1 research outputs found
Complete j-MDP convolutional codes
Maximum distance profile (MDP) convolutional codes have been proven to be
very suitable for transmission over an erasure channel. In addition, the
subclass of complete MDP convolutional codes has the ability to restart
decoding after a burst of erasures. However, there is a lack of constructions
of these codes over fields of small size. In this paper, we introduce the
notion of complete j-MDP convolutional codes, which are a generalization of
complete MDP convolutional codes, and describe their decoding properties. In
particular, we present a decoding algorithm for decoding erasures within a
given time delay T and show that complete T-MDP convolutional codes are optimal
for this algorithm. Moreover, using a computer search with the MAPLE software,
we determine the minimal binary and non-binary field size for the existence of
(2,1,2) complete j-MDP convolutional codes and provide corresponding
constructions. We give a description of all (2,1,2) complete MDP convolutional
codes over the smallest possible fields, namely F_13 and F_16 and we also give
constructions for (2,1,3) complete 4-MDP convolutional codes over F_128
obtained by a randomized computer search.Comment: 2