The capacity of the channel defined by the stochastic nonlinear Schrödinger equation, which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise, is considered in ...the case of zero dispersion. For the first time, the exact capacity subject to peak and average power constraints is numerically quantified using dense multiple ring modulation formats. It is shown that, for a fixed noise power, the per-sample capacity grows unbounded with input signal power. A distribution with a half-Gaussian profile on amplitude and uniform phase is shown to provide a lower bound to the capacity which is simple and asymptotically optimal at high SNRs.
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and ...network code is assumed at the source and destination nodes, the error correction capability of an (outer) code is succinctly described by the rank metric; as a consequence, it is shown that universal network error correcting codes achieving the Singleton bound can be easily constructed and efficiently decoded. For noncoherent network coding, where knowledge of the network topology and network code is not assumed, the error correction capability of a (subspace) code is given exactly by a modified subspace metric, which is closely related to, but different than, the subspace metric of Kotter and Kschischang. In particular, in the case of a non-constantdimension code, the decoder associated with the modified metric is shown to correct more errors then a minimum subspace distance decoder.
A reduced complexity decoding scheme for wireless applications Sajadieh, M.; Kschischang, F.R.
IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320),
1999, Letnik:
3
Conference Proceeding
Cellular transmission standards such as GSM and IS-54 produce data streams with varying degrees of significance at the source encoder level. We propose an unequal error protection scheme based on a ...non-uniform signal set which provides the more important data with a preferential Euclidean distance. The unequal error protection is partly accomplished by the modulator in contrast to the conventional systems where the channel encoder is solely responsible. The coding gain resulting from the asymmetric modulation can be translated into a reduction in the complexity of the channel encoder; specifically a reduction by more than half in the number of encoder states can be expected. We study the interaction between the code complexity and the modulation asymmetry in quantitative terms. For differentially coherent systems, a /spl pi//6-shifted differential embedded QPSK is proposed. Decentralizing the bit protection culminates in an extra degree of freedom which in turn introduces more flexibility into the system design.
The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver \(n\) packets from source to each ...receiver, and the wiretapper can eavesdrop on \(\mu\) arbitrarily chosen links. A coding scheme is proposed that can achieve the maximum possible rate of \(k=n-\mu\) packets that are information-theoretically secure from the adversary. A distinctive feature of our scheme is that it is universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. In fact, even a randomized network code can be used. Our approach is based on Rouayheb-Soljanin's formulation of a wiretap network as a generalization of the Ozarow-Wyner wiretap channel of type II. Essentially, the linear MDS code in Ozarow-Wyner's coset coding scheme is replaced by a maximum-rank-distance code over an extension of the field in which linear network coding operations are performed.
We consider the rate/distance tradeoff for LDPC-coded OOK systems under soft-decision iterative decoding. Below 6000 km, EXIT-chart optimized irregular LDPC codes outperform systems that use a ...nonlinearity-reducing constrained inner code.
The helical window token ring Kschischang, F.R.; Molle, M.L.
IEEE transactions on information theory,
05/1989, Letnik:
35, Številka:
3
Journal Article
Recenzirano
An access rule for token ring local-area networks called the helical-window token-ring protocol is introduced. It features the use of a window that limits the allowable messages a token-holding ...station can send. With the window, the operation of the protocol approaches that of a central single-server queuing system in the sense that messages are delivered in near first-come-first-served order on a network-wide basis. The introduction of the window also makes analysis of the networks tractable. Exact analytical formulas for the capacity and for the mean, variance, and moment-generating function of the message waiting time are derived. Numerical simulation is used to verify the results. Comparisons with continuous polling systems show that the imposition of the windowed access rule can lead to significant reductions in the delay variance (at the cost of increasing the mean system time) when the traffic is heavy and/or the message transmission time is large with respect to the walk time of the ring.< >
Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more ...efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over a finite-ring matrix channel \(Y = AX + BE\), where \(X\) is the channel input, \(Y\) is the channel output, \(E\) is random error, and \(A\) and \(B\) are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under the assumption that \(A\) is uniform over all full-rank matrices and \(BE\) is uniform over all rank-\(t\) matrices, extending the work of Silva, Kschischang and K\"{o}tter (2010), who handled the case of finite fields. This extension is based on several new results, which may be of independent interest, that generalize concepts and methods from matrices over finite fields to matrices over finite chain rings.
While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to "pollution attacks," as the injection of even a single erroneous packet has the ...potential to corrupt each and every packet received by a given destination. Even when suitable error-control coding is applied, an adversary can, in many interesting practical situations, overwhelm the error-correcting capability of the code. To limit the power of potential adversaries, a broadcast transformation is introduced, in which nodes are limited to just a single (broadcast) transmission per generation. Under this broadcast transformation, the multicast capacity of a network is changed (in general reduced) from the number of edge-disjoint paths between source and sink to the number of internally-disjoint paths. Exploiting this fact, we propose a family of networks whose capacity is largely unaffected by a broadcast transformation. This results in a significant achievable transmission rate for such networks, even in the presence of adversaries.
This paper presents a new sub-optimal lattice decoder based on decomposition of the detection lattice into cosets and iterative application of LLL reduction to its primal and dual representations. ...From each coset, a candidate solution is chosen using linear equalization followed by integer quantization. These candidates are then compared and the best amongst them is returned. Because the cosets are identical save for distinct translation vectors, their sub-lattice decoders share common preprocessing and can operate very efficiently in parallel. Exclusive of pre-processing, the computational complexity of the proposed decoder is quadratic in the problem dimension and linear in the number of cosets. Simulation results demonstrate the near-ML bit error rate performance offered by the new decoder in the context of existing QAM-modulated MIMO detection schemes.
Lattice network coding via signal codes Chen Feng; Silva, Danilo; Kschischang, Frank R.
2011 IEEE International Symposium on Information Theory Proceedings,
2011-July
Conference Proceeding
The construction of lattice network coding schemes through signal codes is revisited. First, it is shown that the nominal coding gain of signal codes can be carried over from AWGN channels to lattice ...network coding. This demonstrates the potential of using signal codes in lattice network coding. However, in order to achieve the promised performance gain, all the side information related to shaping should be transmitted to the receiver. Second, the problem of delivering the side information to the receiver is considered. In particular, a generic scheme is proposed which can be optimized by solving a lattice design problem. Finally, two solutions to the lattice design problem are presented and the simulation results suggest that-with a reasonable overhead-the promised performance gain can be achieved by using our proposed scheme.
