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 maybe lost in the process of diffusion-advection propagation through complex topologies and membranes. Existing work has considered Hamming-distance codes for additive counting noise and Hamming-weight codes for transposition errors. Current linear-group codes are not well suited to combating the aforementioned erasure errors. In this paper, we design a novel lowcomplexity 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. We design an iterative soft decoding scheme via successive cancelation to further improve the performance. Numerical simulations show this new rateless code can outperform both standard LT and cascaded Hamming-LT (Raptor) codes, while incurring a lower decoder computational complexity, which is useful for the envisaged resources constrained nano-machines.

Toward Reliable Intra-Body Molecular Communication: An Error Control Perspective

“…An erasure noise consists of particles sent and lost in the diffusion process before reaching the destination. Molecules may be erased by several mechanisms, such as absorption by another receiver or being trapped in biological structures [10].…”

“…One approach lies in sending concentrations of two distinguishable molecule types using a modulated parity check encoder. In [10], the information is encoded into a binary code (i.e., representing the two states of the cell) characterized by the codeword of three symbols. Its decoder computes the a posteriori log-likelihood ratio of the information, symbols to identify possible errors.…”

“…For example, the Hamming distance designs channel codes based on the number of different symbols between two binary sequences. Hamming distance combined with channel timing-based decoding is effective to combat additive noise sources in non-concentration-encoded MC channels [10]. However, it is not well suited to combat erasure errors.…”

“…LT erasure codes and the Hamming code (LT-Hamming) combat the information loss in molecular-scarce (e.g., diffusive channels with erasure noises) communication scenarios. These techniques rely on a random number of generators that consumes computational resource and energy [10]. They allow error detection, but not error correction.…”

Performance Analysis for Hybrid Massive MIMO FSO/RF Links Based on Efficient Channel Codes

“…It depends on knowing the channel conditions at the transmitter immediately to specify International Journal of Intelligent Engineering and Systems, Vol. 14 the suitable modification in the code rates for FSO and RF transmission [4]. Lately, a paper suggests a hybrid FSO/RF schemes based on rateless channel codes for traditional communication channel with single transmitting antenna and single receiving antenna [4].…”