Decoding of Convolutional Codes over the Erasure Channel

TL;DR

This paper investigates the decoding capabilities of maximum distance profile convolutional codes over erasure channels, introducing new subclasses that enhance erasure recovery beyond traditional MDS block codes.

Contribution

It defines reverse-MDP and complete-MDP convolutional codes, demonstrating their superior erasure recovery capabilities compared to MDS block codes.

Findings

Complete-MDP codes outperform MDS block codes in erasure recovery.

Reverse-MDP codes can recover maximum erasures using backward algorithms.

Complete-MDP codes recover decoder state under mild conditions.

Abstract

In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance increase. We show how this strong minimum distance condition of MDP convolutional codes help us to solve error situations that maximum distance separable (MDS) block codes fail to solve. Towards this goal, we define two subclasses of MDP codes: reverse-MDP convolutional codes and complete-MDP convolutional codes. Reverse-MDP codes have the capability to recover a maximum number of erasures using an algorithm which runs backward in time. Complete-MDP convolutional codes are both MDP and reverse-MDP codes. They are capable to recover the state of the decoder under the mildest condition. We show that complete-MDP convolutional codes perform in certain sense better than MDS block codes of the same rate over the erasure channel.