Low Rank Parity Check Codes against Reed-Solomon Codes For Narrow-band PLC Smart Grid Networks

This paper introduces a new family of rank metric codes: the Low Rank Parity Check Codes (LRPC) for which we propose an efficient probabilistic LRPC decoding algorithm concatenated with convolutional code associated with an interleaver. The main idea of decoding LRPC codes is based on calculations of vector spaces over a finite field F-q. This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We compare the performance of this code with the Reed Solomon Code (RS) through a PLC channel. We propose to replace the Reed-Solomon code with a kind of rank metric code (LRPC code) that can correct a whole line or row of a code word, which is arranged in a matrix. Using OFDM modulation, the columns of code matrix contain the OFDM symbols. We show by simulation that the proposed system outperforms the traditional scheme where the PLC channel is subjected to both impulsive noise and narrowband interference.