Finite-length LDPC codes on the q-ary multi-bit channel

In this paper, we address the finite-length decoding performance of LDPC codes over the q-ary multi-bit channel (QMBC). The QMBC is defined over the full q-ary symbols, while addressing the differences in reliability between the bits composing the symbols. We show that unlike the binary erasure channel, the QMBC iterative decoder does not necessarily halt at stopping sets. Instead, its performance depends on the edge-label configuration of the LDPC code graph. We characterize good edge-label configurations, and propose an edge-labeling algorithm for improved iterative-decoding performance. We then provide finite-length maximum-likelihood decoding analysis for both the standard non-binary random ensemble and LDPC ensembles. Finally, simulations are presented to demonstrate the advantages of the proposed edge-labeling algorithm.