1,977 research outputs found
Optimal Routing for the Gaussian Multiple-Relay Channel with Decode-and-Forward
In this paper, we study a routing problem on the Gaussian multiple relay
channel, in which nodes employ a decode-and-forward coding strategy. We are
interested in routes for the information flow through the relays that achieve
the highest DF rate. We first construct an algorithm that provably finds
optimal DF routes. As the algorithm runs in factorial time in the worst case,
we propose a polynomial time heuristic algorithm that finds an optimal route
with high probability. We demonstrate that that the optimal (and near optimal)
DF routes are good in practice by simulating a distributed DF coding scheme
using low density parity check codes with puncturing and incremental
redundancy.Comment: Accepted and to be presented at the 2007 IEEE International Symposium
on Information Theory (ISIT 2007), Acropolis Congress and Exhibition Center,
Nice, France, June 24-29 200
On Algebraic Decoding of -ary Reed-Muller and Product-Reed-Solomon Codes
We consider a list decoding algorithm recently proposed by Pellikaan-Wu
\cite{PW2005} for -ary Reed-Muller codes of
length when . A simple and easily accessible
correctness proof is given which shows that this algorithm achieves a relative
error-correction radius of . This is
an improvement over the proof using one-point Algebraic-Geometric codes given
in \cite{PW2005}. The described algorithm can be adapted to decode
Product-Reed-Solomon codes.
We then propose a new low complexity recursive algebraic decoding algorithm
for Reed-Muller and Product-Reed-Solomon codes. Our algorithm achieves a
relative error correction radius of . This technique is then proved to outperform the Pellikaan-Wu
method in both complexity and error correction radius over a wide range of code
rates.Comment: 5 pages, 5 figures, to be presented at 2007 IEEE International
Symposium on Information Theory, Nice, France (ISIT 2007
Cooperative Multi-Cell Networks: Impact of Limited-Capacity Backhaul and Inter-Users Links
Cooperative technology is expected to have a great impact on the performance
of cellular or, more generally, infrastructure networks. Both multicell
processing (cooperation among base stations) and relaying (cooperation at the
user level) are currently being investigated. In this presentation, recent
results regarding the performance of multicell processing and user cooperation
under the assumption of limited-capacity interbase station and inter-user
links, respectively, are reviewed. The survey focuses on related results
derived for non-fading uplink and downlink channels of simple cellular system
models. The analytical treatment, facilitated by these simple setups, enhances
the insight into the limitations imposed by limited-capacity constraints on the
gains achievable by cooperative techniques
DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models
The work identifies the first general, explicit, and non-random MIMO
encoder-decoder structures that guarantee optimality with respect to the
diversity-multiplexing tradeoff (DMT), without employing a computationally
expensive maximum-likelihood (ML) receiver. Specifically, the work establishes
the DMT optimality of a class of regularized lattice decoders, and more
importantly the DMT optimality of their lattice-reduction (LR)-aided linear
counterparts. The results hold for all channel statistics, for all channel
dimensions, and most interestingly, irrespective of the particular lattice-code
applied. As a special case, it is established that the LLL-based LR-aided
linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal
decoding of any lattice code at a worst-case complexity that grows at most
linearly in the data rate. This represents a fundamental reduction in the
decoding complexity when compared to ML decoding whose complexity is generally
exponential in rate.
The results' generality lends them applicable to a plethora of pertinent
communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI,
cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality
of the LR-aided linear decoder is guaranteed. The adopted approach yields
insight, and motivates further study, into joint transceiver designs with an
improved SNR gap to ML decoding.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions
on Information Theor
On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes
This paper addresses the issue of design of low-rate sparse-graph codes with
linear minimum distance in the blocklength. First, we define a necessary
condition which needs to be satisfied when the linear minimum distance is to be
ensured. The condition is formulated in terms of degree-1 and degree-2 variable
nodes and of low-weight codewords of the underlying code, and it generalizies
results known for turbo codes [8] and LDPC codes. Then, we present a new
ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5],
and which is designed under this necessary condition. The asymptotic analysis
of the ensemble shows that its iterative threshold is situated close to the
Shannon limit. In addition to the linear minimum distance property, it has a
simple structure and enjoys a low decoding complexity and a fast convergence.Comment: submitted to IEEE Trans. on Communication
Trajectory Codes for Flash Memory
Flash memory is well-known for its inherent asymmetry: the flash-cell charge
levels are easy to increase but are hard to decrease. In a general rewriting
model, the stored data changes its value with certain patterns. The patterns of
data updates are determined by the data structure and the application, and are
independent of the constraints imposed by the storage medium. Thus, an
appropriate coding scheme is needed so that the data changes can be updated and
stored efficiently under the storage-medium's constraints.
In this paper, we define the general rewriting problem using a graph model.
It extends many known rewriting models such as floating codes, WOM codes,
buffer codes, etc. We present a new rewriting scheme for flash memories, called
the trajectory code, for rewriting the stored data as many times as possible
without block erasures. We prove that the trajectory code is asymptotically
optimal in a wide range of scenarios.
We also present randomized rewriting codes optimized for expected performance
(given arbitrary rewriting sequences). Our rewriting codes are shown to be
asymptotically optimal.Comment: Submitted to IEEE Trans. on Inform. Theor
Rewriting Codes for Joint Information Storage in Flash Memories
Memories whose storage cells transit irreversibly between
states have been common since the start of the data storage
technology. In recent years, flash memories have become a very
important family of such memories. A flash memory cell has q
states—state 0.1.....q-1 - and can only transit from a lower
state to a higher state before the expensive erasure operation takes
place. We study rewriting codes that enable the data stored in a
group of cells to be rewritten by only shifting the cells to higher
states. Since the considered state transitions are irreversible, the
number of rewrites is bounded. Our objective is to maximize the
number of times the data can be rewritten. We focus on the joint
storage of data in flash memories, and study two rewriting codes
for two different scenarios. The first code, called floating code, is for
the joint storage of multiple variables, where every rewrite changes
one variable. The second code, called buffer code, is for remembering
the most recent data in a data stream. Many of the codes
presented here are either optimal or asymptotically optimal. We
also present bounds to the performance of general codes. The results
show that rewriting codes can integrate a flash memory’s
rewriting capabilities for different variables to a high degree
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