On the decoding failure probability of random network coded cooperation

This paper considers a network of source nodes that transmit data packets to a destination node via relay nodes over erasure channels by using random linear network coding. The probability that the destination node will fail to recover the packets of all source nodes has been bounded and approximated in the literature for the case of relay nodes that randomly assign only nonzero values to the coefficients of linear combinations of data packets. The paper argues for the necessity of giving relay nodes the choice to also assign the zero value to coefficients when arithmetic operations are over finite fields of small size, e.g. GF(2). Alternative probability mass functions for the coefficients are considered, and expressions for the decoding failure probability are re-derived

On the Design of a Novel Joint Network-Channel Coding Scheme for the Multiple Access Relay Channel

This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines -- over a non-binary finite field -- the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.Comment: 28 pages, 9 figures; Submitted to IEEE Journal on Selected Areas in Communications - Special Issue on Theories and Methods for Advanced Wireless Relays, 201

Diversity analysis, code design, and tight error rate lower bound for binary joint network-channel coding

Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly proposed as an alternative to a standard layered construction, such as the OSI-model. The main performance metrics for JNCCs are scalability to larger networks and error rate. The diversity order is one of the most important parameters determining the error rate. The literature on JNCC is growing, but a rigorous diversity analysis is lacking, mainly because of the many degrees of freedom in wireless networks, which makes it very hard to prove general statements on the diversity order. In this article, we consider a network with slowly varying fading point-to-point links, where all sources also act as relay and additional non-source relays may be present. We propose a general structure for JNCCs to be applied in such network. In the relay phase, each relay transmits a linear transform of a set of source codewords. Our main contributions are the proposition of an upper and lower bound on the diversity order, a scalable code design and a new lower bound on the word error rate to assess the performance of the network code. The lower bound on the diversity order is only valid for JNCCs where the relays transform only two source codewords. We then validate this analysis with an example which compares the JNCC performance to that of a standard layered construction. Our numerical results suggest that as networks grow, it is difficult to perform significantly better than a standard layered construction, both on a fundamental level, expressed by the outage probability, as on a practical level, expressed by the word error rate

DMT Optimal Cooperative Protocols with Destination-Based Selection of the Best Relay

We design a cooperative protocol in the context of wireless mesh networks in order to increase the reliability of wireless links. Destination terminals ask for cooperation when they fail in decoding data frames transmitted by source terminals. In that case, each destination terminal D calls a specific relay terminal B with a signaling frame to help its transmission with source terminal S. To select appropriate relays, destination terminals maintain tables of relay terminals, one for each possible source address. These tables are constituted by passively overhearing ongoing transmissions. Hence, when cooperation is needed between S and D, and when a relay B is found by terminal D in the relay table associated with terminal S, the destination terminal sends a negative acknowledgment frame that contains the address of B. When the best relay B has successfully decoded the source message, it sends a copy of the data frame to D using a selective decode-andforward transmission scheme. The on-demand approach allows maximization of the spatial multiplexing gain and the cooperation of the best relay allows maximization of the spatial diversity order. Hence, the proposed protocol achieves optimal diversitymultiplexing trade-off performance. Moreover, this performance is achieved through a collision-free selection process