Reverse-maximum distance profile convolutional codes over the erasure channel

Abstract

The loss of transmitted packets over an erasure channel, such as the Internet, can generate delay of the received information due to retransmission, and this can have adverse effects in real-time applications. Error forward correction is a technique used to avoid this delay. Until now mainly block codes have been used for this purpose and convolutional codes have been much less studied. In this paper we study in detail the use of convolutional codes over this channel and we show that the complexity of decoding is polynomial. We see how maximum distance profile (MDP) convolutional codes can deal with situations which are not possible for a maximum distance separable (MDS) block code and we introduce a new concept: reverse-MDP convolutional codes. Reverse-MDP codes double the potential of MDP convolutional codes since they behave as MDP codes in a forward and a backward sense. Due to this fact, we propose this new kind of codes as very good candidates to improve the decoding process. In addition, we provide a particular construction for reverse-MDP convolutional codes.