15,011 research outputs found
Polynomial-Time Approximation Scheme for Data Broadcast
The data broadcast problem is to find a schedule for broadcasting a given set
of messages over multiple channels. The goal is to minimize the cost of the
broadcast plus the expected response time to clients who periodically and
probabilistically tune in to wait for particular messages.
The problem models disseminating data to clients in asymmetric communication
environments, where there is a much larger capacity from the information source
to the clients than in the reverse direction. Examples include satellites,
cable TV, internet broadcast, and mobile phones. Such environments favor the
``push-based'' model where the server broadcasts (pushes) its information on
the communication medium and multiple clients simultaneously retrieve the
specific information of individual interest.
This paper presents the first polynomial-time approximation scheme (PTAS) for
data broadcast with O(1) channels and when each message has arbitrary
probability, unit length and bounded cost. The best previous polynomial-time
approximation algorithm for this case has a performance ratio of 9/8
On the Degrees of Freedom of Asymmetric MIMO Interference Broadcast Channels
In this paper, we study the degrees of freedom (DoF) of the asymmetric
multi-input-multi-output interference broadcast channel (MIMO-IBC). By
introducing a notion of connection pattern chain, we generalize the genie chain
proposed in [11] to derive and prove the necessary condition of IA feasibility
for asymmetric MIMO-IBC, which is denoted as irreducible condition. It is
necessary for both linear interference alignment (IA) and asymptotic IA
feasibility in MIMO-IBC with arbitrary configurations. In a special class of
asymmetric two-cell MIMOIBC, the irreducible condition is proved to be the
sufficient and necessary condition for asymptotic IA feasibility, while the
combination of proper condition and irreducible condition is proved to the
sufficient and necessary condition for linear IA feasibility. From these
conditions, we derive the information theoretic maximal DoF per user and the
maximal DoF per user achieved by linear IA, and these DoFs are also the DoF per
user upper-bounds of asymmetric G-cell MIMO-IBC with asymptotic IA and linear
IA, respectively.Comment: 6 pages, 3 figures, submitted to ICC 201
Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes
We propose efficient coding schemes for two communication settings: 1.
asymmetric channels, and 2. channels with an informed encoder. These settings
are important in non-volatile memories, as well as optical and broadcast
communication. The schemes are based on non-linear polar codes, and they build
on and improve recent work on these settings. In asymmetric channels, we tackle
the exponential storage requirement of previously known schemes, that resulted
from the use of large Boolean functions. We propose an improved scheme, that
achieves the capacity of asymmetric channels with polynomial computational
complexity and storage requirement.
The proposed non-linear scheme is then generalized to the setting of channel
coding with an informed encoder, using a multicoding technique. We consider
specific instances of the scheme for flash memories, that incorporate
error-correction capabilities together with rewriting. Since the considered
codes are non-linear, they eliminate the requirement of previously known
schemes (called polar write-once-memory codes) for shared randomness between
the encoder and the decoder. Finally, we mention that the multicoding scheme is
also useful for broadcast communication in Marton's region, improving upon
previous schemes for this setting.Comment: Submitted to IEEE Transactions on Information Theory. Partially
presented at ISIT 201
Asymmetric Multi-Party Computation
Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound ?, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources.
We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay ? among themselves, while channels connected to (at least) one slow party have a large delay ? ? ?. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting:
- An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds.
- We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC.
- We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n.
- An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size.
In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction
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