658 research outputs found
Optimal Rate for Irregular LDPC Codes in Binary Erasure Channel
In this paper, we introduce a new practical and general method for solving
the main problem of designing the capacity approaching, optimal rate, irregular
low-density parity-check (LDPC) code ensemble over binary erasure channel
(BEC). Compared to some new researches, which are based on application of
asymptotic analysis tools out of optimization process, the proposed method is
much simpler, faster, accurate and practical. Because of not using any
relaxation or any approximate solution like previous works, the found answer
with this method is optimal. We can construct optimal variable node degree
distribution for any given binary erasure rate, {\epsilon}, and any check node
degree distribution. The presented method is implemented and works well in
practice. The time complexity of this method is of polynomial order. As a
result, we obtain some degree distribution which their rates are close to the
capacity.Comment: 5 pages, to be presented at the 2011 IEEE Information Theory Workshop
(ITW 2011), Paraty, Brazil, October, 201
A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC
We derive a new fast convergent Density Evolution algorithm for finding
optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure
channel (BEC). The fast convergence property comes from the modified Density
Evolution (DE), a numerical method for analyzing the behavior of iterative
decoding convergence of a LDPC code. We have used the method of [16] for
designing of a LDPC code with optimal rate. This has been done for a given
parity check node degree distribution, erasure probability and specified DE
constraint. The fast behavior of DE and found optimal rate with this method
compare with the previous DE constraint.Comment: This Paper is a draft of final paper which represented in 7th
International Symposium on Telecommunications (IST'2014
Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels
This paper describes an efficient implementation of binning for the relay
channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC
codes to approach the theoretically promised rate of the decode-and-forward
relaying strategy by incorporating relay-generated information bits in
specially designed bilayer graphical code structures. While conventional LDPC
codes are sensitively tuned to operate efficiently at a certain channel
parameter, the proposed bilayer LDPC codes are capable of working at two
different channel parameters and two different rates: that at the relay and at
the destination. To analyze the performance of bilayer LDPC codes, bilayer
density evolution is devised as an extension of the standard density evolution
algorithm. Based on bilayer density evolution, a design methodology is
developed for the bilayer codes in which the degree distribution is iteratively
improved using linear programming. Further, in order to approach the
theoretical decode-and-forward rate for a wide range of channel parameters,
this paper proposes two different forms bilayer codes, the bilayer-expurgated
and bilayer-lengthened codes. It is demonstrated that a properly designed
bilayer LDPC code can achieve an asymptotic infinite-length threshold within
0.24 dB gap to the Shannon limits of two different channels simultaneously for
a wide range of channel parameters. By practical code construction,
finite-length bilayer codes are shown to be able to approach within a 0.6 dB
gap to the theoretical decode-and-forward rate of the relay channel at a block
length of and a bit-error probability (BER) of . Finally, it is
demonstrated that a generalized version of the proposed bilayer code
construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor
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