# A Block Diagonal Markov Model for Indoor Software-Defined Power Line Communication

## TL;DR

This paper introduces a computationally efficient Block Diagonal Markov Model for indoor power line communication channels, enabling faster system design and evaluation through a modified Baum-Welch algorithm.

## Contribution

It proposes a novel Block Diagonal Markov Model and a modified Baum-Welch algorithm for efficient estimation from empirical error sequences in indoor PLC systems.

## Key findings

- Efficient estimation of Markov models for PLC channels.
- Accelerated design and evaluation of PLC systems.
- Improved modeling of bursty error channels.

## Abstract

A Semi-Hidden Markov Model (SHMM) for bursty error channels is defined by a state transition probability matrix $A$, a prior probability vector $\Pi$, and the state dependent output symbol error probability matrix $B$. Several processes are utilized for estimating $A$, $\Pi$ and $B$ from a given empirically obtained or simulated error sequence. However, despite placing some restrictions on the underlying Markov model structure, we still have a computationally intensive estimation procedure, especially given a large error sequence containing long burst of identical symbols. Thus, in this paper, we utilize under some moderate assumptions, a Markov model with random state transition matrix $A$ equivalent to a unique Block Diagonal Markov model with state transition matrix $\Lambda$ to model an indoor software-defined power line communication system. A computationally efficient modified Baum-Welch algorithm for estimation of $\Lambda$ given an experimentally obtained error sequence from the indoor PLC channel is utilized. Resulting Equivalent Block Diagonal Markov models assist designers to accelerate and facilitate the procedure of novel PLC systems design and evaluation.