Manjunath V. Hegde

On the error probability of coded frequency-hopped spread-spectrum multiple-access systems

A simple, exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency-hopped, spread-spectrum, multiple-access communication system. While the sequence of hits is not Markovian, there is an underlying Markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion. Knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers, including receivers with both errors and erasures. The numerical results show that both the approximation obtained by assuming the actual sequence of hits is Markovian and the approximation obtained by assuming the hits are independent are very good. When the number of frequency slots is not too small (less than five), calculations show that assuming the independence of hits gives an error probability accurate to within 1% of the actual error probability. Assuming the hits are Markovian gives error probabilities which are accurate to within 0.001%. >

Capacity of frequency-hop spread-spectrum multiple-access communication systems

The information theoretic capacity is considered. In order to account for independent encoding and decoding and private (to the sender and receiver) hopping patterns, an interference channel model is adopted with K sender-receiver pairs with the ith receiver only interested in the message transmitted by the ith sender. Both synchronous and asynchronous hopping patterns are investigated. Although the channel exhibits memory in the latter case, it is possible to compute the capacity region. The asymptotic normalized sum capacity is also computed. >

Asymptotic performance of M-ary orthogonal signals in worst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E/sub b//N/sub I/) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E/sub b//N/sub I/(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E/sub b//N/sub 0/) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E/sub b//N/sub 0/ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication. >

On the capacity of channels with unknown interference

The process of communicating in the presence of interference that is unknown or hostile is modeled as a two-person zero-sum game with the communicator and the jammer as the players. The objective function considered is the rate of reliable communication. The communicators strategies are encoders and distributions on a set of quantizers. The jammers strategies are distributions on the noise power subject to certain constraints. Various conditions are considered on the jammers strategy set and on the communicators knowledge. For the case where the decoder is uninformed of the actual quantizer chosen, it is shown that, from the communicators perspective, the worst-case jamming strategy is a distribution concentrated on a finite number of points, thereby converting a functional optimization problem into a nonlinear programming problem. Moreover, the worst-case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify. For the case where the decoder is informed of the actual quantizer chosen, the existence of saddle-point strategies is demonstrated. The analysis is also seen to be valid for a number of situations where the jammer is adaptive. >

Implied costs in wireless networks

We calculate implied costs for wireless networks and use them for evaluating trade-offs between calls of different rates. We model user mobility by assigning probabilities for the departure of calls. We use fixed channel assignment (FCA) with priority for handoffs over new call arrivals by reserving a number of channels for handoff calls in all the cells. The performance measures used are new call blocking and handoff drop probabilities. The implied cost is calculated for the network net revenue which considers the revenue generated by accepting a new call arrival into the network as well as the cost of a handoff drop in any cell. Simulation and numerical results are presented as well as confidence intervals showing the accuracy of the model. The implied costs also show that matching capacity distribution to not only exogenous traffic but also to mobility can significantly increase network revenue and quantifies this increase.

A multiple shared memory switch

One of the problems that shared memory switches have is that in order to build large switches the memory access requirements become stringent. One way to overcome this is to utilize multiple buffers which space division multiplex the input lines and thereby alleviate the memory access requirements. However, previous attempts to implement multi-buffered shared memory switches have suffered from serious limitations. The authors describe in this work a multi-buffered architecture that offers tremendous potential. It is able to fully share the buffer, it guarantees the minimum delay switching of all cells, it can accomplish multi-cast and multi-channel switching, it can accommodate various priorities and classes of traffic while maintaining high performance on account of very efficient buffer utilization.

Shadow prices for LLR and ALBA

Shadow prices are calculated for least loaded routing (LLR) and aggregated least busy alternative (ALBA) routing in circuit-switched networks for the blocking probability obtained from fixed point algorithms. Numerical results are presented for the calculation of these shadow prices in small networks. As an application of these shadow prices, we also formulate a constrained optimization problem to calculate the sum capacity of LLR and ALBA for a given network. Comparison of the sum capacities indicate that the optimization using shadow prices results in a significant improvement. This provides evidence that matching capacity distribution to traffic is important even when adaptive routing schemes such as LLR and ALBA are used in the network. We also calculate upper bounds on the sum capacity which serve to indicate how well the optimized LLR and ALBA perform. The numerical results also confirm that with a small number of states the capacity of ALBA approaches that of LLR.

Nonblocking copy networks in multi-channel switching

This paper develops a copy network architecture that can maintain the cell sequence integrity in multi-channel ATM switching. The architecture is internally nonblocking in the sense that the copying process of cells is constrained only by the availability of output channels. By using a relative ordering among the inputs, shared buffering, and a new switching paradigm called the nonblocking binary group network, we show how the cell sequence integrity can be maintained. Next, assuming the fanout request values of cells are distributed independently from cell to cell, we formulate a method of analyzing the performance of the copy network. This method uses the technique of tagged Markov chains to derive the stationary distributions for the number of cells in the copy network from which, delay, throughput, and cell loss probability can be accurately calculated as critical performance measures. We conduct a numerical study for the proposed architecture using this method wherein the effects of key network and traffic variables such as buffer and network sizes, and the mean and the variance of fanout request values are determined under arbitrary types of fanout distribution. Finally, we quantify the performance improvement due to fanout splitting which allows the fanout request from a single cell to be satisfied over multiple time slots.

Multiple-Access Capability of Frequency-Hop Spread-Spectrum Communication

The multiple-access capability of frequency-hop spread-spectrum communication is considered from an information theoretic viewpoint. The model adopted is that of an interference channel with T source-receiver pairs with ith receiver only interested in the message produced by the ith source. Different transmitters use different frequency-hopping patterns which we model as random hopping patterns. We propose some simple models for the resulting channels. We consider both the case where all users are synchronized and the totally asynchronous case. We also consider the cases when the receiver can detect when two or more transmitters hop to the same frequency at the same time. This allows for erasure correction in decoding. Without this information the channel is modeled as a noisy M-ary symmetric channel. when there is a hit and a noise-less M-ary symmetric channel in the absence of a hit. For this channel model we determine the capacity region.

Convolutional coding for finite-state channels

We propose new decoders for decoding convolutional codes over finite-state channels. These decoders are sequential and utilize the information about the channel state sequence contained in the channel output sequence. The performance of these decoders is evaluated by simulation and compared to the performance of memoryless decoders with and without interleaving. Our results show that the performance of these decoders is good whenever the channel statistics are such that the joint estimate of the channel state sequence and the channel input sequence is good, as, for example, when the channel is bursty. In these cases using even a partial search decoder such as the Fano decoder over the appropriate trellis is nearly optimal. However, when the information between the output sequence and the sequence of channel states and inputs diminishes, the memoryless decoder with interleaving outperforms even the optimal decoder which knows the channel state.