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In a recent work, Nazer and Gastpar proposed the compute-and-forward strategy as a physical-layer network coding scheme. They described a code structure based on nested lattices whose algebraic structure makes the scheme reliable and efficient. In a more recent paper, Feng et al. introduced an algebraic approach to the lattice implementation. In this work, we consider some problems not addressed in...
We consider two uniploar OFDM techniques for optical wireless communications: asymmetric clipped optical OFDM (ACO-OFDM) and Flip-OFDM. Both techniques can be used to compensate multipath distortion effects in optical wireless channels. However, ACO-OFDM has been widely studied in the literature, while the performance of Flip-OFDM has never been investigated. In this paper, we conduct the performance...
The Generalized Distributive Law (GDL) is a message passing algorithm which can efficiently solve a certain class of computational problems, and includes as special cases the Viterbi's algorithm, the BCJR algorithm, the Fast-Fourier Transform, Turbo and LDPC decoding algorithms. In this paper GDL based maximum-likelihood (ML) decoding of Space-Time Block Codes (STBCs) is introduced and a sufficient...
We explore the capacity of sub-Nyquist sampled analog channels based on modulation and filter bank sampling techniques. In particular, we derive the capacity of sampled analog channels under sampling via modulation banks and filter banks. A connection between these sampling mechanisms and MIMO Gaussian channels is illuminated. For sampling with a single branch of modulation and filtering, we identify...
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are “symmetric” while the outputs are drawn from a ternary alphabet. Using an information-theoretic approach, we derive sufficient and necessary conditions for the number of tests required for noise-free and noisy reconstructions...
A general construction for deletion/insertion — correcting codes is proposed by concatenating codes derived from a heuristic maximal independent set algorithm on an appropriately defined graph. Our heuristic algorithm is polynomial with respect to the number of nodes in the graph. This methodology may be used for construction of any length n, s-deletion code. Our experimental results show that cardinalities...
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as little as two live nodes can be contacted to regenerate the data of a failed node. In this paper, we propose a new instance of self-repairing codes, based on constructions...
The expected write deficiency of the index-less indexed flash codes (ILIFC) is studied, and a technique is developed to improve the write deficiency of ILIFC. ILIFC is a coding scheme for flash memory, and consists of two stages with different coding techniques. This study first clarify the average write deficiency of the first stage of ILIFC, and shows that omitting the second stage of ILIFC can...
A Write-Once Memory (WOM)-code is a coding scheme that allows information to be written in a memory block multiple times, but in a way that the stored values are not decreased across writes. This work studies non-binary WOM-codes with applications to flash memory. We present two constructions of non-binary WOM-codes that leverage existing high sum-rate WOM-codes defined over smaller alphabets. In...
In a distributed storage system, codes for efficient repair of failed nodes has attracted significant recent research attention. Ideas from network coding and interference alignment have been used successfully to show bounds and construct coding schemes for efficient repair. In this article, we use ideas from classical algebraic codes to interpret the requirements of efficient repair as existence...
The secure networking problem of embedding information flows into cover traffic is addressed. When relayed packets must obey a causal delay constraint, this naturally remaps to a matching problem between point processes (here taken as arbitrary renewal processes). The best hiding policy is thus characterized in terms of the maximum fraction of matched points, which is accordingly referred to as embedding...
Recently, Dziembowski et al. introduced the notion of non-malleable codes (NMC), inspired from the notion of non-malleability in cryptography and the work of Gennaro et al. in 2004 on tamper proof security. Informally, when using NMC, if an attacker modifies a codeword, decoding this modified codeword will return either the original message or a completely unrelated value. The definition of NMC is...
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against...
We characterize the secret message capacity of a wiretapped erasure channel where causal channel state information of the honest nodes is publicly available. In doing so, we establish an intimate connection between message secrecy and secret key generation for the same channel setup. We propose a linear coding scheme that has polynomial encoding/decoding complexity, and prove a converse that shows...
Secrecy gain has been proposed as a criterion to design wiretap lattice codes. Its analysis relies on the theta series of a lattice, which is closely related to the union bound on the decoding error probability. In this paper, theta series of trellis codes are computed by using a modified transfer function originally for the union bound. We find that the low SNR region of the union bound dominates...
We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all those hypotheses are considered. The source is discrete and arbitrarily varying (AVS). The tradeoffs among error probability exponents/reliabilities associated with...
We consider the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities...
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