On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis

We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for uncoordinated multiple access, where users join the system on a slot-by-slot basis according to a Poisson random process and, in contrast to standard frame synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the performance of FA-CSA in terms of packet loss rate and delay. In particular, we derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if the receiver can monitor the system before anyone starts transmitting, a boundary effect similar to that of spatially-coupled codes occurs, which greatly improves the iterative decoding threshold. Furthermore, we derive tight approximations of the error floor (EF) for the finite frame length regime, based on the probability of occurrence of the most frequent stopping sets. We show that, in general, FA-CSA provides better performance in both the EF and waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay properties than FS-CSA.Comment: 13 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1604.0629

Repair Scheduling in Wireless Distributed Storage with D2D Communication

We consider distributed storage (DS) for a wireless network where mobile devices arrive and depart according to a Poisson random process. Content is stored in a number of mobile devices, using an erasure correcting code. When requesting a piece of content, a user retrieves the content from the mobile devices using device-to-device communication or, if not possible, from the base station (BS), at the expense of a higher communication cost. We consider the repair problem when a device that stores data leaves the network. In particular, we introduce a repair scheduling where repair is performed (from storage devices or the BS) periodically. We derive analytical expressions for the overall communication cost of repair and download as a function of the repair interval. We illustrate the analysis by giving results for maximum distance separable codes and regenerating codes. Our results indicate that DS can reduce the overall communication cost with respect to the case where content is only downloaded from the BS, provided that repairs are performed frequently enough. The required repair frequency depends on the code used for storage and the network parameters. In particular, minimum bandwidth regenerating codes require very frequent repairs, while maximum distance separable codes give better performance if repair is performed less frequently. We also show that instantaneous repair is not always optimal.Comment: To be presented at IEEE Information Theory Workshop (ITW) 2015, Jeju Island, Korea, October 201

A Family of Erasure Correcting Codes with Low Repair Bandwidth and Low Repair Complexity

We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the first class of symbols is to provide good erasure correcting capability, while the second class facilitates node repair, reducing the repair bandwidth and the repair complexity. We compare the proposed codes with other codes proposed in the literature.Comment: Accepted, will appear in the proceedings of Globecom 2015 (Selected Areas in Communications: Data Storage

Distributed Storage in Mobile Wireless Networks with Device-to-Device Communication

We consider the use of distributed storage (DS) to reduce the communication cost of content delivery in wireless networks. Content is stored (cached) in a number of mobile devices using an erasure correcting code. Users retrieve content from other devices using device-to-device communication or from the base station (BS), at the expense of higher communication cost. We address the repair problem when a device storing data leaves the cell. We introduce a repair scheduling where repair is performed periodically and derive analytical expressions for the overall communication cost of content download and data repair as a function of the repair interval. The derived expressions are then used to evaluate the communication cost entailed by DS using several erasure correcting codes. Our results show that DS can reduce the communication cost with respect to the case where content is downloaded only from the BS, provided that repairs are performed frequently enough. If devices storing content arrive to the cell, the communication cost using DS is further reduced and, for large enough arrival rate, it is always beneficial. Interestingly, we show that MDS codes, which do not perform well for classical DS, can yield a low overall communication cost in wireless DS.Comment: After final editing for publication in TCO

Optimized Bit Mappings for Spatially Coupled LDPC Codes over Parallel Binary Erasure Channels

In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly employed to determine how the coded bits are allocated to the channels. In this paper, we study spatially coupled low-density parity check codes over parallel channels and optimize the bit mapper using BICM as the driving example. For simplicity, the parallel bit channels that arise in BICM are replaced by independent binary erasure channels (BECs). For two parallel BECs modeled according to a 4-PAM constellation labeled by the binary reflected Gray code, the optimization results show that the decoding threshold can be improved over a uniform random bit mapper, or, alternatively, the spatial chain length of the code can be reduced for a given gap to capacity. It is also shown that for rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be initiated using only an optimized bit mapper

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454

Spatially-Coupled Codes for Optical Communications: State-of-the-Art and Open Problems

We give a brief survey of a particularly interesting class of codes, called spatially-coupled codes, which are strong candidates for future optical communication systems. We discuss some recent research on this class of codes in the area of optical communications, and summarize some open research problems

Terminated and Tailbiting Spatially-Coupled Codes with Optimized Bit Mappings for Spectrally Efficient Fiber-Optical Systems

We study the design of spectrally efficient fiber-optical communication systems based on different spatially coupled (SC) forward error correction (FEC) schemes. In particular, we optimize the allocation of the coded bits from the FEC encoder to the modulation bits of the signal constellation. Two SC code classes are considered. The codes in the first class are protograph-based low-density parity-check (LDPC) codes which are decoded using iterative soft-decision decoding. The codes in the second class are generalized LDPC codes which are decoded using iterative hard-decision decoding. For both code classes, the bit allocation is optimized for the terminated and tailbiting SC cases based on a density evolution analysis. An optimized bit allocation can significantly improve the performance of tailbiting SC codes codes over the baseline sequential allocation, up to the point where they have a comparable gap to capacity as their terminated counterparts, at a lower FEC overhead. For the considered terminated SC codes, the optimization only results in marginal performance improvements, suggesting that in this case a sequential allocation is close to optimal.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

Code Constructions for Distributed Storage With Low Repair Bandwidth and Low Repair Complexity

We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where the primary goal of the first class of codes is to provide fault tolerance, while the second class aims at reducing the repair bandwidth and repair complexity. The repair procedure is a two- step procedure where parts of the failed node are repaired in the first step using the first code. The downloaded symbols during the first step are cached in the memory and used to repair the remaining erased data symbols at minimal additional read cost during the second step. The first class of codes is based on MDS codes modified using piggybacks, while the second class is designed to reduce the number of additional symbols that need to be downloaded to repair the remaining erased symbols. We numerically show that the proposed codes achieve better repair bandwidth compared to MDS codes, codes constructed using piggybacks, and local reconstruction/Pyramid codes, while a better repair complexity is achieved when compared to MDS, Zigzag, Pyramid codes, and codes constructed using piggybacks.Comment: To appear in IEEE Transactions on Communication

Dynamic Coded Caching in Wireless Networks

We consider distributed and dynamic caching of coded content at small base stations (SBSs) in an area served by a macro base station (MBS). Specifically, content is encoded using a maximum distance separable code and cached according to a time-to-live (TTL) cache eviction policy, which allows coded packets to be removed from the caches at periodic times. Mobile users requesting a particular content download coded packets from SBSs within communication range. If additional packets are required to decode the file, these are downloaded from the MBS. We formulate an optimization problem that is efficiently solved numerically, providing TTL caching policies minimizing the overall network load. We demonstrate that distributed coded caching using TTL caching policies can offer significant reductions in terms of network load when request arrivals are bursty. We show how the distributed coded caching problem utilizing TTL caching policies can be analyzed as a specific single cache, convex optimization problem. Our problem encompasses static caching and the single cache as special cases. We prove that, interestingly, static caching is optimal under a Poisson request process, and that for a single cache the optimization problem has a surprisingly simple solution.Comment: To appear in IEEE Transactions on Communication