LDPC Code Performance and Optimum Code Rate for Contention Resolution Diversity ALOHA Christian Kissling, Federico Clazzer DLR, Institute of Communications and Navigation, 82234 Weßling, Munich, Germany {christian.kissling, federico.clazzer}@dlr.de Abstract—In this paper we investigate several central aspects of using the unslotted Contention Resolution Diversity ALOHA (CRA) scheme with Successive Interference Cancellation (SIC). A model for the co-user-interference under consideration of time-, phase- and frequency-offsets is presented. With this model, the throughput and Packet Loss Ratio (PLR) performance of CRA is investigated when using Low Density Parity Check (LDPC) codes, showing that CRA can achieve remarkable performance also in these conditions. Moreover, the throughput and PLR gain of CRA in presence of power unbalance is studied, showing that significant gains can be expected. Following this, the central question is answered which channel rates optimize the goodput of CRA, showing that for CRA with few replicas a low, robust channel rate achieves optimum while for high numbers of replicas a high channel rate performs optimum. Finally an investigation of the interference distribution of an asynchronous TDMA scheme with replicas and the SIC operations in it are shown. I. I NTRODUCTION After being used in communication systems for decades now, Random Access (RA) systems attract new attention, going far beyond providing a channel access for log-on, or signalling. In the last couple years, significant enhancements of the well known ALOHA [1] and Slotted ALOHA (SA) [2] schemes were developed, being based on Successive Inter- ference Cancellation (SIC). Contention Resolution Diversity Slotted ALOHA (CRDSA) [3] and its extensions CRDSA++ [4], Irregular Repetition Slotted ALOHA (IRSA) [5] and coded slotted ALOHA [6] pave the way for new fields of application, exploiting the presence of a RA channel also for transmission of user data. Since these new and highly efficient schemes have been introduced, research has spread into several different directions, some focussing on the efficient integration of Demand Assigned Multiple Access (DAMA) with RA channels [7], others on the further extension of the efficiency, e.g. by applying variable rate coding to the SIC [6]. The stability of SIC based RA schemes is investigated e.g. in [8] for channels with retransmissions while [9] investigates the coded slotted ALOHA technique, where reliability is achieved without retransmissions. This work has been accepted for publication in the proceedings of the IEEE Global Communication Conference (GLOBECOM) 2013; DOI: 10.1109/GLOCOM.2013.6831520 c 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works Also recent standards, such as DVB-RCS2, have adopted CRDSA for transmission of signalling as well as user data. The usage of RA channels is particularly appealing for traffic profiles where small messages have to be delivered within a short time interval. Especially in Geostationary Orbit (GEO) satellite scenarios, where the procedure of requesting and assignment of capacity on a DAMA channel requires addi- tional signalling (for the request and later for the assignment message) and generates additional delay (1 Round Trip Time (RTT) ≈ 500 ms is required for the request and assignment message exchange), the user data in a RA channel can in best case be transmitted directly, saving signalling overhead and delay. It was shown in [7] that the efficient integration of a CRDSA RA channel with a DAMA channel can improve the overall delay for this reason. While the aforementioned applications are based on slotted RA schemes, where users need to be synchronized to time slots and can only transmit a fixed amount of data in each slot, an asynchronous TDMA scheme exploiting SIC, named Con- tention Resolution Diversity ALOHA (CRA), was proposed in [10]. There, also a first performance estimation showing the potential of this scheme was presented, assuming the decoding threshold resulting from the Shannon capacity limit. It was shown there that the CRA scheme can benefit from strong Forward Error Correction (FEC) and the presence of partial interference, which naturally occurs in unslotted schemes 1 , achieving theoretical throughputs far beyond SA and reaching even the basic version of CRDSA with 2 replicas. At the same time the asynchronous scheme can achieve very low PLR for low to moderate offered traffic loads G, even below the one of slotted SIC schemes in a basic configuration, such as CRDSA with 2 replicas. This makes CRA a very appealing protocol in scenarios where a large number of user terminals shall access the medium in order to save the synchronization and fragmentation overhead, or where small and bursty data is generated, but needs to arrive very reliably. CRA allows the transmission of variable packet lengths without the need of fragmentation into slots and thus avoids the fragment header signalling and padding overheads. Fur- thermore the timing requirements can be relaxed compared to slotted schemes. While slotted schemes have to comply 1 Compared to slotted schemes where interference is always affecting an entire slot.