1 research outputs found
Rate Systematic MDS Convolutional Codes over
A systematic convolutional encoder of rate and maximum degree
generates a code of free distance at most and, at best, a
column distance profile (CDP) of . A code is
\emph{Maximum Distance Separable} (MDS) if it possesses this CDP. Applied on a
communication channel over which packets are transmitted sequentially and which
loses (erases) packets randomly, such a code allows the recovery from any
pattern of erasures in the first -packet blocks for ,
with a delay of at most blocks counting from the first erasure. This paper
addresses the problem of finding the largest for which a systematic
rate code over exists, for given and . In
particular, constructions for rates and are
presented which provide optimum values of equal to 3 and 4,
respectively. A search algorithm is also developed, which produces new codes
for for field sizes . Using a complete search
version of the algorithm, the maximum value of , and codes that
achieve it, are determined for all code rates and every field size
for (and for some rates for )