Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column distances, are able to correct a maximal number of erasures in decoding windows of fixed sizes. However, the required field size in the known constructions for MDP convolutional codes increases rapidly with the code parameters. On the other hand, if the code parameters are small, larger bursts of erasures cannot be corrected. In this paper, we present a new class of convolutional codes, which we call Pseudo-MDP convolutional codes. By definition these codes can correct large bursts of erasures within a prescribed time-delay and still keep part of the advantageous properties of MDP convolutional codes, in the sense that we require some but not all column distances to be optimal. This release in the condition on the column distances allows us to construct Pseudo-MDP convolutional codes over fields of smaller size than those required for MDP convolutional codes with the same code parameters.

翻译：卷积码是一类在低延迟要求的擦除信道上性能优异的纠错码。特别是，最大距离分布（MDP）卷积码被定义为具有最优列距离，能够在固定大小的译码窗口中纠正最大数量的擦除。然而，已知的MDP卷积码构造对域大小的需求随着码参数的增加而迅速增长。另一方面，若码参数较小，则无法纠正更大的擦除突发。本文提出一类新的卷积码，称为伪MDP卷积码。根据定义，这些码能在规定时延内纠正大量擦除突发，同时保留MDP卷积码的部分有利性质——即要求部分（而非全部）列距离达到最优。这种对列距离条件的放宽，使得我们能在比相同参数的MDP卷积码所需域更小的域上构造伪MDP卷积码。