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首页> 外文期刊>IEEE Transactions on Information Theory >Reliable and Secure Multishot Network Coding Using Linearized Reed-Solomon Codes
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Reliable and Secure Multishot Network Coding Using Linearized Reed-Solomon Codes

机译：使用线性化Reed-Solomon码的可靠和安全的多发网络编码

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摘要

Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to rho packets, and wire-tap up to mu links, all throughout l shots of a linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may be random and change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ln' - 2t - rho - mu packets for coherent communication, where n' is the number of outgoing links at the source, for any packet length m >= n' (largest possible range). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. The required field size is q(m), where q > l, thus q(m) approximate to l(n'), which is always smaller than that of a Gabidulin code tailored for l shots, which would be at least 2(ln)'. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ln', and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication. Combined with the obtained field size, the given decoding complexity is of O(n('4)l(2)log(l)(2)) operations in F-2, whereas the most efficient known decoding algorithm for a Gabidulin code has a complexity of O(n('3.69) l(3.69) log(l)(2)) operations in F-2, assuming a multiplication in a finite field F costs about log(|F|)(2) operations in F-2.
机译：在最坏情况的对抗环境中考虑了多发网络编码，在这种情况下，具有无限计算资源的无所不知的对手可能会在最多t个链路中注入错误的数据包，最多可达t个链路，擦除多达rho个数据包，并窃听多达mu个链路。线性编码网络。假设不了解底层线性网络代码（特别是网络拓扑结构和底层线性代码可能是随机的且随时间变化），则基于线性化的Reed-Solomon码，可获得实现零错误通信和完美保密的编码方案。该方案实现了用于相干通信的ln'-2t-rho-mu数据包的最大可能的秘密消息大小，其中n'是源的出站链路数，对于任何长度 n'的数据包（最大可能范围） 。通过取消这种构造，可获得用于非相干通信的编码方案，其信息速率接近于实际情况的最佳。所需的字段大小为q（m），其中q> l，因此q（m）近似于l（n'），该大小始终小于为l次拍摄量身定制的Gabidulin代码的大小（至少为2（ ln）'。提供了一种用于线性化Reed-Solomon码的Welch-Berlekamp和秩解码算法，该算法在总长度n = ln'中具有二次复杂度，不仅可以处理错误，而且还可以处理擦除，窃听观察和不连贯的沟通。结合获得的字段大小，给定的解码复杂度为F-2中的O（n（'4）l（2）log（l）（2））个运算，而最有效的Gabidulin码解码算法具有F-2中O（n（'3.69）l（3.69）log（l）（2））运算的复杂度，假设有限域F中的乘法的开销约为F中log（| F |）（2）运算-2。

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