Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0772

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.Comment: 18 page

AirSync: Enabling Distributed Multiuser MIMO with Full Spatial Multiplexing

The enormous success of advanced wireless devices is pushing the demand for higher wireless data rates. Denser spectrum reuse through the deployment of more access points per square mile has the potential to successfully meet the increasing demand for more bandwidth. In theory, the best approach to density increase is via distributed multiuser MIMO, where several access points are connected to a central server and operate as a large distributed multi-antenna access point, ensuring that all transmitted signal power serves the purpose of data transmission, rather than creating "interference." In practice, while enterprise networks offer a natural setup in which distributed MIMO might be possible, there are serious implementation difficulties, the primary one being the need to eliminate phase and timing offsets between the jointly coordinated access points. In this paper we propose AirSync, a novel scheme which provides not only time but also phase synchronization, thus enabling distributed MIMO with full spatial multiplexing gains. AirSync locks the phase of all access points using a common reference broadcasted over the air in conjunction with a Kalman filter which closely tracks the phase drift. We have implemented AirSync as a digital circuit in the FPGA of the WARP radio platform. Our experimental testbed, comprised of two access points and two clients, shows that AirSync is able to achieve phase synchronization within a few degrees, and allows the system to nearly achieve the theoretical optimal multiplexing gain. We also discuss MAC and higher layer aspects of a practical deployment. To the best of our knowledge, AirSync offers the first ever realization of the full multiuser MIMO gain, namely the ability to increase the number of wireless clients linearly with the number of jointly coordinated access points, without reducing the per client rate.Comment: Submitted to Transactions on Networkin

Raptor Codes for BIAWGN Channel: SNR Mismatch and the Optimality of the Inner and Outer Rates

Fountain codes are a class of rateless codes with two interesting properties, first, they can generate potentially limitless numbers of encoded symbols given a finite set of source symbols, and second, the source symbols can be recovered from any subset of encoded symbols with cardinality greater than the number of source symbols. Raptor codes are the first implementation of fountain codes with linear complexity and vanishing error floors on noisy channels. Raptor codes are designed by the serial concatenation of an inner Luby trans-form (LT) code, the first practical realization of fountain codes, and an outer low-density parity-check (LDPC) code. Raptor codes were designed to operate on the binary erasure channel (BEC), however, since their invention they received considerable attention in or-der to improve their performance on noisy channels, and especially additive white Gaussiannoise (AWGN) channels. This dissertation considers two issues that face Raptor codes on the binary input additive white Gaussian noise (BIAWGN) channel: inaccurate estimation of signal to noise ratio (SNR) and the optimality of inner and outer rates. First, for codes that use a belief propagation algorithm (BPA) in decoding, such as Raptor codes on the BIAWGN channel, accurate estimation of the channel SNR is crucial to achieving optimal performance by the decoder. A difference between the estimated SNR and the actual channel SNR is known as signal to noise ratio mismatch (SNRM). Using asymptomatic analysis and simulation, we show the degrading effects of SNRM on Raptor codes and observe that if the mismatch is large enough, it can cause the decoding to fail. Using the discretized density evolution (DDE) algorithm with the modifications required to simulate the asymptotic performance in the case of SNRM, we determine the decoding threshold of Raptor codes for different values of SNRM ratio. Determining the threshold under SNRM enables us to quantify its effects which in turn can be used to reach important conclusions about the effects of SNRM on Raptor codes. Also, it can be used to compare Raptor codes with different designs in terms of their tolerance to SNRM. Based on the threshold response to SNRM, we observe that SNR underestimation is slightly less detrimental to Raptor codes than SNR overestimation for lower levels of mismatch ratio, however, as the mismatch increases, underestimation becomes more detrimental. Further, it can help estimate the tolerance of a Raptor code, with certain code parameters when transmitted at some SNR value, to SNRM. Or equivalently, help estimate the SNR needed for a given code to achieve a certain level of tolerance to SNRM. Using our observations about the performance of Raptor codes under SNRM, we propose an optimization method to design output degree distributions of the LT part that can be used to construct Raptor codes with more tolerance to high levels of SNRM. Second, we study the effects of choosing different values of inner and outer code rate pairs on the decoding threshold and performance of Raptor codes on the BIAWGN channel. For concatenated codes such as Raptor codes, given any instance of the overall code rate R, different inner (Ri) and outer (Ro) code rate combinations can be used to share the available redundancy as long asR=RiRo. Determining the optimal inner and outer rate pair can improve the threshold and performance of Raptor codes. Using asymptotic analysis, we show the effect of the rate pair choice on the threshold of Raptor codes on the BIAWGN channel and how the optimal rate pair is decided. We also show that Raptor codes with different output degree distributions can have different optimal rate pairs, therefore, by identifying the optimal rate pair we can further improve the performance and avoid suboptimal use of the code. We make the observation that as the outer rate of Raptor codes increases the potential of achieving better threshold increases, and provide the reason why the optimal outer rate of Raptor codes cannot occur at lower values. Finally, we present an optimization method that considers the optimality of the inner and outer rates in designing the output degree distribution of the inner LT part of Raptor codes. The designed distributions show improvement in both the decoding threshold and performance compared to other code designs that do not consider the optimality of the inner and outer rates

Evaluation of cross-layer reliability mechanisms for satellite digital multimedia broadcast

This paper presents a study of some reliability mechanisms which may be put at work in the context of Satellite Digital Multimedia Broadcasting (SDMB) to mobile devices such as handheld phones. These mechanisms include error correcting codes, interleaving at the physical layer, erasure codes at intermediate layers and error concealment on the video decoder. The evaluation is made on a realistic satellite channel and takes into account practical constraints such as the maximum zapping time and the user mobility at several speeds. The evaluation is done by simulating different scenarii with complete protocol stacks. The simulations indicate that, under the assumptions taken here, the scenario using highly compressed video protected by erasure codes at intermediate layers seems to be the best solution on this kind of channel