capacity. We further empirically show that in the proposed scheme for
non-symmetric binary-input discrete memoryless channels, the equivocation rate
achieves its upper bound in the whole capacity-equivocation region
The Binary Energy Harvesting Channel with a Unit-Sized Battery
We consider a binary energy harvesting communication channel with a
finite-sized battery at the transmitter. In this model, the channel input is
constrained by the available energy at each channel use, which is driven by an
external energy harvesting process, the size of the battery, and the previous
channel inputs. We consider an abstraction where energy is harvested in binary
units and stored in a battery with the capacity of a single unit, and the
channel inputs are binary. Viewing the available energy in the battery as a
state, this is a state-dependent channel with input-dependent states, memory in
the states, and causal state information available at the transmitter only. We
find an equivalent representation for this channel based on the timings of the
symbols, and determine the capacity of the resulting equivalent timing channel
via an auxiliary random variable. We give achievable rates based on certain
selections of this auxiliary random variable which resemble lattice coding for
the timing channel. We develop upper bounds for the capacity by using a
genie-aided method, and also by quantifying the leakage of the state
information to the receiver. We show that the proposed achievable rates are
asymptotically capacity achieving for small energy harvesting rates. We extend
the results to the case of ternary channel inputs. Our achievable rates give
the capacity of the binary channel within 0.03 bits/channel use, the ternary
channel within 0.05 bits/channel use, and outperform basic Shannon strategies
that only consider instantaneous battery states, for all parameter values.Comment: Submitted to IEEE Transactions on Information Theory, August 201
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