Ali Eslami

A practical approach to polar codes

In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density Parity-Check (LDPC) codes. We will show that our proposed scheme outperforms conventional concatenation schemes formed by LDPC and Reed-Solomon (RS) codes. We then study two rate-compatible coding schemes using polar codes. We will see that polar codes can be designed as universally capacity achieving rate-compatible codes over a set of physically degraded channels. We also study the effect of puncturing on polar codes to design rate-compatible codes.

On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design

This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief propagation as the decoding method. We provide a stopping set analysis for the factor graph of polar codes, where we find the size of the minimum stopping set. We also find the girth of the graph for polar codes. Our analysis along with bit error rate (BER) simulations demonstrate that finite-length polar codes show superior error floor performance compared to the conventional capacity-approaching coding techniques. In order to take advantage from this property while avoiding the shortcomings of polar codes, we consider the idea of combining polar codes with other coding schemes. We propose a polar code-based concatenated scheme to be used in Optical Transport Networks (OTNs) as a potential real-world application. Comparing against conventional concatenation techniques for OTNs, we show that the proposed scheme outperforms the existing methods by closing the gap to the capacity while avoiding error floor, and maintaining a low complexity at the same time.

On bit error rate performance of polar codes in finite regime

Polar codes have been recently proposed as the first low complexity class of codes that can provably achieve the capacity of symmetric binary-input memoryless channels. Here, we study the bit error rate performance of finite-length polar codes under Belief Propagation (BP) decoding. We analyze the stopping sets of polar codes and the size of the minimal stopping set, called “stopping distance”. Stopping sets, as they contribute to the decoding failure, play an important role in bit error rate and error floor performance of the code. We show that the stopping distance for binary polar codes, if carefully designed, grows as O(√N) where N is the code-length. We provide bit error rate (BER) simulations for polar codes over binary erasure and gaussian channels, showing no sign of error floor down to the BERs of 10−11. Our simulations asserts that while finite-length polar codes do not perform as good as LDPC codes in terms of bit error rate, they show superior error floor performance. Motivated by good error floor performance, we introduce a modified version of BP decoding employing a guessing algorithm to improve the BER performance of polar codes. Our simulations for this guessing algorithm show two orders of magnitude improvement over simple BP decoding for the binary erasure channel (BEC), and up to 0.3 dB improvement for the gaussian channel at BERs of 10−6.

Scaling Laws for Distance Limited Communications in Vehicular Ad Hoc Networks

In this paper we propose a framework to study the asymptotical capacity of vehicular ad hoc networks (VANET)s when nodes are expected to communicate only when they reside in a certain distance of each other. This is quite a favorable scenario for VANETs when they are utilized for accident avoidance and safety applications. Moreover we develop formulations to predict the behavior of VANETs with specific geometrical shapes like the single road and grid topologies. Also, the capacity scaling behavior of VANETs when a node needs to transmit to all its neighbors within a certain range, is studied. Results are obtained by combining geometrical analysis, network flow arguments, and probabilistic study of VANETs.

The capacity of Vehicular Ad Hoc Networks with infrastructure

In this paper, we initiate a framework to address the capacity scaling trends in vehicular ad hoc networks (VANET)s with arbitrary topologies. Towards this end we utilize the conventional definition of transport capacity in which destination nodes are chosen at random by the source nodes. Also, to get more VANET-specific, we set up a new variation of transport capacity in which the destination nodes are again chosen at random, but this time are within a distance d of the source node which is called the distance-limited capacity. Emergency and accident avoidance scenarios are just, some of the direct applications of distance-limited capacity. Moving on further, we study the effect of infrastructure node deployment in the capacity analysis of VANETs. Wepsilave initiated this trend with our focus on the distance-limited capacity of a single road VANET. Using analytical expressions we show that exploiting any number of infrastructure nodes beyond a certain amount, enhances the achievable capacity.

Results on finite wireless sensor networks: Connectivity and coverage

Many analytic results for the connectivity, coverage, and capacity of wireless networks have been reported for the case where the number of nodes, n, tends to infinity (large-scale networks). The majority of these results have not been extended for small or moderate values of n; whereas in many practical networks, n is not very large. In this article, we consider finite (small-scale) wireless sensor networks. We first show that previous asymptotic results provide poor approximations for such networks. We provide a set of differences between small-scale and large-scale analysis and propose a methodology for analysis of finite sensor networks. Furthermore, we consider two models for such networks: unreliable sensor grids and sensor networks with random node deployment. We provide easily computable expressions for bounds on the coverage and connectivity of these networks. With validation from simulations, we show that the derived analytic expressions give very good estimates of such quantities for finite sensor networks. Our investigation confirms the fact that small-scale networks possess unique characteristics different from their large-scale counterparts, necessitating the development of a new framework for their analysis and design.

Writing without Disturb on Phase Change Memories by Integrating Coding and Layout Design

We integrate coding techniques and layout design to eliminate write-disturb in phase change memories (PCMs), while enhancing lifetime and host-visible capacity. We first propose a checkerboard configuration for cell layout to eliminate write-disturb while doubling the memory lifetime. We then introduce two methods to jointly design Write-Once-Memory (WOM) codes and layout. The first WOM-layout design improves the lifetime by more than double without compromising the host-visible capacity. The second design applies WOM codes to even more dense layouts to achieve both lifetime and capacity gains. The constructions demonstrate that substantial improvements to lifetime and host-visible capacity are possible by co-designing coding and cell layout in PCM.

Joint random spectrum sensing and access scheme for decentralized cognitive radio networks

In this paper we consider a cognitive radio network with access to N licensed primary frequency bands and their usage statistics, where the decentralized secondary users are subject to certain inter-network interference constraint. In particular, to limit the interference to the primary network, secondary users are equipped with spectrum sensors and are capable of sensing and accessing a limited number of channels at the same time due to hardware limitations. We consider both the error-free and erroneous spectrum sensing scenarios, and establish the jointly optimal random sensing and access scheme, which maximizes the secondary network expected sum throughput while honoring the primary interference constraint. We show that under certain conditions the optimal sensing and access scheme is independent of the primary frequency bandwidths and usage statistics; otherwise, they follow water-filling-like strategies. Moreover, we show that the performance of the secondary network depends on the ratio between the “opportunity-detection” probability and the “mis-detection” probability if the former is larger; otherwise, it depends on the ratio between the “false-alarm” probability and the “detection” probability. Finally, we demonstrate a binary behavior for the optimal access scheme at each channel, depending on whether the opportunity-detection probability or mis-detection probability is larger in that channel.

Results on Finite Wireless Networks on a Line

Analysis of finite wireless networks is a fundamental problem in the area of wireless networking. Today, due to the vast amount of literature on large-scale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. We refer to networks as being finite when the number of nodes is less than a few hundred. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the networks properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the Medium Access (MAC) layer capacity, i.e. the maximum number of possible concurrent transmissions. Towards this goal, we provide a linear time algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity.

Results on finite wireless networks on a line

Today, due to the vast amount of literature on large-scale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. We refer to networks as being finite when the number of nodes is less than a few hundred. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the networks properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the medium access (MAC) layer capacity, i.e. the maximum number of possible concurrent transmissions. Towards this goal, we provide an algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity.