Necessary Field Size and Probability for MDP and Complete MDP Convolutional Codes

TL;DR

This paper establishes improved bounds on the field size needed for MDP and complete MDP convolutional codes and analyzes the probability of randomly selecting such codes, enhancing understanding of their existence and properties.

Contribution

It derives tighter upper bounds on the field size for MDP and complete MDP codes and provides lower bounds on the probability of their random occurrence.

Findings

Improved upper bounds on necessary field size for MDP codes.

Enhanced bounds on field size for complete MDP codes.

Lower bounds on the probability that a random code is MDP or complete MDP.

Abstract

It has been shown that maximum distance profile (MDP) convolutional codes have optimal recovery rate for windows of a certain length, when transmitting over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. In this paper, we derive upper bounds on the necessary field size for the existence of MDP and complete MDP convolutional codes and show that these bounds improve the already existing ones. Moreover, we derive lower bounds for the probability that a random code is MDP respective complete MDP.