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      LDPC Code Design for the BPSK-constrained Gaussian Wiretap Channel

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          Abstract

          A coding scheme based on irregular low-density parity-check (LDPC) codes is proposed to send secret messages from a source over the Gaussian wiretap channel to a destination in the presence of a wiretapper, with the restriction that the source can send only binary phase-shift keyed (BPSK) symbols. The secrecy performance of the proposed coding scheme is measured by the secret message rate through the wiretap channel as well as the equivocation rate about the message at the wiretapper. A code search procedure is suggested to obtain irregular LDPC codes that achieve good secrecy performance in such context.

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          The capacity of low-density parity-check codes under message-passing decoding

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            Design of capacity-approaching irregular low-density parity-check codes

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              Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels

              (2009)
              A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity \(I(W)\) of any given binary-input discrete memoryless channel (B-DMC) \(W\). The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of \(N\) independent copies of a given B-DMC \(W\), a second set of \(N\) binary-input channels \(\{W_N^{(i)}:1\le i\le N\}\) such that, as \(N\) becomes large, the fraction of indices \(i\) for which \(I(W_N^{(i)})\) is near 1 approaches \(I(W)\) and the fraction for which \(I(W_N^{(i)})\) is near 0 approaches \(1-I(W)\). The polarized channels \(\{W_N^{(i)}\}\) are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC \(W\) with \(I(W)>0\) and any target rate \(R < I(W)\), there exists a sequence of polar codes \(\{{\mathscr C}_n;n\ge 1\}\) such that \({\mathscr C}_n\) has block-length \(N=2^n\), rate \(\ge R\), and probability of block error under successive cancellation decoding bounded as \(P_{e}(N,R) \le \bigoh(N^{-\frac14})\) independently of the code rate. This performance is achievable by encoders and decoders with complexity \(O(N\log N)\) for each.
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                Author and article information

                Journal
                2011-03-20
                Article
                10.1109/GLOCOMW.2011.6162586
                1103.3915
                978f23e0-5bf9-44b9-8047-a3646cea0655

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                submitted to IEEE GLOBECOM 2011 - Communication Theory Symposium
                cs.IT math.IT

                Numerical methods,Information systems & theory
                Numerical methods, Information systems & theory

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