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We provide a variational characterization for the various Rényi information measures via their Shannon counterparts, and demonstrate how properties of the former can be recovered from first principle via the associated properties of the latter. Motivated by this characterization, we give a new operational interpretation for the Rényi divergence in a two-sensor composite hypothesis testing framework.
Random-coding exact characterizations and bounds to the error probability of joint source-channel coding are presented. In particular, upper bounds using maximum-a-posteriori and threshold decoding are derived as well as a lower bound motivated by Verdú-Han's lemma.
We consider a line of terminals which is connected by packet erasure channels and where random linear network coding is carried out at each node prior to transmission. In particular, we address an online approach in which each terminal has local information to be conveyed to the base station at the end of the line and provide a queueing theoretic analysis of this scenario. First, a genie-aided scenario...
We investigate the capacity of a multiple access channel with cooperating encoders where partial state information is known to each encoder in a non-causal way and full state information is known to the decoder. The cooperation between the encoders has a two-fold purpose: to generate empirical state coordination between the encoders, and to share information about the private messages that each encoder...
In this paper, we propose a cooperative spectrum sharing protocol (CSSP) between two overlapping static ad hoc wireless networks where the primary and secondary networks consist of n and m randomly distributed nodes respectively. The secondary network achieves spectrum access along with the primary network by allowing its nodes to relay the primary traffic. Taking advantage of the broadcast nature...
We consider the N-relay Gaussian diamond network when the source and the destination have ns ≥ 2 and nd ≥ 2 antennas respectively. We show that when ns = nd = 2 and when the individual MISO channels from the source to each relay and the SIMO channels from each relay to the destination have the same capacity, there exists a two relay sub-network that achieves approximately all the capacity of the network...
In this paper, we first investigate erasure-only list decoding of Reed-Solomon and BCH codes. We consider the scenario in which some locations of a received word are pre-corrected. Accordingly, the rational curve fitting algorithm does not interpolate the known locations, and thus effectively increases the list error correction capability (LECC). For a Reed-Solomon code C(n, k, d), let n* be the effective...
To lower the complexity of network codes over packet line networks with arbitrary schedules, chunked codes (CC) and overlapped chunked codes (OCC) were proposed in earlier works. These codes have been previously analyzed for relatively large chunks. In this paper, we prove that for smaller chunks, CC and OCC asymptotically approach the capacity with an arbitrarily small but non-zero constant gap....
It has been well established that reverse-carpooling based network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment when there are no opportunities to code because of packets without coding pairs, should these packets wait for a future opportunity or should they be transmitted without coding? To help answer that question we formulate...
Minimal list decoding for a code C refers to list decoding with radius L(y), where L(y) is the minimum of the distances between the received word y and any codeword in C. In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Our approach involves a parametrization of the interpolating polynomials of a minimal Gröbner basis G. We then demonstrate that our parametric...
We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study Gray codes for the local rank-modulation scheme in order to simulate conventional...
Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes is based on Bounded Minimum Distance (BMD) decoders with an erasure option. Such decoders have error/erasure tradeoff factor λ = 2, which means that an error is twice as expensive as an erasure in terms of the code's minimum distance. The Guruswami-Sudan (GS) list decoder can be considered as state of the art in algebraic...
For designing low-density parity-check (LDPC) codes for quantum error-correction, we desire to satisfy the conflicting requirements below simultaneously. 1) The row weights of parity-check “should be large”: The minimum distances are bounded above by the minimum row weights of parity-check matrices of constituent classical codes. Small minimum distance tends to result in poor decoding performance...
In this paper, we study cyclic stabiliser codes over Fp of length dividing pt + 1 for some positive integer t. We call these t-Frobenius codes or just Frobenius codes for short. We give methods to construct them and show that they have efficient decoding algorithms.
In this paper, we study the asymptotic minimum distance of non-binary cluster-LDPC codes whose subjacent binary parity-check matrix is composed of localized density of ones, concentrated in clusters of bits. A particular attention is given to cluster codes represented by ultra-sparse bipartite graphs, in the sense that each symbol-node is connected to exactly dv = 2 constraint-nodes. We derive a lower...
1 Random access communication is used in practical systems to deliver bursty short messages. Because users only transmit occasionally, it is often difficult for the receiver to keep track of the time varying wireless channel states. Under this motivation, we develop channel coding theorems for random multiple access communication over compound channels with finite codeword length. Error performance...
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is fixed. We show that the network routing capacity region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the...
Secret key generation is considered for a pair of terminals that observe correlated sources and communicate interactively over a public channel. It is argued that optimum rate secret key generation is linked inherently to the Wyner's notion of common information between two dependent random variables. The minimum rate of interactive public communication required to generate an optimum rate secret...
A symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms, was recently introduced. Many communication problems can be recast as dispersion problems in this setup. The so-called min-cut of a term set represents its number of degrees of freedom. For any assignment of function symbols, its dispersion measures the amount of information...
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