Block-Markov LDPC scheme for half- and full-duplex erasure relay channel

Abstract

The asymptotic iterative performance of the blockMarkov encoding scheme, defined over bilayer LDPC codes, is analyzed. This analysis is carried out for both half-duplex and full-duplex regimes. For the sake of clarity and simplicity, a transmission over the binary erasure relay channel is assumed. To analyze the iterative performance of the coding scheme, the asymptotic threshold boundary γ( 1, 2) is used as a performance measure. It is derived for two sparse-graph ensembles: BlockMarkov Bilayer-Expurgated and -Lengthened LDPC ensembles.

Erasure-correcting vs. erasure-detecting codes for the full-duplex binary erasure relay channel

“…(D) D receives erased versions of X 1 and X 2 , by orthogonal reception (OR) or non-orthogonal reception (NOR): (i) for OR, the erased versions of X 1 and X 2 (denote them by Y S and Y R ) are received separately, via independent binary erasure channels with respective erasure probabilities SD and RD ; (ii) for NOR, the link from S and R to D is a multiple access channel (MAC) with output Y . W.l.o.g, it is assumed to be the sum mod-2 MAC [5] such that…”

“…Density evolution equations for some BM schemes have been first derived in [5]. However, here we present them by means of transfer functions F fwd , F bwd , G fwd and G bwd .…”

“…Note that the FD case is more involved than the HD case: the FD communication often assumes the non-orthogonal multiple access at the destination end, thus implying a potential decrease in performance of sparse-graph codes (see, for instance, [5] where the observed performance of B-LDPC codes over the FD binary erasure relay channel is not impressive).…”