Linear Coding Scheme Research Articles

The Explicit Decoding Delay Probability Distribution Based on Random Linear Coding Scheme

Under random linear coding (RLC) scheme, we present a simple expression of the probability distribution p(D=K) for decoding delay D incurred by the lossy channel, where K is a positive integer. In contrast with the previous contribution, our focus is firstly on deriving the cumulative distribution function of the discrete random variable D over a perfect channel. One benefit of such dispose is that, from the overall viewpoint, computing the cumulative distribution function of delay D can be related with calculating the cardinalities of sets of some special matrices, so that the former can be obtained from the latter. Moreover, our expression of the probability distribution is an explicit form, and is valid for any number of packets M, freewill field size q and arbitrary channel loss rate ε.

Multimedia Streaming for Ad Hoc Wireless Mesh Networks Using Network Coding

Over the past years, we have witnessed an explosive growth in the use of multimedia applications such as audio and video streaming with mobile and static devices. Multimedia streaming applications need new approaches to multimedia transmissions to meet the growing volume demand and quality expectations of multimedia traffic. This paper studies network coding which is a promising paradigm that has the potential to improve the performance of networks for multimedia streaming applications in terms of packet delivery ratio (PDR), latency and jitter. This paper examines several network coding protocols for ad hoc wireless mesh networks and compares their performance on multimedia streaming applications with optimized broadcast protocols, e.g., BCast, Simplified Multicast Forwarding (SMF), and Partial Dominant Pruning (PDP). The results show that the performance increases significantly with the Random Linear Network Coding (RLNC) scheme.

Linear Network Coding Strategies for the Multiple Access Relay Channel with Packet Erasures

The multiple access relay channel (MARC) where multiple users send independent information to a single destination aided by a single relay under large-scale path loss and slow fading is investigated. At the beginning, the users take turns to transmit their packets. The relay is not aware of the erasure status of each packet at the destination but has the knowledge of the average signal-to-noise-ratio (SNR) of every communication link. With this knowledge, the relay applies network coded retransmission on the overheard packets so as to maximize the expected total number of recovered packets or minimize the average packet loss rate at the destination. Several network coding (NC) strategies at the relay are designed. In particular, for the case where the relay is given only one time slot for retransmission, an optimal NC construction is derived. For the multiple-slot case, three sub-optimal schemes are investigated, namely network coding with maximum distance separable (MDS) code (NC-MDS), the worst-user-first (WUF) scheme and a hybrid of NC-MDS and WUF. We prove that NC-MDS and WUF are asymptotically optimal in the high and low SNR regimes, respectively. A lower bound on the average packet loss rate has been derived. Numerical studies show that, in a cellular system, the hybrid scheme offers significant performance gain over a number of existing schemes in a wide range of SNR. We also observe that performance curves of both WUF and the hybrid scheme touch the derived lower bound in the low SNR regime.

Asymptotically Optimal Error-Rate Performance of Linear Physical-Layer Network Coding in Rayleigh Fading Two-Way Relay Channels

We study a new linear physical-layer network coding (LPNC) scheme for fading two-way relay channels. In the uplink phase, two users transmit simultaneously. The relay selects some integer coefficients and computes a linear combination (in a size-q finite set) of the two users' messages, which is broadcast in the downlink phase. We develop a design criterion for choosing the integer coefficients that minimizes the error probability. Based on that, we derive an asymptotically tight bound, in a closed-form, for the error probability of the LPNC scheme over Rayleigh fading channels. Our analysis shows that the error-rate performance of the LPNC scheme becomes asymptotically optimal at a high SNR, and our designed LPNC scheme significantly outperforms existing schemes in the literature.

Distributed Space-Time Coding for Full-Duplex Asynchronous Cooperative Communications

In this paper, we propose two distributed linear convolutional space-time coding (DLC-STC) schemes for full-duplex (FD) asynchronous cooperative communications. The DLC-STC Scheme 1 is for the case of the complete loop channel cancellation, which achieves the full asynchronous cooperative diversity. The DLC-STC Scheme 2 is for the case of the partial loop channel cancellation and amplifying, where some loop signals are used as the self-coding instead of treated as interference to be directly cancelled. We show this scheme can achieve full asynchronous cooperative diversity. We then evaluate the performance of the two schemes when loop channel information is not accurate and present an amplifying factor control method for the DLC-STC Scheme 2 to improve its performance with inaccurate loop channel information. Simulation results show that the DLC-STC Scheme 1 outperforms the DLC-STC Scheme 2 and the delay diversity scheme if perfect or high quality loop channel information is available at the relay, while the DLC-STC Scheme 2 achieves better performance if the loop channel information is imperfect.

Unequal Error Protection Random Linear Coding Strategies for Erasure Channels

In this paper, we provide the performance analysis of unequal error protection (UEP) random linear coding (RLC) strategies designed for transmission of source messages containing packets of different importance over lossy packet erasure links. By introducing the probabilistic encoding framework, we first derive the general performance limits for the packet-level UEP coding strategies that encode the packets of each importance class of the source message independently (non-overlapping windowing strategy) or jointly (expanding windowing strategy). Then, we demonstrate that the general performance limits of both strategies are achievable by the probabilistic encoding over non-overlapping and expanding windows based on RLC and the Gaussian Elimination (GE) decoding. Throughout the paper, we present a number of examples that investigate the performance and optimization of code design parameters of the expanding window RLC strategy and compare it with the non-overlapping RLC strategy selected as a reference.

Notes on "Exact Decoding Probability Under Random Linear Network Coding"

In a recent letter, Trullols-Cruces et al. derived the exact decoding probability P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ns</sub> (K,N) that a receiver node obtained N linearly independent coded packets among K (K≥ N) received coded packets, when the source node uses a random linear coding scheme over a Galois Field GF(q). They discussed P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ns</sub> (K,N) both in the case of the source node sending the random linear combination of the original packets, including all-zero combinations, as well as the case of excluding all-zero combinations. However, their derivations are a bit complicated. In this note, we demonstrate simple derivations of the exact decoding probability P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ns</sub> (K,N) in both cases. Furthermore, we point out that there is a more succinct expression of P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ns</sub> (K,N) for the latter case.

Queueing Delay Analysis for Multicast With Random Linear Coding

We analyze the queueing delay performance when random linear coding is performed over packets randomly arriving at a source node for multicast transmission over packet erasure channels. We model random coding of packets as a bulk-service queueing system, where packets are served and depart the queue in groups. In this framework, we analyze two different block-based random linear coding schemes. The first scheme involves coding over a fixed blocksize, which leads to simpler analysis but also to a delay penalty for lightly-loaded systems. The second scheme adapts to the traffic load by allowing for a variable blocksize, thereby removing the delay penalty at low loads. We provide results on the maximum stable arrival rate of packets at the source and on the queueing delay as a function of the arrival rate.

Network Coding in Node-Constrained Line and Star Networks

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.

ComboCoding: Combined intra-/inter-flow network coding for TCP over disruptive MANETs

TCP over wireless networks is challenging due to random losses and ACK interference. Although network coding schemes have been proposed to improve TCP robustness against extreme random losses, a critical problem still remains of DATA–ACK interference. To address this issue, we use inter-flow coding between DATA and ACK to reduce the number of transmissions among nodes. In addition, we also utilize a “pipeline” random linear coding scheme with adaptive redundancy to overcome high packet loss over unreliable links. The resulting coding scheme, ComboCoding, combines intra-flow and inter-flow coding to provide robust TCP transmission in disruptive wireless networks. The main contributions of our scheme are twofold; the efficient combination of random linear coding and XOR coding on bi-directional streams (DATA and ACK), and the novel redundancy control scheme that adapts to time-varying and space-varying link loss. The adaptive ComboCoding was tested on a variable hop string topology with unstable links and on a multipath MANET with dynamic topology. Simulation results show that TCP with ComboCoding delivers higher throughput than with other coding options in high loss and mobile scenarios, while introducing minimal overhead in normal operation.

FTS: A Distributed Energy-Efficient Broadcasting Scheme Using Fountain Codes for Multihop Wireless Networks

We investigate the problem of reliable and energy-efficient one-to-all broadcasting in multihop wireless networks, and propose fractional transmission scheme (FTS) - a low-complexity and scalable broadcasting scheme. FTS exploits the broadcasting nature of wireless channels and random encoding of rateless codes to reduce energy consumption while ensuring reliable delivery of packets to all nodes in the network. In the proposed scheme, different neighbors of a node share the responsibility of transmitting packets by sending only a fraction of encoded packets required by the node to successfully receive the data sent by the source. A detailed analysis of the performance of FTS is presented for grid and random deployment networks. Further, extensive simulations compare our scheme with present energy-efficient methods such as random linear coding, multipoint relaying, dominant pruning, and broadcast incremental power scheme. Simulations reveal that FTS offers good performance and adaptability at a low computational cost.

On Linear Coding Schemes for Stabilizing LTI Control with Multiple Sensors

We examine the problem of designing the encoding and control policies of a linear stochastic control system, where the communication channel between the plant state observer (sensor) and the controller is a lossy wireless channel that is constrained in terms of transmit power and bandwidth. For a first-order ARMA modeled plant with Gaussian statistics, when there are two sensors observing the plant, nonlinear encoding is shown to result in smaller cost at time instant [Formula: see text] compared to the linear schemes, if transmissions are carried out over parallel Gaussian independent channels. In this paper, optimal linear coding schemes for the case of multiple sensors are examined. They are shown to minimize the control cost at the infinite time horizon, when the wireless channel is accessed using time division multiplexing. Our analysis is carried out for when separation between the state estimation and control is possible, and the optimal steady state control law is certainty equivalent. The distortion lower bound for estimating the plant state is derived, along with the necessary conditions on the transmit power that minimize the steady state control cost. We also propose a linear scheme that reaches the distortion bound asymptotically under relaxed conditions.

A Novel Linear Combinatorial Coding Scheme for Optical CDMA and its Performance

A novel linear combinatorial code (LCC) is first proposed for optical code division multiple access (OCDMA) communication. The LCCs are constructed with some time-domain (one-dimensional) / wavelength-time (two-dimensional) codes with uniform code length in a family of optical orthogonal or pseudo-orthogonal codes. The preference of the proposed LCC is analyzed in comparison with that of optical orthogonal codes. The schemes of encoder and decoder are analyzed. In the proposed scheme, the two important system parameters, namely the probability of error (bit error rate) in terms of multiuser interference and the capacity of codes, are improved notably. Moreover, the bit error rate can be controlled by varying the combinatorial code parameters.

Optimum linear causal coding schemes for Gaussian stochastic processes in the presence of correlated jamming

The complete solution is obtained to the following problem. A Gaussian stochastic process ( theta /sub t/,t in (0,t/sub f/)) satisfying a certain stochastic differential equation is to be transmitted through a stochastic channel to a receiver under minimum mean-squared error distortion measure. The channel is to be used for exactly t/sub f/ seconds, and, in addition to white Gaussian noise with a given energy level, the channel is corrupted by another source whose output may be correlated with the input to the channel and which satisfied a given power constraint. There is an input power constraint to the channel, and noiseless feedback is allowed between the receiver (decoder) and the transmitter (encoder). The authors determine the linear causal encoder and decoder structures that function optimally under the worst admissible noise inputs to the channel. The least favorable probability distribution for this unknown noise is found to be Gaussian and is correlated with the transmitted signal. Also included is a comparative study of these results with earlier ones that addressed a similar problem without a causality restriction imposed on the transmitter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal linear coding schemes for feedback communication with noisy side information (Corresp.)

Optimal linear coding schemes for feedback communication with noisy side information are derived. The performance of two schemes with side information are compared with the information-theoretic bounds. The side information at the transmitter Significantly reduces the mean-squared error. The corresponding continuous-time system is briefly mentioned.