Hamming–Luby rateless codes for molecular erasure channels

Abstract

Nano-scale molecular communications encode digital information into discrete macro-molecules. In many nano-scale systems, due to limited molecular energy, each information symbol is encoded into a small number of molecules. As such, information may be lost in the process of diffusion–advection propagation through complex topologies and membranes. Existing Hamming-distance codes for additive counting noise are not well suited to combat the aforementioned erasure errors. Rateless Luby-Transform (LT) code and cascaded Hamming-LT (Raptor) are suitable for information-loss, however may consume substantially computational energy due to the repeated uses of random number generator and exclusive OR (XOR). In this paper, we design a novel low-complexity erasure combating encoding scheme: the rateless Hamming–Luby Transform code. The proposed rateless code combines the superior efficiency of Hamming codes with the performance guarantee advantage of Luby Transform (LT) codes, therefore can reduce the number of random number generator utilizations. We design an iterative soft decoding scheme via successive cancelation to further improve the performance. Numerical simulations show this new rateless code can provide comparable performance comparing with both standard LT and Raptor codes, while incurring a lower decoder computational complexity, which is useful for the envisaged resources constrained nano-machines.