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• W3048475761 abstract "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 article, we introduce the notion of complete 3-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 3-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 <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>13</sub> and F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>16</sub> and we also give constructions for (2, 1, 3) complete 4-MDP convolutional codes over F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>128</sub> obtained by a randomized computer search." @default.
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• W3048475761 date "2020-12-01" @default.
• W3048475761 modified "2023-10-18" @default.
• W3048475761 title "Complete <i>j</i>-MDP Convolutional Codes" @default.
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• W3048475761 doi "https://doi.org/10.1109/tit.2020.3015698" @default.
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