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  • 1.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Coding and Transmission Strategies for Secrecy2014Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we consider several problems relating to information theoretic security. The wiretap channel is the simplest information theoretic setting which takes security into account, and in the first chapters of the thesis we design some practical coding schemes for this channel model.

    First we consider the design of two edge type low density parity check (LDPC) codes for the binary erasure wiretap channel (BEC-WT). For the scenario when the main channel is error free and the wiretapper's channel is a binary erasure channel (BEC) we find secrecy capacity achieving code sequences based on standard LDPC code sequences for the BEC. However, this construction does not work when there are also erasures on the main channel. For this case we develop a method based on linear programming to optimize two edge type degree distributions. Using this method we find code ensembles that perform close to the secrecy capacity of the BEC-WT. We generalize a method of Méasson, Montanari, and Urbanke in order to compute the conditional entropy of the message at the wiretapper. We apply this method to relatively simple ensembles and find very good secrecy performance.

    We then show that Arikan's polar codes can be used to achieve the whole capacity-equivocation region of for any degraded symmetric binary input wiretap channel. We also design capacity achieving polar codes for the decode-and-forward scheme for the physically degraded relay channel, and for the bidirectional broadcast channel with common and confidential messages.

    In the subsequent chapter we consider a Gaussian system model. We show that sparse regression codes (SPARCS) as introduced by Joseph and Barron achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel, and can be used to implement the decode-and-forward scheme for the Gaussian relay channel. We also consider secret key agreement using correlated Gaussian random variables and a rate-limited public channel. We show that SPARCs attain the capacity region also for this problem.

    Finally we consider secret key agreement over reciprocal fading channels. We first consider a multiple-antenna setup in the high signal-to-noise-ratio (SNR) regime and propose a scheme based on training and randomness sharing. We then consider a single antenna setup in the low SNR regime, where one of the terminals is only allowed to transmit pilot signals. We propose a bursty transmission scheme based on training and opportunistic transmission using a wiretap channel code, and show that this scheme is optimal.

  • 2.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Coding for the Wiretap Channel2011Licentiate thesis, monograph (Other academic)
    Abstract [en]

    We consider code design for Wyner’s wiretap channel. Optimal coding schemes for this channel require an overall code that is capacity achieving for the main channel, partitioned into smaller subcodes, all of which are capacity achieving for the wiretapper’s channel. To accomplish this we introduce two edge type low density parity check (LDPC) ensembles for the wiretap channel. For the scenario when the main channel is error free and the wiretapper’s channel is a binary erasure channel (BEC) we find secrecy capacity achieving code sequences based on standard LDPC code sequences for the BEC. However, this construction does not work when there are also erasures on the main channel. For this case we develop a method based on linear programming to optimize two edge type degree distributions. Using this method we find code ensembles that perform close to the secrecy capacity of the binary erasure wiretap channel (BEC- WT). We generalize a method of M ́easson, Montanari, and Urbanke in order to compute the conditional entropy of the message at the wire- tapper. This conditional entropy is a measure of how much information is leaked to the wiretapper. We apply this method to relatively simple ensembles and find that they show very good secrecy performance.

    Based on the work of Kudekar, Richardson, and Urbanke, which showed that regular spatially coupled codes are capacity achieving for the BEC, we construct a regular two edge type spatially coupled ensem- ble. We show that this ensemble achieves the whole capacity-equivocation region for the BEC-WT.

    We also find a coding scheme using Arıkans polar codes. These codes achieve the whole capacity-equivocation region for any symmetric binary input wiretap channel where the wiretapper’s channel is degraded with respect to the main channel.

     

  • 3.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Khisti, A.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Secure key agreement over reciprocal fading channels in the low SNR regime2013In: 2013 IEEE  14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC, IEEE , 2013, p. 674-678Conference paper (Refereed)
    Abstract [en]

    We study the low SNR scaling of the non-coherent secret-key agreement capacity over a reciprocal, block-fading channel. For the restricted class of strategies, where one of the nodes is constrained to transmit pilot-only symbols, we show that the secret-key capacity scales as SNR ·log T if T ≤ 1/SNR, where T denotes the coherence period, and as SNR·log(1/SNR) otherwise. Our upper bound is inspired by the genie-aided argument of Borade and Zheng (IT-Trans 2010). Our lower bound is based on bursty communication, channel training, and secret message transmission.

  • 4.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Khisti, Ashish
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Secret-key agreement over a non-coherent block-fading MIMO wiretap channel2012In: Information Theory Workshop (ITW), 2012 IEEE, IEEE , 2012, p. 153-157Conference paper (Refereed)
    Abstract [en]

    We study secret-key agreement over a non-coherent block-fading multiple input multiple output (MIMO) wiretap channel. We give an achievable scheme based on training and source emulation and analyze the rate in the high SNR regime. Based on this analysis we find the optimal number of antennas to use for training. Our main result is that if the sum of the number of antennas at Alice and Bob is larger than the coherence time of the channel, the achievable rate does not depend on the number of antennas at Eve. In this case source emulation is not needed, and using only training is optimal. We also consider the case when there is no public channel available. In this case we show that secret-key agreement is still possible by using the wireless channel for discussion, giving the same number of secure degrees of freedom as in the case with a public channel.

  • 5.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Rathi, Vishwambhar
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Kliewer, Joerg
    Klipsch School of Electrical and Computer Engineering New Mexico State University.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Equivocation of Eve using two edge type LDPC codes for the binary erasure wiretap channel2010In: 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2010, p. 2045-2049Conference paper (Refereed)
    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.

  • 6.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Rathi, Vishwambhar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kliewer, Jorg
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Nested Polar Codes for Wiretap and Relay Channels2010In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 14, no 8, p. 752-754Article in journal (Refereed)
    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.

  • 7.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Schaefer, Rafael F.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Polar Coding for Bidirectional Broadcast Channels with Common and Confidential Messages2013In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 31, no 9, p. 1901-1908Article in journal (Refereed)
    Abstract [en]

    The integration of multiple services such as the transmission of private, common, and confidential messages at the physical layer is becoming important for future wireless networks in order to increase spectral efficiency. In this paper, bidirectional relay networks are considered, in which a relay node establishes bidirectional communication between two other nodes using a decode-and-forward protocol. In the broadcast phase, the relay transmits additional common and confidential messages, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. This channel generalizes the broadcast channel with receiver side information considered by Kramer and Shamai. Low complexity polar codes are constructed that achieve the capacity region of both the degraded symmetric BBC, and the BBC with common and confidential messages. The use of polar codes allows an intuitive interpretation of how to incorporate receiver side information and secrecy constraints as different sets of frozen bits at the different receivers for an optimal code design. In order to show that the constructed codes achieve capacity, a tighter bound on the cardinality of an auxiliary random variable used in the converse is found using a method by Salehi.

  • 8.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Wyrembelski, R. F.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Polar codes for bidirectional broadcast channels with common and confidential messages2012In: International Symposium on Wireless Communication Systems (ISWCS), 2012, IEEE conference proceedings, 2012, p. 1014-1018Conference paper (Refereed)
    Abstract [en]

    We consider the bidirectional broadcast channel with common and confidential messages. We show that polar codes achieve the capacity of binary input symmetrical bidirectional broadcast channels with confidential messages, if one node's channel is a degraded version of the other node's channel. We also find a new bound on the cardinality of the auxiliary random variable in this setup.

  • 9.
    Andersson, Mattias
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Zaidi, Syed Ali Abbas
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Wernersson, Niklas
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Nonlinear distributed sensing for closed-loop control over Gaussian channels2011In: Communication Technologies Workshop (Swe-CTW), 2011 IEEE Swedish, IEEE conference proceedings, 2011, p. 19-23Conference paper (Refereed)
    Abstract [en]

    A scenario of distributed sensing for networked control systems is considered and a new approach to distributed sensing and transmission is presented. The state process of a scalar first order linear time invariant dynamical system is sensed by a network of wireless sensors, which then instantaneously transmit their measurements to a remotely situated control unit over parallel Gaussian channels. The control unit aims to stabilize the system in mean square sense. The proposed non-linear delay-free sensing and transmission strategy is compared with the well-known amplify-and-forward strategy, using the LQG control cost as a figure of merit. It is demonstrated that the proposed nonlinear scheme outperforms the best linear scheme even when there are only two sensors in the network. The proposed sensing and transmission scheme can be implemented with a reasonable complexity and it is shown to be robust to the uncertainties in the knowledge of the sensors about the statistics of the measurement noise and the channel noise.

  • 10.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rathi, Vishwambhar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Polar Codes for Cooperative Relaying2012In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 60, no 11, p. 3263-3273Article in journal (Refereed)
    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.

  • 11.
    Oechtering, Tobias J.
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Arimoto-Blahut algorithm for the bidirectional broadcast channel with side information2009In: 2009 IEEE Information Theory Workshop: ITW 2009, Taormina, Sicily, 2009, Vol. ITW 2009, p. 394-398Conference paper (Refereed)
    Abstract [en]

    The bidirectional broadcast channel with random states known at the encoder denotes a broadcast channel with two receivers where each receiver knows the message intended for the other and the transmitter knows the channel state. For such a channel we derive an Arimoto-Blahut-like algorithm to compute the weighted-rate sum maxima. To this end we provide an equivalent characterization of the achievable rate region using Shannon's method of transmit strategies, which we use to show that the optimal coding does not gain from time-sharing. Finally, the trade-off of the input distribution and the impact of the random state is discussed in two examples.

  • 12.
    Rathi, Vishwambhar
    et al.
    Nvidia Corporation, United States.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kliewer, Joerg
    Klipsch School of Electrical and Computer Engineering New Mexico State University.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Performance analysis and design of two edge-type LDPC codes for the BEC wiretap channel2013In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 59, no 2, p. 1048-1064Article in journal (Refereed)
    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.

  • 13.
    Rathi, Vishwambhar
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragner
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kliewer, Jörg
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Two edge type LDPC codes for the wiretap channel2009In: Conference Record - Asilomar Conference on Signals, 2009, Vol. Systems and Computers, p. 834-838Conference paper (Refereed)
    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.

  • 14.
    Rathi, Vishwambhar
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Urbanke, Rüdiger
    Information processing group, École Polytechnique Fédérale de Lausanne.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Rate-equivocation optimal spatially coupled LDPC codes for the BEC wiretap channel2011In: IEEE International Symposium on Information Theorys (ISIT), 2011, IEEE Press, 2011, p. 2393-2397Conference paper (Refereed)
    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.

  • 15.
    Schrammar, Nicolas
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Approximate Capacity of the General Gaussian Parallel Relay Network2011In: Proc. IEEE Intl. Symposium of Information Theory 2011, IEEE conference proceedings, 2011, p. 89-93Conference paper (Refereed)
    Abstract [en]

    We approximate the capacity of the Gaussian parallel relay network with general channel gains. Our strategy is to find capacity approximations for the corresponding network in the discrete superposition model and to use the fact that those are an approximation for the Gaussian capacity. The gap between our approximation and the Gaussian capacity is a constant depending only on the number of relays, hence it is a valuable characterization for the regime of high SNR and high rate.

  • 16.
    Si, Zhongwei
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Mattias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rate-compatible LDPC convolutional codes for capacity-approaching hybrid ARQ2011In: 2011 IEEE Information Theory Workshop (ITW), 2011, p. 513-517Conference paper (Refereed)
    Abstract [en]

    In this paper we construct a family of rate-compatible LDPC convolutional codes for Type-II HARQ systems. For each code family, the codes of lower rates are constructed by successively extending the graph of the high-rate base code. Theoretically, the proposed rate-compatible family includes all rates from 0 to 1. We prove analytically that all LDPC convolutional codes in the family are capacity achieving over the binary erasure channel (BEC). Thus, if applied to an idealized HARQ system over the BEC where the channel parameter stays constant within one complete information delivery, the throughput achieves the capacity of the channel. Moreover, the code construction is realized by regular degree distributions, which greatly simplifies the optimization.

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