Rate $(n-1)/n$ Systematic Memory Maximum Distance Separable Convolutional Codes
Ángela I. Barbero, Øyvind Ytrehus · IEEE Transactions on Information Theory · 2018
A systematic convolutional encoder of rate (n-1)/n and maximum memory D generates a code of free distance at most V = D + 2 and, at best, a column distance profile (CDP) of [2,3, .. . , D]. A code is memory maximum distance separable 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 j erasures in the first j n-packet blocks for jm- 1)/pmand V equal to 3 over GF(pm) and rate (2m-1-1)/2m-1and V equal to 4 over GF(2m) are presented, which provide optimum values of V in their respective cases. A search algorithm is also developed, which produces new codes for V for field sizes 2m≤ 214. Using a complete search version of the algorithm, the maximum value of V, and codes that achieve it, are determined for all code rates ≥ 1/2 and every field size GF(2m) for m ≤ 5 (and for some rates for m = 6).