Incremental Redundancy Cooperative Coding for Wireless Networks: Cooperative Diversity, Coding, and Transmission Energy Gains

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We study an <emphasis emphasistype="boldital">incremental redundancy</emphasis> (IR) cooperative coding scheme for wireless networks. To exploit the distributed spatial diversity we propose a cluster-based collaborating strategy for a quasi-static Rayleigh-fading channel model. Our scheme allows for enhancing the reliability performance of a direct communication over a single hop. The collaborative cluster consists of <emphasis><formula formulatype="inline"> <tex>$M-1$</tex></formula></emphasis> nodes between the sender and the destination. The transmitted message is encoded using a mother code which is partitioned into <emphasis><formula formulatype="inline"><tex>$M$</tex></formula></emphasis> blocks each assigned to one of <emphasis><formula formulatype="inline"><tex>$M$</tex> </formula></emphasis> transmission slots. In the first slot, the sender broadcasts its information by transmitting the first block, and its helpers attempt to decode this message. In the remaining slots, each of the next <emphasis><formula formulatype="inline"><tex>$M-1$</tex></formula></emphasis> blocks is sent either through a helper which has successfully decoded the message or directly by the sender where a dynamic schedule is based on the ACK-based feedback from the cluster. By employing powerful <emphasis emphasistype="boldital">good codes</emphasis> including turbo, low-density parity-check (LDPC), and repeat–accumulate (RA) codes, our approach illustrates the benefit of collaboration through not only a cooperation diversity gain but also a coding advantage. The basis of our error rate performance analysis is based on a derived code threshold for the Bhattacharyya distance which describes the behavior of good codes. The new simple code threshold is based on the modified Shulman–Feder bound and the relationship between the Bhattacharyya parameter and the channel capacity for an arbitrary binary-input symmetric-output memoryless channel. An average frame-error rate (FER) upper bound and its asymptotic (in signal-to-noise ratio (SNR)) version are derived as a function of the average fading channel SNRs and the code threshold. Based on the asymptotic bound, we investigate both the diversity, the coding, and the transmission energy gain in the high and moderate SNR regimes for three different scenarios: transmitter clustering, receiver clustering, and cluster hopping. We observe that the energy saving of the IR cooperative coding scheme is <emphasis emphasistype="boldital">universal</emphasis> for all good code families in the sense that the gain does not depend on the sender-to-destination distance and the code threshold. </para>