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

User-Antenna Selection for Physical-Layer Network Coding based on Euclidean Distance

In this paper, we present the error performance analysis of a multiple-input multiple-output (MIMO) physical-layer network coding (PNC) system with two different user-antenna selection (AS) schemes in asymmetric channel conditions. For the first antenna selection scheme (AS1), where the user-antenna is selected in order to maximize the overall channel gain between the user and the relay, we give an explicit analytical proof that for binary modulations, the system achieves full diversity order of $min(N_A , N_B ) \times N_R$ in the multiple-access (MA) phase, where $N_A$, $N_B$ and $N_R$ denote the number of antennas at user $A$, user $B$ and relay $R$ respectively. We present a detailed investigation of the diversity order for the MIMO-PNC system with AS1 in the MA phase for any modulation order. A tight closed-form upper bound on the average SER is also derived for the special case when $N_R = 1$, which is valid for any modulation order. We show that in this case the system fails to achieve transmit diversity in the MA phase, as the system diversity order drops to $1$ irrespective of the number of transmit antennas at the user nodes. Additionally, we propose a Euclidean distance (ED) based user-antenna selection scheme (AS2) which outperforms the first scheme in terms of error performance. Moreover, by deriving upper and lower bounds on the diversity order for the MIMO-PNC system with AS2, we show that this system enjoys both transmit and receive diversity, achieving full diversity order of $\min(N_A, N_B) \times N_R$ in the MA phase for any modulation order. Monte Carlo simulations are provided which confirm the correctness of the derived analytical results.Comment: IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1709.0445

Source-Channel Diversity for Parallel Channels

We consider transmitting a source across a pair of independent, non-ergodic channels with random states (e.g., slow fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or at the application layer through multiple description source coding. For on-off channel models, source coding diversity offers better performance. For channels with a continuous range of reception quality, we show the reverse is true. Specifically, we introduce a new figure of merit called the distortion exponent which measures how fast the average distortion decays with SNR. For continuous-state models such as additive white Gaussian noise channels with multiplicative Rayleigh fading, optimal channel coding diversity at the physical layer is more efficient than source coding diversity at the application layer in that the former achieves a better distortion exponent. Finally, we consider a third decoding architecture: multiple description encoding with a joint source-channel decoding. We show that this architecture achieves the same distortion exponent as systems with optimal channel coding diversity for continuous-state channels, and maintains the the advantages of multiple description systems for on-off channels. Thus, the multiple description system with joint decoding achieves the best performance, from among the three architectures considered, on both continuous-state and on-off channels.Comment: 48 pages, 14 figure

Short Block-length Codes for Ultra-Reliable Low-Latency Communications

This paper reviews the state of the art channel coding techniques for ultra-reliable low latency communication (URLLC). The stringent requirements of URLLC services, such as ultra-high reliability and low latency, have made it the most challenging feature of the fifth generation (5G) mobile systems. The problem is even more challenging for the services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and failure rate as low as $10^{-9}$. The very low latency requirements of URLLC do not allow traditional approaches such as re-transmission to be used to increase the reliability. On the other hand, to guarantee the delay requirements, the block length needs to be small, so conventional channel codes, originally designed and optimised for moderate-to-long block-lengths, show notable deficiencies for short blocks. This paper provides an overview on channel coding techniques for short block lengths and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail with several possible solutions.Comment: Accepted for publication in IEEE Communications Magazin

Analysis and construction of full-diversity joint network-LDPC codes for cooperative communications

Cooperative communication is a well known technique to yield transmit diversity and network coding can increase the spectral efficiency. These two techniques can be combined to achieve a double diversity order for a maximum coding rate Rc = 2/3 on the Multiple Access Relay Channel (MARC); Transmit diversity is necessary in harsh environments to reduce the required transmit power for achieving a given error performance at a certain transmission rate. In networks; where two sources share a common relay in their transmission to the destination. However; codes have to be carefully designed to obtain the intrinsic diversity offered by the MARC. This paper presents the principles to design a family of full-diversity LDPC codes with maximum rate. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full-diversity