We investigate cooperative wireless relay networks in which the nodes can help each other in data transmission. We study different coding strategies in the single-source single-destination network with many relay nodes. Given the myriad of ways in which nodes can cooperate, there is a natural routing problem, i.e., determining an ordered set of nodes to relay the data from the source to the destination. We find that for a given route, the decode- and-forward strategy, which is an information theoretic cooperative coding strategy, achieves rates significantly higher than that achievable by the usual multi-hop coding strategy, which is a point-to-point non-cooperative coding strategy. We construct an algorithm to find an optimal route (in terms of rate maximizing) for the decode-and- forward strategy. Since the algorithm runs in factorial time in the worst case, we propose a heuristic algorithm that runs in polynomial time. The heuristic algorithm outputs an optimal route when the nodes transmit independent codewords. We implement these coding strategies using practical low density parity check codes to compare the performance of the strategies on different routes.
@cite_11: Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.
@cite_8: A novel coding technique is proposed for the quasi-static fading relay channel. The source broadcasts a recursive code to both relay and destination. The relay decodes, interleaves, and re-encodes the message prior to forwarding. Because the destination receives both codes in parallel, a distributed turbo code is embedded in the relay channel. Results indicate a combined diversity and coding gain, which is significant even for simple constituent codes.
@cite_1: In this paper, turbo-based coding scheme for relay systems together with iterative decoding algorithms is designed. The performance of the proposed schemes is about 1.0-1.5 dB away from the information theoretical limits for various channel models.
@cite_6: A decode-and-forward LDPC-based coding and decoding scheme is proposed and applied to the BAWGN single-relay channel. The source broadcasts information to both the relay and the destination. The relay is able to simultaneously receive and transmit. Both the relay and the destination apply successive iterative decoding using belief propagation. In the proposed scheme, the LDPC code used by the source and the LDPC code used by the relay are designed independently of each other. Optimality properties of this approach are established via information-theoretic upper and lower bounds. Asymptotic analysis shows that the performance of the proposed scheme can be as close as 0.02 dB away from the theoretical limit for any decode-and-forward scheme, and simulation results show that its performance for a block code of length 214 can be within 0.65 dB away from the same limit with a corresponding bit error probability of 10?6.
@cite_27: In this paper, we investigate achievable rates for data transmission from sources to sinks through multiple relay networks. We consider myopic coding, a constrained communication strategy in which each node has only a local view of the network, meaning that nodes can only transmit to and decode from neighboring nodes. We compare this with omniscient coding, in which every node has a global view of the network and all nodes can cooperate. Using Gaussian channels as examples, we find that when the nodes transmit at low power, the rates achievable with two-hop myopic coding are as large as that under omniscient coding in a five-node multiple relay channel and close to that under omniscient coding in a six-node multiple relay channel. These results suggest that we may do local coding and cooperation without compromising much on the transmission rate. Practically, myopic coding schemes are more robust to topology changes because encoding and decoding at a node are not affected when there are changes at remote nodes. Furthermore, myopic coding mitigates the high computational complexity and large buffer memory requirements of omniscient coding
@cite_23: This paper describes a methodology for efficient implementation of binning and block-Markov coding for the relay channel using powerful features of low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated random linear paritybits in a specially designed bilayer graphical code structure. Bilayer density evolution is devised as a novel extension of the standard density evolution algorithm to analyze the performance of the proposed bilayer LDPC code. Based on this bilayer density evolution technique, an EXIT-chart-based code design method using linear programming is developed. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC code is capable of working at two different channel parameters, the signal-to-noise ratio (SNR) at the relay and the SNR at the destination. In this paper, for specific channel parameters, it is demonstrated that a bilayer LDPC code can approach the theoretical decode-and-forward rate of the relay channel within a 0.19 dB gap to the source-relay channel capacity and a 0.34 dB gap to the relay-destination channel capacity.
@cite_2: For the multiple-level relay channel, an achievable rate formula, and a simple coding scheme to achieve it, are presented. Generally, higher rates can be achieved with this coding scheme in the multiple-level relay case than previously known. For a class of degraded channels, this achievable rate is shown to be the exact capacity. An application of the coding scheme to the allcast problem is also discussed.
@cite_16: Recent information theoretical results have shown a considerable improvement in the performance of communication systems through the use of relaying and cooperation. Despite a collection of strong information theoretical results on the relay channel, there has been almost no attention to real code design for the relay channel. In this paper, we present a powerful modular code design approach for the relay channel and corresponding decoding algorithms based on the factor graph representation of the code. For most of the relay channel conditions, the constructed codes with a low-complexity simple relay protocol outperforms any possible code design for the direct channel by achieving an E sub b N sub 0 below the minimum required E sub b N sub 0 of single-link transmission. Moreover, the designed codes achieve a gap of less than 1 dB (at a BER of 10 sup -6 ) to the Shannon limit for the relay channel with a code length of only 2 spl times 10 sup 4 bits.
@cite_20: We investigate the achievable rate of data transmission from sources to sinks through a multiple-relay network. We study achievable rates for omniscient coding, in which all nodes are considered in the coding design at each node. We find that, when maximizing the achievable rate, not all nodes need to cooperate'' with all other nodes in terms of coding and decoding. This leads us to suggest a constrained network, whereby each node only considers a few neighboring nodes during encoding and decoding. We term this myopic coding and calculate achievable rates for myopic coding. We show by examples that, when nodes transmit at low SNR, these rates are close to that achievable by omniscient coding, when the network is unconstrained . This suggests that a myopic view of the network might be as good as a global view. In addition, myopic coding has the practical advantage of being more robust to topology changes. It also mitigates the high computational complexity and large buffer memory requirements of omniscient coding schemes.
@cite_17: We propose Low Density Parity Check (LDPC) code designs for the half-duplex relay channel. Our designs are based on the information theoretic random coding scheme for decode-and-forward relaying. The source transmission is decoded with the help of side information in the form of additional parity bits from the relay. We derive the exact relationships that the component LDPC code profiles in the relay coding scheme must satisfy. These relationships act as constraints for the density evolution algorithm which is used to search for good relay code profiles. To speed up optimization, we outline a Gaussian approximation of density evolution for the relay channel. The asymptotic noise thresholds of the discovered relay code profiles are a fraction of a decibel away from the achievable lower bound for decode-and-forward relaying. With random component LDPC codes, the overall relay coding scheme performs within 1.2 dB of the theoretical limit.
Communications in wireless networks has been progressing from MH to that using cooperative strategies. More research is being directed toward designing codes that are based on information theoretic cooperative coding strategies to harvest the gain in transmission rates predicted by information theory. Examples of codes based on cooperative coding strategies include DF-based Turbo codes @cite_8 @cite_1 and LDPC codes @cite_16 @cite_17 @cite_6 @cite_23 for the single relay channel. It has been mentioned that some of these codes can be extended to the multiple relay channel @cite_2 @cite_11 @cite_20 @cite_27 .