45,594 research outputs found
Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints
In this paper, we present two low complexity algorithms that achieve capacity
for the noiseless (d,k) constrained channel when k=2d+1, or when k-d+1 is not
prime. The first algorithm, called symbol sliding, is a generalized version of
the bit flipping algorithm introduced by Aviran et al. [1]. In addition to
achieving capacity for (d,2d+1) constraints, it comes close to capacity in
other cases. The second algorithm is based on interleaving, and is a
generalized version of the bit stuffing algorithm introduced by Bender and Wolf
[2]. This method uses fewer than k-d biased bit streams to achieve capacity for
(d,k) constraints with k-d+1 not prime. In particular, the encoder for
(d,d+2^m-1) constraints, 1\le m<\infty, requires only m biased bit streams.Comment: 16 pages, submitted to the IEEE Transactions on Information Theor
Achieving Marton's Region for Broadcast Channels Using Polar Codes
This paper presents polar coding schemes for the 2-user discrete memoryless
broadcast channel (DM-BC) which achieve Marton's region with both common and
private messages. This is the best achievable rate region known to date, and it
is tight for all classes of 2-user DM-BCs whose capacity regions are known. To
accomplish this task, we first construct polar codes for both the superposition
as well as the binning strategy. By combining these two schemes, we obtain
Marton's region with private messages only. Finally, we show how to handle the
case of common information. The proposed coding schemes possess the usual
advantages of polar codes, i.e., they have low encoding and decoding complexity
and a super-polynomial decay rate of the error probability.
We follow the lead of Goela, Abbe, and Gastpar, who recently introduced polar
codes emulating the superposition and binning schemes. In order to align the
polar indices, for both schemes, their solution involves some degradedness
constraints that are assumed to hold between the auxiliary random variables and
the channel outputs. To remove these constraints, we consider the transmission
of blocks and employ a chaining construction that guarantees the proper
alignment of the polarized indices. The techniques described in this work are
quite general, and they can be adopted to many other multi-terminal scenarios
whenever there polar indices need to be aligned.Comment: 26 pages, 11 figures, accepted to IEEE Trans. Inform. Theory and
presented in part at ISIT'1
Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for the Erasure Channel with Bounded Complexity
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes
which asymptotically achieve capacity on the binary erasure channel (BEC) with
{\em bounded complexity}, per information bit, of encoding and decoding. It
also introduces symmetry properties which play a central role in the
construction of capacity-achieving ensembles for the BEC with bounded
complexity. The results here improve on the tradeoff between performance and
complexity provided by previous constructions of capacity-achieving ensembles
of codes defined on graphs. The superiority of ARA codes with moderate to large
block length is exemplified by computer simulations which compare their
performance with those of previously reported capacity-achieving ensembles of
LDPC and IRA codes. The ARA codes also have the advantage of being systematic.Comment: Submitted to IEEE Trans. on Information Theory, December 1st, 2005.
Includes 50 pages and 13 figure
Secure Cooperative Regenerating Codes for Distributed Storage Systems
Regenerating codes enable trading off repair bandwidth for storage in
distributed storage systems (DSS). Due to their distributed nature, these
systems are intrinsically susceptible to attacks, and they may also be subject
to multiple simultaneous node failures. Cooperative regenerating codes allow
bandwidth efficient repair of multiple simultaneous node failures. This paper
analyzes storage systems that employ cooperative regenerating codes that are
robust to (passive) eavesdroppers. The analysis is divided into two parts,
studying both minimum bandwidth and minimum storage cooperative regenerating
scenarios. First, the secrecy capacity for minimum bandwidth cooperative
regenerating codes is characterized. Second, for minimum storage cooperative
regenerating codes, a secure file size upper bound and achievability results
are provided. These results establish the secrecy capacity for the minimum
storage scenario for certain special cases. In all scenarios, the achievability
results correspond to exact repair, and secure file size upper bounds are
obtained using min-cut analyses over a suitable secrecy graph representation of
DSS. The main achievability argument is based on an appropriate pre-coding of
the data to eliminate the information leakage to the eavesdropper
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