Codes With Local Regeneration and Erasure Correction

Regenerating codes and codes with locality are two coding schemes that have recently been proposed, which in addition to ensuring data collection and reliability, also enable efficient node repair. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. This paper presents results in two directions. In one, this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures, by employing local codes having minimum distance >2. An upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed. The second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes. These codes, termed here as codes with local regeneration, are codes with locality over a vector alphabet, in which the local codes themselves are regenerating codes. We derive an upper bound on the minimum distance of vector-alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property. This property is possessed by both minimum storage regeneration (MSR) and minimum bandwidth regeneration (MBR) codes. We provide several constructions of codes with local regeneration which achieve this bound, where the local codes are either MSR or MBR codes. Also included in this paper, is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance.

Interference-Constrained Optimal Power-Adaptive Amplify-and-Forward Relaying and Selection for Underlay Cognitive Radios

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

Optimal Binary Power Control for Underlay CR With Different Interference Constraints and Impact of Channel Estimation Errors

Adapting the power of secondary users (SUs) while adhering to constraints on the interference caused to primary receivers (PRxs) is a critical issue in underlay cognitive radio (CR). This adaptation is driven by the interference and transmit power constraints imposed on the secondary transmitter (STx). Its performance also depends on the quality of channel state information (CSI) available at the STx of the links from the STx to the secondary receiver and to the PRxs. For a system in which an STx is subject to an average interference constraint or an interference outage probability constraint at each of the PRxs, we derive novel symbol error probability (SEP)-optimal, practically motivated binary transmit power control policies. As a reference, we also present the corresponding SEP-optimal continuous transmit power control policies for one PRx. We then analyze the robustness of the optimal policies when the STx knows noisy channel estimates of the links between the SU and the PRxs. Altogether, our work develops a holistic understanding of the critical role played by different transmit and interference constraints in driving power control in underlay CR and the impact of CSI on its performance.

Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

Space-Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using coordinate interleaved orthogonal designs (CIODs). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space-time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, adaptive network coding (ANC) is employed at the relay and the relay transmits a CIOD space time block code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBCs are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of O(M-3) for an arbitrary signal set and O(M-2 root M) for square QAM signal set. Simulation results show that the proposed schemes performs better than the existing ANC schemes under perfect and imperfect channel state information.

Efficient Dictionary for Salted Password Analysis

User authentication is essential for accessing computing resources, network resources, email accounts, online portals etc. To authenticate a user, system stores user credentials (user id and password pair) in system. It has been an interested field problem to discover user password from a system and similarly protecting them against any such possible attack. In this work we show that passwords are still vulnerable to hash chain based and efficient dictionary attacks. Human generated passwords use some identifiable patterns. We have analysed a sample of 19 million passwords, of different lengths, available online and studied the distribution of the symbols in the password strings. We show that the distribution of symbols in user passwords is affected by the native language of the user. From symbol distributions we can build smart and efficient dictionaries, which are smaller in size and their coverage of plausible passwords from Key-space is large. These smart dictionaries make dictionary based attacks practical.

Direct Link-Aware Optimal Relay Selection and a Low Feedback Variant for Underlay CR

Cooperative relaying combined with selection has been extensively studied in the literature to improve the performance of interference-constrained secondary users in underlay cognitive radio (CR). We present a novel symbol error probability (SEP)-optimal amplify-and-forward relay selection rule for an average interference-constrained underlay CR system. A fundamental principle, which is unique to average interference-constrained underlay CR, that the proposed rule brings out is that the choice of the optimal relay is affected not just by the source-to-relay, relay-to-destination, and relay-to-primary receiver links, which are local to the relay, but also by the direct source-to-destination (SD) link, even though it is not local to any relay. We also propose a simpler, practically amenable variant of the optimal rule called the 1-bit rule, which requires just one bit of feedback about the SD link gain to the relays, and incurs a marginal performance loss relative to the optimal rule. We analyze its SEP and develop an insightful asymptotic SEP analysis. The proposed rules markedly outperform several ad hoc SD link-unaware rules proposed in the literature. They also generalize the interference-unconstrained and SD link-unaware optimal rules considered in the literature.

Spatial Modulation Aided Zero-Padded Single Carrier Transmission for Dispersive Channels

In this paper, we consider spatial modulation (SM) operating in a frequency-selective single-carrier (SC) communication scenario and propose zero-padding instead of the cyclic-prefix considered in the existing literature. We show that the zero-padded single-carrier (ZP-SC) SM system offers full multipath diversity under maximum-likelihood (ML) detection, unlike the cyclic-prefix based SM system. Furthermore, we show that the order of ML detection complexity in our proposed ZP-SC SM system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver. Thus, we show that the zero-padding applied in the SC SM system has two advantages over the cyclic prefix: 1) achieves full multipath diversity, and 2) imposes a relatively low ML detection complexity. Furthermore, we extend the partial interference cancellation receiver (PIC-R) proposed by Guo and Xia for the detection of space-time block codes (STBCs) in order to convert the ZP-SC system into a set of narrowband subsystems experiencing flat-fading. We show that full rank STBC transmissions over these subsystems achieves full transmit, receive as well as multipath diversity for the PIC-R. Furthermore, we show that the ZP-SC SM system achieves receive and multipath diversity for the PIC-R at a detection complexity order which is the same as that of the SM system in flat-fading scenario. Our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the ZP-SC SM system is significantly better than that of the SM in cyclic prefix based orthogonal frequency division multiplexing as well as of the SM in the cyclic-prefixed and zero-padded single carrier systems relying on zero-forcing/minimum mean-squared error equalizer based receivers.

Quantifying the Transmit Diversity Order of Euclidean Distance Based Antenna Selection in Spatial Modulation

In this letter, we quantify the transmit diversity order of the SM system operating in a closed-loop scenario. Specifically, the SM system relying on Euclidean distance based antenna subset selection (EDAS) is considered and the achievable diversity gain is evaluated. Furthermore, the resultant trade-off between the achievable diversity gain and switching gain is studied. Simulation results confirm our theoretical results. Specifically, at a symbol error rate of about 10(-4) the signal-to-noise ratio gain achieved by EDAS is about 7 dB in case of 16-QAM and about 5 dB in case of 64-QAM.

Novel Relay Selection Rules for Average Interference-Constrained Cognitive AF Relay Networks

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. However, unlike conventional relaying, the state of the links between the relay and the primary receiver affects the choice of the relay. Further, while the optimal amplify-and-forward (AF) relay selection rule for underlay CR is well understood for the peak interference-constraint, this is not so for the less conservative average interference constraint. For the latter, we present three novel AF relay selection (RS) rules, namely, symbol error probability (SEP)-optimal, inverse-of-affine (IOA), and linear rules. We analyze the SEPs of the IOA and linear rules and also develop a novel, accurate approximation technique for analyzing the performance of AF relays. Extensive numerical results show that all the three rules outperform several RS rules proposed in the literature and generalize the conventional AF RS rule.

Recognition of open vocabulary, online handwritten pages in Tamil script

In this work, we describe a system, which recognises open vocabulary, isolated, online handwritten Tamil words and extend it to recognize a paragraph of writing. We explain in detail each step involved in the process: segmentation, preprocessing, feature extraction, classification and bigram-based post-processing. On our database of 45,000 handwritten words obtained through tablet PC, we have obtained symbol level accuracy of 78.5% and 85.3% without and with the usage of post-processing using symbol level language models, respectively. Word level accuracies for the same are 40.1% and 59.6%. A line and word level segmentation strategy is proposed, which gives promising results of 100% line segmentation and 98.1% word segmentation accuracies on our initial trials of 40 handwritten paragraphs. The two modules have been combined to obtain a full-fledged page recognition system for online handwritten Tamil data. To the knowledge of the authors, this is the first ever attempt on recognition of open vocabulary, online handwritten paragraphs in any Indian language.

Direct Link-Aware Relay Selection for Average Interference-Constrained Underlay Cognitive Radio

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio network. We present a novel and optimal relay selection (RS) rule that minimizes the symbol error probability (SEP) of an average interference-constrained underlay secondary system that uses amplify-and-forward relays. A key point that the rule highlights for the first time is that, for the average interference constraint, the signal-to-interference-plus-noise-ratio (SINR) of the direct source-to-destination (SI)) link affects the choice of the optimal relay. Furthermore, as the SINR increases, the odds that no relay transmits increase. We also propose a simpler, more practical, and near-optimal variant of the optimal rule that requires just one bit of feedback about the state of the SD link to the relays. Compared to the SD-unaware ad hoc RS rules proposed in the literature, the proposed rules markedly reduce the SEP by up to two orders of magnitude.