9,308 research outputs found
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
Distributed Storage in Mobile Wireless Networks with Device-to-Device Communication
We consider the use of distributed storage (DS) to reduce the communication
cost of content delivery in wireless networks. Content is stored (cached) in a
number of mobile devices using an erasure correcting code. Users retrieve
content from other devices using device-to-device communication or from the
base station (BS), at the expense of higher communication cost. We address the
repair problem when a device storing data leaves the cell. We introduce a
repair scheduling where repair is performed periodically and derive analytical
expressions for the overall communication cost of content download and data
repair as a function of the repair interval. The derived expressions are then
used to evaluate the communication cost entailed by DS using several erasure
correcting codes. Our results show that DS can reduce the communication cost
with respect to the case where content is downloaded only from the BS, provided
that repairs are performed frequently enough. If devices storing content arrive
to the cell, the communication cost using DS is further reduced and, for large
enough arrival rate, it is always beneficial. Interestingly, we show that MDS
codes, which do not perform well for classical DS, can yield a low overall
communication cost in wireless DS.Comment: After final editing for publication in TCO
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
- …