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  • 1.
    Andersson, Mattias
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Thobaben, Ragnar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Kliewer, Joerg
    Klipsch School of Electrical and Computer Engineering New Mexico State University.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Equivocation of Eve using two edge type LDPC codes for the binary erasure wiretap channel2010Ingår i: 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2010, s. 2045-2049Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider transmission over a binary erasure wiretap channel using the code construction method introduced by Rathi et al. based on two edge type Low-Density Parity-Check (LDPC) codes and the coset encoding scheme. By generalizing the method of computing conditional entropy for standard LDPC ensembles introduced by Méasson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity.

  • 2.
    Andersson, Mattias
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Kliewer, Jorg
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Nested Polar Codes for Wiretap and Relay Channels2010Ingår i: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 14, nr 8, s. 752-754Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.

  • 3. Andriyanova, I.
    et al.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Tillich, J. -P
    Binary weight distribution of non-binary LDPC codes2009Ingår i: 2009 IEEE International Symposium on Information Theory, IEEE , 2009, s. 65-69Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper is the first part of an investigation if the capacity of a binary-input memoryless symmetric channel under ML decoding can be achieved asymptotically by using non-binary LDPC codes. We consider (l.r)-regular LDPC codes both over finite fields and over the general linear group and compute their asymptotic binary weight distributions in the limit of large blocklength and of large alphabet size. A surprising fact, the average binary weight distributions that we obtain do not tend to the binomial one for values of normalized binary weights ω smaller than 1-2-l/r. However, it does not mean that non-binary codes do not achieve the capacity asymptotically, but rather that there exists some exponentially small fraction of codes in the ensemble, which contains an exponentially large number of codewords of poor weight. The justification of this fact is beyond the scope of this paper and will be given in [1].

  • 4.
    Blasco-Serrano, Ricardo
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Polar Codes for Cooperative Relaying2012Ingår i: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 60, nr 11, s. 3263-3273Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the symmetric discrete memoryless relay channel with orthogonal receiver components and show that polar codes are suitable for decode-and-forward and compress-and-forward relaying. In the first case we prove that polar codes are capacity achieving for the physically degraded relay channel; for stochastically degraded relay channels our construction provides an achievable rate. In the second case we construct sequences of polar codes that achieve the compress-and-forward rate by nesting polar codes for source compression into polar codes for channel coding. In both cases our constructions inherit most of the properties of polar codes. In particular, the encoding and decoding algorithms and the bound on the block error probability O(2 (N beta)) which holds for any 0 < beta < 1/2.

  • 5.
    Blasco-Serrano, Ricardo
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Polar codes for compress-and-forward in binary relay channels2010Ingår i: 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010, IEEE conference proceedings, 2010, s. 1743-1747Konferensbidrag (Refereegranskat)
    Abstract [en]

    We construct polar codes for binary relay channels with orthogonal receiver components. We show that polar codes achieve the cut-set bound when the channels are symmetric and the relay-destination link supports compress-and-forward relaying based on Slepian-Wolf coding. More generally, we show that a particular version of the compress-and-forward rate is achievable using polar codes for Wyner-Ziv coding. In both cases the block error probability can be bounded as O(2-Nβ) for 0 < β < 1/2 and sufficiently large block length N.

  • 6.
    Demay, Gregory
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehöj
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Optimality of LDGM-LDPC compound codes for lossy compression of binary erasure source2010Ingår i: 2010 20th International Symposium on Information Theory and Its Applications, ISITA 2010 and the 2010 20th International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 2010, 2010, s. 589-594Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider the Binary Erasure Source (BES) introduced by Martinian and Yedidia. Based on the technique introduced by Martinian and Wainwright, we upper bound the rate-distortion performance of the check regular Poisson LDGM ensemble and the compound LDGM-LDPC ensemble for the BES. We also show that there exist compound LDGM-LDPC codes, with degrees independent of the block-length, which can achieve any given point on the Shannon rate-distortion curve of the BES.

  • 7.
    Demay, Gregory
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehöj
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rate distortion bounds for binary erasure source using sparse graph codes2010Ingår i: Data Compression Conference, DCC 2010, 2010, s. 49-58Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider lower bounds on the rate-distortion performance for the binary erasure source (BES) introduced by Martinian and Yedidia, using sparse graph codes for compression. Our approach follows that of Kudekar and Urbanke, where lower bounds on the rate distortion performance of low-density generator matrix (LDGM) codes for the binary symmetric source (BSS) are derived. They introduced two methods for deriving lower bounds, namely the counting method and the test channel method. Based on numerical results they observed that the two methods lead to the same bound. We generalize these two methods for the BES and prove that indeed both methods lead to identical rate-distortion bounds for the BES and hence, also for the BSS.

  • 8.
    Oechtering, Tobias
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rathi, Vishwambhar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Coding of streaming sources for the bidirectional broadcast channel: (Invited Paper)2010Ingår i: 2010 5th International ICST Conference on Communications and Networking in China, ChinaCom 2010, IEEE , 2010, s. 5684634-Konferensbidrag (Refereegranskat)
    Abstract [en]

    The bidirectional broadcast channel denotes a broadcast channel with two receivers where each receiver knows the message intended for the other. We consider streaming sources where messages of each user arrive as bit-stream to the encoder. Thus our main quantity of interest is the bit error probability. By extending Sahai's argument to bidirectional broadcast channel, we show that under maximum-likelihood decoding the bit error probability decays exponentially in delay with positive exponent for all the rate pairs inside the capacity region. We also show existence of deterministic codes which achieve exponentially decaying bit error probability with delay.

  • 9.
    Rathi, Vishwambhar
    et al.
    Nvidia Corporation, United States.
    Andersson, Mattias
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Kliewer, Joerg
    Klipsch School of Electrical and Computer Engineering New Mexico State University.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Performance analysis and design of two edge-type LDPC codes for the BEC wiretap channel2013Ingår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 59, nr 2, s. 1048-1064Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are binary erasure channels (BEC). A code construction method is proposed using two edge-type low-density parity-check (LDPC) codes based on the coset encoding scheme. Using a single edge-type LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge-type LDPC ensemble with the same threshold. If the given single edge-type LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the main channel. In order to circumvent this problem, the degree distribution of the two edge-type LDPC ensemble is numerically optimized. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. Further, a method to compute the ensemble average equivocation of two edge-type LDPC ensembles is provided by generalizing a recently published approach to measure the equivocation of single edge-type ensembles for transmission over the BEC in the point-to-point setting. From this analysis, we find that relatively simple constructions give very good secrecy performance.

  • 10.
    Rathi, Vishwambhar
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Thobaben, Ragner
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Kliewer, Jörg
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Two edge type LDPC codes for the wiretap channel2009Ingår i: Conference Record - Asilomar Conference on Signals, 2009, Vol. Systems and Computers, s. 834-838Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction using two edge type LDPC codes based on the method of Thangaraj, Dihidar, Calderbank, McLaughlin and Merolla. The advantage of our construction is that we can easily calculate the threshold over the main channel. Using standard LDPC codes with a given threshold over the BEC we give a construction for a two edge type LDPC code with the same threshold. Since this construction gives a code for the main channel with threshold zero we also give numerical methods to find two edge type LDPC codes with non-zero threshold for the main channel.

  • 11.
    Rathi, Vishwambhar
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Andriyanova, Iryna
    Some Results on MAP Decoding of Non-Binary LDPC Codes Over the BEC2011Ingår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, nr 4, s. 2225-2242Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the transmission over the binary erasure channel (BEC) using non-binary LDPC (NBLDPC) codes is considered. The concept of peeling decoder and stopping sets is generalized to NBLDPC codes. Using these generalizations, a combinatorial characterization of decoding failures of NBLDPC codes is given, under assumption that the Belief Propagation (BP) decoder is used. Then, the residual ensemble of codes resulted by the BP decoder is defined and the design rate and the expectation of total number of codewords of the residual ensemble are computed. The decoding failure criterion combined with the density evolution analysis helps us to compute the asymptotic residual degree distribution for NBLDPC codes. Our approach to compute the residual degree distribution on the check node side is not efficient as it is based on enumeration of all the possible connections on the check node side which satisfy the decoding failure criterion. So, the computation of the asymptotic check node side residual degree distribution and further part of our analysis is performed for NBLDPC codes over GF(2)(m) with m = 2. In order to show that asymptotically almost every code in such LDPC ensemble has a rate equal to the design rate, we generalize the argument of the Maxwell construction to NBLDPC codes, defined over FG(2)(2). It is also observed that, like in the binary setting, the Maxwell construction, relating the performance of MAP and BP decoding holds in this setting.

  • 12.
    Rathi, Vishwambhar
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Aurell, Erik
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehöj
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Bounds on Threshold of Regular Random k-SAT2010Ingår i: Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349, Vol. 6175, s. 264-277Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. in [6]. In [6], it was shown that the threshold for regular random 2-SAT is equal to unity. Also, upper and lower bound on the threshold for regular random 3-SAT were derived. Using the first moment method, we derive an upper bound on the threshold for regular random k-SAT for any k >= 3 and show that for large k the threshold is upper bounded by 2(k) ln(2). We also derive upper bounds on the threshold for Not-All-Equal (NAE) satisfiability for k >= 3 and show that for large k, the NAE-satisfiability threshold is upper bounded by 2(k-1) ln(2). For both satisfiability and NAE-satisfiability, the obtained upper bound matches with the corresponding bound for the uniform model of formula generation [9, 1]. For the uniform model, in a series of break through papers Achlioptas, Moore, and Peres showed that a careful application of the second moment method yields a significantly better lower bound on threshold as compared to any rigorously proven algorithmic bound [3, I]. The second moment method shows the existence of a satisfying assignment with uniform positive probability (w.u.p.p.). Thanks to the result of Friedgut for uniform model [ 1 0], existence of a satisfying assignment w.u.p.p. translates to existence of a satisfying assignment with high probability (w.h.p.). Thus, the second moment method gives a lower bound on the threshold. As there is no known Friedgut type result for regular random model, we assume that for regular random model existence of a satisfying assignments w.u.p.p. translates to existence of a satisfying assignments w.h.p. We derive the second moment of the number of satisfying assignments for regular random k-SAT for k >= 3. There are two aspects in deriving the lower bound using the second moment method. The first aspect is given any k, numerically evaluate the lower bound on the threshold. The second aspect is to derive the lower bound as a function of k for large enough k. We address the first aspect and evaluate the lower bound on threshold. The numerical evaluation suggests that as k increases the obtained lower bound on the satisfiability threshold of a regular random formula converges to the lower bound obtained for the uniform model. Similarly, we obtain lower bounds on the NAE-satisfiability threshold of the regular random formulas and observe that the obtained lower bound seems to converge to the corresponding lower bound for the uniform model as k increases.

  • 13.
    Rathi, Vishwambhar
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Aurell, Erik
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB.
    Rasmussen, Lars Kildehöj
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Bounds on thresholds related to maximum satisfiability of regular random formulas2010Ingår i: 6th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 2010, s. 107-111Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider the regular balanced model of satisfiability formula generation in conjunctive normal form (CNF), where each literal participates in equal number of clauses and there are k literals participating in a clause. We say that a formula is p-satisfying if there is a truth assignment satisfying 1 - 2-k + p2- fraction of clauses. Using the first moment method we determine upper bound on the threshold clause density such that there are no p-satisfying assignments with high probability above this upper bound. There are two aspects in deriving the lower bound using the second moment method. The first aspect is, given any p ∈ (0,1) and k, evaluate the lower bound on the threshold. This evaluation is numerical in nature. The second aspect is to derive the lower bound as a function of p for large enough k. We address the first aspect and evaluate the lower bound on the p-satisfying threshold using the second moment method. Based on the numerical evaluation, we observe that as k increases the ratio of the lower bound and the upper bound seems to converge to one.

  • 14.
    Rathi, Vishwambhar
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Urbanke, Rüdiger
    Information processing group, École Polytechnique Fédérale de Lausanne.
    Andersson, Mattias
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Skoglund, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsteori.
    Rate-equivocation optimal spatially coupled LDPC codes for the BEC wiretap channel2011Ingår i: IEEE International Symposium on Information Theorys (ISIT), 2011, IEEE Press, 2011, s. 2393-2397Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use regular convolutional LDPC ensembles, introduced by Felström and Zigangirov, together with Wyner's coset encoding scheme. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. This result is based on the recent observation by Kudekar, Richardson, and Urbanke who proved that convolutional LDPC ensembles exhibit a “threshold saturation” phenomenon which converts the MAP threshold into the BP threshold for transmission over the BEC. Although our present result is less general (since we only consider the BEC) than the elegant code constructions based on polar codes which were recently introduced by several research groups, we see two potential advantages which we believe makes our construction worth considering. First, the proposed codes have a significantly better performance already for moderate lengths. Second, and perhaps more importantly, the proposed construction has the potential of being universal. More precisely, the phenomenon of spatial coupling has been observed empirically to hold for general binary memoryless symmetric channels as well. Hence, we conjecture that our construction is a universal rate-equivocation achieving construction when the main channel and wiretapper's channel are binary memoryless symmetric channels, and the wiretapper's channel is degraded with respect to the main channel.

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