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Complete MDP convolutional codes

机译：完整的MDP卷积码

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Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a certain length. Reverse MDP convolutional codes have the additional advantage that they are suitable for forward and backward decoding algorithms. Beyond that the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. The first main result of this paper is to show the existence and genericity of (n,k,delta) complete MDP convolutional codes for all code parameters with (n - k) vertical bar delta as well as that complete MDP convolutional codes cannot exist if (n - k) (sic) delta. The second main contribution is the presentation of two concrete construction techniques to obtain complete MDP convolutional codes. These constructions work for all code parameters with (n - k) vertical bar delta but require that the size of the underlying base field is (sufficiently) large.
机译：最大距离曲线（MDP）卷积码具有它们的柱距离尽可能大的性质。已经表明，通过擦除信道发送，这些代码具有一定长度的窗口具有最佳回收率。反向MDP卷积码具有额外的优点，即它们适用于前向和后向解码算法。除了完整的MDP卷积码的子类之外，能够减少解码期间的等待时间。本文的第一主要结果是显示所有代码参数的（n，k，delta）完整的MDP卷积码与（n-k）垂直条Δtea以及完整的MDP卷积码，如果（n - k）（sic）delta。第二种主要贡献是两个具体施工技术的呈现，以获得完整的MDP卷积码。这些构造适用于所有代码参数（n - k）垂直条Δtta，但要求底层基场的大小是（足够的）大。

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