Josephine P. K. Chu

Low-Complexity Cooperative Coding for Sensor Networks using Rateless and LDGM Codes

Given limitations with current technology, nodes in a sensor network have stringent energy and complexity constraints. This paper presents a scheme for cooperative error-control coding, using rateless and low-density generator-matrix codes, for sensor networks. Assuming knowledge of the source-relay channel quality, we show that the proposed scheme achieves good performance and a good energy tradeoff despite low computational complexity. The scheme exploits the flexibility of rateless and LDGM codes to permit, depending on the channel conditions, independent, relay and cooperative modes of operation. As a motivating example, we analyze networks of two cooperating nodes communicating with a more sophisticated receiver. We also discuss the generalization of our framework to a multi-node system.

Low complexity and fractional coded cooperation for wireless networks

Wireless networks, and especially wireless sensor networks, have complexity and energy constraints, within which they must confront the challenging wireless fading environment. In this paper, fractional cooperation is introduced, which is shown to provide energy-efficient and low-complexity diversity gains for constant energy costs per bit throughout the network. To minimize complexity, cooperation is based on demodulate- and-forward, wherein the relay nodes encode demodulated, not decoded symbols. A scheme is presented for cooperative error- control coding in complexity-constrained networks, using low- density generator-matrix codes and repeat-accumulate codes, both chosen for being simple to encode, as well as for their easily adaptable rates. It is shown that these codes, coupled with fractional cooperation, are robust to system parameters and conditions, and introduce little added complexity at the receiver, while providing excellent performance.

Relay Selection for Low-Complexity Coded Cooperation

This paper explores relay selection and selection diversity for coded cooperation in wireless sensor networks, with complexity constraints for the sensor nodes. In previous work, a relaying scheme based on repeat-accumulate (RA) codes was introduced, where it was assumed that the relay does not perform decoding and simply uses demodulated bits to form codewords. However, in a network setting with multiple potential relays where relays do not decode the source transmission, it is not obvious how to select the best relay. The optimal choice involves finding the best relay possibly using density evolution, but is quite complex and time-consuming. It is shown here that the mutual information of the equivalent relay channel, which is much simpler than using DE, is a good selection heuristic. With surprisingly poor performance when a naive selection scheme is used, the importance of a good relay selection scheme is emphasized.

Using the Bhattacharyya parameter for design and analysis of cooperative wireless systems

A simplified method of analysis and design based on the Bhattacharyya parameter (BP) in conjunction with the union bound and weight enumeration is presented for relay channels using coded cooperation. This method is particularly suitable for low-complexity relay systems employing demodulate-and-forward, focusing on the problems of relay selection and outage analysis. These applications are chosen to illustrate the use of the BP in scenarios where analytical solutions are otherwise unattainable. In terms of relay selection, it is shown that BP-based relay selection has essentially the same performance as density evolution, though with much lower complexity. It is further shown that BP-based relay selection can be applied to fractional cooperation, where each relay only forwards a fraction of the source codeword. In terms of analysis, it is shown that weight enumeration with BP can be used to provide a close approximate to the upper bound on the outage probability of fractional cooperation, again with much lower computational complexity than density evolution.

Fractional Cooperation using Coded Demodulate-and-Forward

Since the introduction of cooperative diversity, many different implementations have been proposed to increase the reliability and/or power efficiency of distributed networks via relaying. One simple and flexible scheme introduced is coded demodulate-and-forward, where the relay only demodulates, instead of decodes, the received data, to create and forward a new codeword to the destination. This reduces the complexity of hardware as well as the energy consumption by the relay. In this paper, we consider another flexible feature of the coded demodulate-and-forward scheme, where the relay uses only a fraction of its codeword to assist the source, and saves the rest of the codeword for transmitting its own information. Previous schemes have generally focused on all-or-nothing cooperation where a relay either contributes all its resources or none at all to the source. Depending on the channel conditions, improved diversity order of the source codeword can be achieved with some small loss in the relays own transmission performance. Here we identify the necessary criterion for the source to achieve a diversity order of 2.

Relay Selection for Low-Complexity Coded Cooperation Using the Bhattacharyya Parameter

Demodulate-and-forward (DmF) is an attractive approach when using cooperative diversity schemes in networks where only nodes with strict complexity constraints are allowed, such as sensor networks. In using DmF, the relay only demodulates, but does not decode, the received signal from the source node. Coding can be used at the relay to improve the performance over the relay-destination link. In unrelated work, relay selection has been shown to achieve full diversity order with low overhead by choosing the best relay node out of a pool of available relays to assist the source. A simple heuristic scheme for relay selection while using DmF is available, but this involves the exchange of channel parameters between the nodes, hence increasing the overhead. In this paper, we propose the use of the Bhattacharyya parameter (BP) to facilitate relay selection. The use of BP has the distinct advantage of incorporating the specific coding scheme used while retaining low computation load. As illustrated in our simulation results, the use of BP provides frame error rates quite similar to that obtained from exhaustive search. We should note that this BP-based relay selection scheme can also be applied to cooperation schemes where decoding is performed at the relay.

Optimization for Fractional Cooperation in Multiple-Source Multiple-Relay Systems

In fractional cooperation, many relays simultaneously assist the source, and each relay is responsible to relay only a fraction of the source transmission. In this paper, the problem of fractional cooperation is considered in the presence of multiple sources and multiple relays. In particular, optimization problems are formulated that can be used to allocate the relay resources between multiple sources to either minimize the energy consumed to achieve a given probability of error threshold, or minimize the maximum probability of error experienced by each source node.

Diversity analysis of irregular fractional cooperation

In fractional cooperation, each available relay node selects a small fraction of the sources transmission to be relayed. In previous work, it was assumed that every node relayed the same number of source symbols, and large diversity order gains were observed. In this paper, a theoretical basis is developed for irregular fractional cooperation, in which each node relays a different number of symbols. A general expression of the system diversity order is derived. A bound is introduced on the system performance of fractional cooperation, known as the erasure channel bound. Distributions of diversity order using this bound are given when the fraction relayed by each user is random.

Characterization of Relay Channels Using the Bhattacharyya Parameter

Relay systems have large and complex parameter spaces, which makes it difficult to determine the parameter region where the system achieves a given performance criterion, such as probability of frame error. In this paper, we show that the union bound (UB) and the Bhattacharyya parameter (BP) can be used for fast analysis of the parameter space when error-control coding is used. This is applicable when amplify-and-forward (AF) or demodulate-and-forward (DemF) are used. For a given code ensemble, the associated UB threshold is found and can be used to define the signal-to-noise region where a given frame error rate can be achieved. Using asymptotic results, the UB threshold can be used to specify the signal-to-noise ratio region where successful decoding can be achieved for large blocklength. In addition, the UB with BP can be used when fractional cooperation is used, where each relay only relays a fraction of the source codeword. This makes the UB with BP a valuable tool in the system design of relay networks.

Cooperative diversity using message passing in wireless sensor networks

Cooperative diversity schemes have been introduced in earlier works to achieve diversity in a block fading channel. However, most of these schemes ignore the quality of the source-relay (S-R) channel in the decoding process, even though it is this channel that limits the performance of cooperation schemes. This paper introduces a simple yet robust scheme for cooperative diversity based on message passing in the decoding process, which accounts for the quality of the S-R channel. In our scheme, the relay decodes the source symbols and forms parity bits, which are in turn used by the destination (D) to decode the source message. By accounting for the reliability of the parity bits, performance measures, such as bit error rate, are not limited by the S-R channel quality and improve with increasing signal-to-noise ratio on the S-D and R-D channels. With our scheme, feedback signals to the source node are not required, with only simple decoding and encoding required at the relay.