Mathematical Analysis of Throughput Bounds in Random Access with Z IG Z AG Decoding Jeongyeup Paek Department of Computer Science University of Southern California jpaek@usc.edu Michael J. Neely Department of Electrical Engineering University of Southern California mjneely@usc.edu Abstract— We investigate the throughput improvement that ZIGZAG decoding (Gollakota and Katabi (2008)) can achieve in multi-user random access systems. ZIGZAG is a recently proposed 802.11 receiver design that allows successful reception of packets despite collision. Thus, the maximum achievable throughput of a wireless LAN can be significantly improved by using ZIGZAG decoding. We analyze the throughput bounds in three different idealized slotted multi-access system models for the case when ZIGZAG decoding is used. We also provide results for the Aloha and CSMA models where exact closed form solutions are infeasible to calculate. Our analysis and simulation results show that ZIGZAG decoding can significantly improve the maximum throughput of the random access system. I. I NTRODUCTION In this paper, we investigate how much throughput improve- ment ZIGZAG decoding [1] can achieve. ZIGZAG is a recently proposed 802.11 receiver design that combats hidden terminals. In ZIGZAG, the receiver can decode two consecutive signals of two colliding packets and successfully receive both packets despite collision. In other words, if the same two packets collide twice (with a small bit offset difference), the receiver can receive both of those packets. Thus, the maximum achievable throughput of a wireless LAN can be significantly improved by using ZIGZAG decoding. We look at three different idealized slotted multi-access system models to investigate the performance benefits of ZIGZAG decoding; 1) N -user slotted random access system, 2) stabilized slotted Aloha, and 3) slotted CSMA with mini- slots. Prior work has already analyzed these simple systems and has given throughput bounds (see, for example, [2], [3] for summaries and reviews of prior work). We extend these well known results to the case when ZIGZAG decoding is used. We also provide results for the Aloha [4] and CSMA [5] models where exact closed form solutions are infeasible to calculate. We concentrate on simple random access protocols and do not consider conflict resolution techniques such as [6], [7] or capture effects (e.g. [8], [9]) for the simplicity of analysis. Related recent work in [10] considers random Aloha-type protocols in networks with “soft collisions” and multi-packet reception capabilities (such as CDMA systems). The ZIGZAG This material is supported in part by one or more of the following: the DARPA IT-MANET program grant W911NF-07-0028, the NSF grant OCE 0520324, the NSF Career grant CCF-0747525. decoding feature that we consider in the present paper can be viewed as a form of multi-packet reception, but is structurally quite different from the work in [10] and it does not require a CDMA structure. Most of the classical assumptions for idealized slotted multi- access models used in prior work also hold in our work unless stated otherwise. For example, our models have slotted time with slot boundaries at integer times (t ∈{0, 1, 2, ...}), packets have fixed sizes and their transmission time equals exactly one slot, and if just one node sends a packet in a given slot, the packet is correctly received at the receiver. Also, we assume that each packet involved in a collision must be retransmitted later until the packet is successfully received. A node with a packet that must be retransmitted is said to be backlogged. However, to apply ZIGZAG into our analysis, we redefine the term ‘Collision’ and make the following simplified as- sumptions: Now, ‘Collision’ occurs on a slot when 3 or more users attempt transmission in a given time slot. In this case, no packets are delivered to the receiver. If exactly 2 users transmit packets on a slot, we say that this is a ‘ZIGZAG’ case which is decodable using ZIGZAG decoding. Either an ‘Idle,’ ‘Success,’ ‘ZIGZAG,’ or ‘Collision’ event happens on every slot, (corresponding to whether 0, 1, 2, or more than 2 packets were transmitted in that slot, respectively) and this feedback is explicitly given (‘0,’ ‘1,’ ‘ZIGZAG,’ ‘C’) to all users at the end of each slot. If a ‘ZIGZAG’ event occurs, that slot is automatically extended into 2 slots. The two colliding users know that they have collided in a ZIGZAG event, and always retransmit the same packet in the next slot. Other users also know about this and thus remain silent in the next slot. If a ‘ZIGZAG’ event occurs, exactly 2 packets can be perfectly received at the receiver during 2 time slots. Hence the average throughput during this period is 1 packet/slot. Finally, we ignore other aspects of ZIGZAG decoding such as decoding failure or 3 packet decoding. 1 While we use a slotted model here, it is important to recall that ZIGZAG decoding relies on packet transmissions to arrive at the receiver so that the first bits of each packets are non- aligned. This is consistent with a slotted model if slot sizes are 1 In a real system, there could be cases where ZIGZAG decoding may fail for some practical reasons. Also, there could be cases where 3 or more colliding packets are decodable. The ZIGZAG paper [1] does describe these cases but we ignore them for simplicity of analysis.