Collision Helps - Algebraic Collision Recovery for Wireless Erasure Networks

Current medium access control mechanisms are based on collision avoidance and collided packets are discarded. The recent work on ZigZag decoding departs from this approach by recovering the original packets from multiple collisions. In this paper, we present an algebraic representation of collisions which allows us to view each collision as a linear combination of the original packets. The transmitted, colliding packets may themselves be a coded version of the original packets. We propose a new acknowledgment (ACK) mechanism for collisions based on the idea that if a set of packets collide, the receiver can afford to ACK exactly one of them and still decode all the packets eventually. We analytically compare delay and throughput performance of such collision recovery schemes with other collision avoidance approaches in the context of a single hop wireless erasure network. In the multiple receiver case, the broadcast constraint calls for combining collision recovery methods with network coding across packets at the sender. From the delay perspective, our scheme, without any coordination, outperforms not only a ALOHA-type random access mechanisms, but also centralized scheduling. For the case of streaming arrivals, we propose a priority-based ACK mechanism and show that its stability region coincides with the cut-set bound of the packet erasure network

Sign-Compute-Resolve for Random Access

We present an approach to random access that is based on three elements: physical-layer network coding, signature codes and tree splitting. Upon occurrence of a collision, physical-layer network coding enables the receiver to decode the sum of the information that was transmitted by the individual users. For each user this information consists of the data that the user wants to communicate as well as the user's signature. As long as no more than $K$ users collide, their identities can be recovered from the sum of their signatures. A splitting protocol is used to deal with the case that more than $K$ users collide. We measure the performance of the proposed method in terms of user resolution rate as well as overall throughput of the system. The results show that our approach significantly increases the performance of the system even compared to coded random access, where collisions are not wasted, but are reused in successive interference cancellation.Comment: Accepted for presentation at 52nd Annual Allerton Conference on Communication, Control, and Computin

Broadcast Coded Slotted ALOHA: A Finite Frame Length Analysis

We propose an uncoordinated medium access control (MAC) protocol, called all-to-all broadcast coded slotted ALOHA (B-CSA) for reliable all-to-all broadcast with strict latency constraints. In B-CSA, each user acts as both transmitter and receiver in a half-duplex mode. The half-duplex mode gives rise to a double unequal error protection (DUEP) phenomenon: the more a user repeats its packet, the higher the probability that this packet is decoded by other users, but the lower the probability for this user to decode packets from others. We analyze the performance of B-CSA over the packet erasure channel for a finite frame length. In particular, we provide a general analysis of stopping sets for B-CSA and derive an analytical approximation of the performance in the error floor (EF) region, which captures the DUEP feature of B-CSA. Simulation results reveal that the proposed approximation predicts very well the performance of B-CSA in the EF region. Finally, we consider the application of B-CSA to vehicular communications and compare its performance with that of carrier sense multiple access (CSMA), the current MAC protocol in vehicular networks. The results show that B-CSA is able to support a much larger number of users than CSMA with the same reliability.Comment: arXiv admin note: text overlap with arXiv:1501.0338

Sign-Compute-Resolve for Tree Splitting Random Access

We present a framework for random access that is based on three elements: physical-layer network coding (PLNC), signature codes and tree splitting. In presence of a collision, physical-layer network coding enables the receiver to decode, i.e. compute, the sum of the packets that were transmitted by the individual users. For each user, the packet consists of the user's signature, as well as the data that the user wants to communicate. As long as no more than K users collide, their identities can be recovered from the sum of their signatures. This framework for creating and transmitting packets can be used as a fundamental building block in random access algorithms, since it helps to deal efficiently with the uncertainty of the set of contending terminals. In this paper we show how to apply the framework in conjunction with a tree-splitting algorithm, which is required to deal with the case that more than K users collide. We demonstrate that our approach achieves throughput that tends to 1 rapidly as K increases. We also present results on net data-rate of the system, showing the impact of the overheads of the constituent elements of the proposed protocol. We compare the performance of our scheme with an upper bound that is obtained under the assumption that the active users are a priori known. Also, we consider an upper bound on the net data-rate for any PLNC based strategy in which one linear equation per slot is decoded. We show that already at modest packet lengths, the net data-rate of our scheme becomes close to the second upper bound, i.e. the overhead of the contention resolution algorithm and the signature codes vanishes.Comment: This is an extended version of arXiv:1409.6902. Accepted for publication in the IEEE Transactions on Information Theor

MAC Design for Analog Network Coding

Most medium access control mechanisms discard collided packets and consider interference harmful. Recent work on Analog Network Coding (ANC) suggests a different approach, in which multiple interfering transmissions are strategically scheduled. The received collisions are collected and then used in a decoding process, such as the ZigZag decoding process, where the packets involved in the collisions are extracted. In this paper, we present an algebraic representation of collisions and describe a general approach to recovering collisions using ANC. To study the eect of using ANC on the performance of MAC layers, we develop an ANC-based algorithm that implements an abstract MAC layer service, as defined in [1, 2], and analyze its performance. This study proves that ANC can significantly improve the performance of MAC layer services, in terms of probabilistic time guarantees for packet delivery. We illustrate how this improvement at the MAC layer can translate into faster higher-level algorithms, by analyzing the time complexity of a multiple-message network-wide broadcast algorithm that uses our ANC-based MAC service

Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

A hybrid packet loss recovery technique in wireless ad hoc networks

TCP utilization in wireless networks poses certain problems due to its inability to distinguish packet losses caused by congestion from those caused by frequent wireless errors, leading to degraded network performance. To avoid these problems and to minimize the effect of intensive channel contention in wireless networks, this work presents a new Hybrid ARQ technique for reliable and efficient packets transfer in static wireless ad hoc network. It is a combination of recent FEC based Raptor coding technique with ARQ based selective retransmission method, which outperforms purely ARQ based method. In contrast to most Hybrid ARQ techniques, which usually employ a byte level FEC, we mostly use packet level FEC in our simulations for the data transfer, on top of less frequent ARQ to recover the residual errors. Existing packet level FEC methods are mostly based on simple parity check codes or Reed Solomon codes with erasure decoding; in this work we use the recent raptor codes. We also introduce the notion of adaptive redundancy which helps to achieve better average network performance and to further improve the redundancy efficiency

Bit-Wise Decoders for Coded Modulation and Broadcast Coded Slotted ALOHA

This thesis deals with two aspects of wireless communications. The first aspect is about efficient point-to-point data transmission. To achieve high spectral efficiency, coded modulation, which is a concatenation of higher order modulation with error correction coding, is used. Bit-interleaved coded modulation (BICM) is a pragmatic approach to coded modulation, where soft information on encoded bits is calculated at the receiver and passed to a bit-wise decoder. Soft information is usually obtained in the form of log-likelihood ratios (also known as L-values), calculated using the max-log approximation. In this thesis, we analyze bit-wise decoders for pulse-amplitude modulation (PAM) constellations over the additive white Gaussian noise (AWGN) channel when the max-log approximation is used for calculating L-values. First, we analyze BICM systems from an information theoretic perspective. We prove that the max-log approximation causes information loss for all PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We then analyze how the max-log approximation affects the generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder. Second, we compare the performance of the standard BICM decoder with that of the ML decoder. We show that, when the signal-to-noise ratio (SNR) goes to infinity, the loss in terms of pairwise error probability is bounded by 1.25 dB for any two codewords. The analysis further shows that the loss is zero for a wide range of linear codes. The second aspect of wireless communications treated in this thesis is multiple channel access. Our main objective here is to provide reliable message exchange between nodes in a wireless ad hoc network with stringent delay constraints. To that end, we propose an uncoordinated medium access control protocol, termed all-to-all broadcast coded slotted ALOHA (B-CSA), that exploits coding over packets at the transmitter side and successive interference cancellation at the receiver side. The protocol resembles low-density parity-check codes and can be analyzed using the theory of codes on graphs. The packet loss rate performance of the protocol exhibits a threshold behavior with distinct error floor and waterfall regions. We derive a tight error floor approximation that is used for the optimization of the protocol. We also show how the error floor approximation can be used to design protocols for networks, where users have different reliability requirements. We use B-CSA in vehicular networks and show that it outperforms carrier sense multiple access currently adopted as the MAC protocol for vehicular communications. Finally, we investigate the possibility of establishing a handshake in vehicular networks by means of B-CSA

Topics in Distributed Algorithms: On Wireless Networks, Distributed Storage and Streaming

Distributed algorithms are executed on a set of computational instances. Werefer to these instances as nodes. Nodes are runningconcurrently and are independent from each other. Furthermore, they have their own instructions and information. In this context, the challenges are to show thatthe algorithm is correct, regardless of computational, or communication delaysand to show bounds on the usage of communication.We are especially interested the behaviour after transient faults and underthe existence of Byzantine nodes.This thesis discusses fundamental communication models for distributed algorithms. These models are implementing abstract communication methods. First, we address medium access control for a wireless medium with guaranteeson the communication delay. We discuss time division multiple access(TDMA) protocols for ad-hoc networks and we introduce an algorithm that creates aTDMA schedule without using external references for localisation, or time. We justify our algorithm by experimental results.The second topic is the emulation of shared memory on message passingnetworks. Both, shared memory and message passing are basic interprocessorcommunication models for distributed algorithms. We are providing a way ofemulating shared memory on top of an existing message passing network underthe presence of data corruption and stop-failed nodes. Additionally, we ensurethe privacy of the data that is stored in the shared memory. The third topic looks into streaming algorithms and optimisation. We study the problem of sorting a stream ofvehicles on a highway with severallanes so that each vehicle reaches its target lane. We look into optimality interms of minimising the number of move operations, as well as, minimising the length of the output stream. We present an exact algorithm for the case oftwo lanes and show that NP-Hardness for a increasing number of lanes