| Research |
Recently network-based alternatives to improve performance in scenarios that do not allow the use of physical antenna arrays have been investigated. All of these schemes exploit the broadcast nature of the wireless channel wherein any node within range of the transmitter can listen to the transmission. The users that receive the transmission can function as elements of a virtual, distributed antenna array, and can collaborate with each other to achieve diversity gains. Diversity achieved when users in a network collaborate to improve each other's performance has been termed cooperative diversity. Existing cooperation techniques are all based on variants of the relay-channel approach. In this approach, intermediate nodes called relays receive information from the source and forward some information about the source message to the destination. The destination uses this information to resolve any ambiguity that it might have about the original source transmission. This approach incurs a high overhead and is not easily scalable (in terms of practical implementation) to large cooperating groups. The fundamental flaw in this approach is that the relays form their transmissions based on their own decisions only. We propose Collaborative Decoding as an approach to cooperation with reduced overhead. In Collaborative Decoding, the relays form their transmissions based on some information about decoding at the destination and other relays. This is an iterative technique wherein the nodes in the cooperating cluster first exchange some information about their individual decoding decisions and then use this information to decide what information is to be forwarded to the destination/other relays. Our approach uses soft-input soft-output (SISO) decoders to extract information about decoding at a particular relay, r and this information is sent to other relays/destination to provide an idea about decoding at relay r. We have shown that collaborative decoding achieves full diversity in the number of cooperating nodes with a fraction of the overhead required for traditional combining schemes like maximal-ratio combining MRC. Decoders that operate on floating-point inputs and produce floating-point outputs instead of hard-decisions are called soft-input soft-output (SISO) decoders. The sign of the soft-output gives the hard-decision value, while the magnitude of the soft-output is called the reliability of the bit decision. In recent years, a number of algorithms have been proposed that make explicit use of soft-information or reliability. Reliability based Hybrid ARQ and cooperative diversity techniques using SISO decoders are common examples. The analysis and design of these techniques require a mathematical characterization of reliabilities associated with the SISO decoder output. Reliabilities at the output of soft-decision decoders are random variables and hence are characterized by their density function. Density functions of reliabilities have been computed based on probabilities involving the projection of the noise in directions corresponding to different error events. Each such projection results in a random variable, and two approaches have been taken to compute probabilities involving these random variables. In the first approach, the random variables are treated as if they are independent; in the second approach, correlations between the random variables are taken into account. The former approach results in conservative estimates and a relatively simpler expression for the PDF, whereas the latter approach produces good estimates but results in a complicated expression. The mathematical expressions found using either approach are generally too complicated for further use in analytical work. In this work, we present a closed-form approximation for the density function of reliabilities associated with the Max-Log-MAP decoding of convolutional codes. We also propose a simple approach to account for the correlation between the random variables resulting from the projection of noise onto directions specified by different error events. Under this approach, we reduce the number of random variables that are considered in the computation of the PDF by eliminating those that are highly correlated. Working with this condensed set of random variables produces results that are close to the true values even if the independence assumption is used. A mathematically tractable estimate of the PDF is also presented, and the validity of this estimate is demonstrated by comparing the estimate of the PDF with simulation results. This PDF estimate can be used to analyze several communication schemes that utilize reliabilities as a design tool. |