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

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder

Exit charts based analysis and design of rateless codes for the erasure and Gaussian channels

Luby Transform Codes were the first class of universal erasure codes introduced to fully realize the concept of scalable and fault‐tolerant distribution of data over computer networks, also called Digital Fountain. Later Raptor codes, a generalization of the LT codes were introduced to trade off complexity with performance. In this work, we show that an even broader class of codes exists that are near optimal for the erasure channel and that the Raptor codes form a special case. More precisely, Raptorlike codes can be designed based on an iterative (joint) decoding schedule wherein information is transferred between the LT decoder and an outer decoder in an iterative manner. The design of these codes can be formulated as a LP problem using EXIT Charts and density evolution. In our work, we show the existence of codes, other than the Raptor codes, that perform as good as the existing ones. We extend this framework of joint decoding of the component codes to the additive white Gaussian noise channels and introduce the design of Rateless codes for these channels. Under this setting, for asymptotic lengths, it is possible to design codes that work for a class of channels defined by the signal‐to‐noise ratio. In our work, we show that good profiles can be designed using density evolution and Gaussian approximation. EXIT charts prove to be an intuitive tool and aid in formulating the code design problem as a LP problem. EXIT charts are not exact because of the inherent approximations. Therefore, we use density evolution to analyze the performance of these codes. In the Gaussian case, we show that for asymptotic lengths, a range of designs of Rateless codes exists to choose from based on the required complexity and the overhead. Moreover, under this framework, we can design incrementally redundant schemes for already existing outer codes to make the communication system more robust to channel noise variations

Joint Coding and Scheduling Optimization in Wireless Systems with Varying Delay Sensitivities

Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications.We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum ordered inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitters. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitters to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations.Comment: 9 pages, 10 figure

Spectrum Sensing and Security Challenges and Solutions: Contemporary Affirmation of the Recent Literature

Cognitive radio (CR) has been recently proposed as a promising technology to improve spectrum utilization by enabling secondary access to unused licensed bands. A prerequisite to this secondary access is having no interference to the primary system. This requirement makes spectrum sensing a key function in cognitive radio systems. Among common spectrum sensing techniques, energy detection is an engaging method due to its simplicity and efficiency. However, the major disadvantage of energy detection is the hidden node problem, in which the sensing node cannot distinguish between an idle and a deeply faded or shadowed band. Cooperative spectrum sensing (CSS) which uses a distributed detection model has been considered to overcome that problem. On other dimension of this cooperative spectrum sensing, this is vulnerable to sensing data falsification attacks due to the distributed nature of cooperative spectrum sensing. As the goal of a sensing data falsification attack is to cause an incorrect decision on the presence/absence of a PU signal, malicious or compromised SUs may intentionally distort the measured RSSs and share them with other SUs. Then, the effect of erroneous sensing results propagates to the entire CRN. This type of attacks can be easily launched since the openness of programmable software defined radio (SDR) devices makes it easy for (malicious or compromised) SUs to access low layer protocol stacks, such as PHY and MAC. However, detecting such attacks is challenging due to the lack of coordination between PUs and SUs, and unpredictability in wireless channel signal propagation, thus calling for efficient mechanisms to protect CRNs. Here in this paper we attempt to perform contemporary affirmation of the recent literature of benchmarking strategies that enable the trusted and secure cooperative spectrum sensing among Cognitive Radios