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

Design of diversity-achieving LDPC codes for H-ARQ with cross-packet channel coding

In wireless scenarios an effective protocol to increase the reliability for time-varying channels is the hybrid automatic repeat request (H-ARQ). The H-ARQ scheme with cross-packet channel coding (CPC) is a recently published extension of H-ARQ with several advantages. No full-diversity low-density parity-check (LDPC) code design for the whole range of coding rates yielding full-diversity has been published. In this paper the authors provide a new outage behavior analysis and a new structured LDPC code ensemble achieving full-diversity for H-ARQ with CPC by exploiting the rootcheck principle. Simulation results show that the new code design outperforms the previous approaches, providing full-diversity and good coding gain, also at high coding rates

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

A full-diversity joint network-channel code construction for cooperative communications

Cooperative communications is a well known technique to yield transmit diversity in a multi-user environment. Network coding can increase the spectral efficiency in networks. 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), where two sources share a common relay in their transmission to the destination. However, codes have to be carefully designed to obtain the intrinsic channel diversity. Up till now, no full-diversity capacity achieving code for the MARC at a coding rate Rc = 2/3 has been published. We present a strategy to produce excellent low-density parity-check (LDPC) codes with rate 2/3, i.e., exhibiting full-diversity and operating close to the outage probability limit. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full-diversity

Analysis and Construction of Full-Diversity Joint Network-LDPC Codes for Cooperative Communications

<p/> <p>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, 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 <inline-formula> <graphic file="1687-1499-2010-805216-i1.gif"/></inline-formula> on the Multiple-Access Relay Channel (MARC), 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.</p

Towards full-diversity joint network-channel coding for large networks

Network coding and cooperative channel coding have both proved their importance for cooperative communications in wireless networks. It has been shown that it is beneficial to perform both techniques jointly. However, no diversity analysis for this framework has been made. Furthermore, the network codes in the state of the art have weak points from a coding point of view. This paper proposes a new general technique to construct network codes as an integral part of the channel code. The diversity order of this framework is analyzed. Simulation of the word error rate performance of the new proposed joint network-channel code illustrates the benefit of joint network-channel coding

Non-binary decoding of structured LDPC codes: Density evolution

International audienc

Nonbinary decoding of structured LDPC codes

International audienc