A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

In this paper, a time-variant decoding model of a convolutional network code (CNC) is proposed. New necessary and sufficient conditions are established for the decodability of a CNC at a node r with delay L. They only involve the first L + 1 terms in the power series expansion of the global encoding kernel matrix at r. Concomitantly, a time-variant decoding algorithm is proposed with a decoding matrix over the base symbol field. The present time-variant decoding model only deals with partial information of the global encoding kernel matrix, and hence potentially makes CNCs applicable in a decentralized manner.

In this article, we address the problem of robust waveform optimization for improving the worst-case detection performance of multi-input multi-output (MIMO) space-time adaptive processing (STAP) in the presence of colored Gaussian disturbance. A novel diagonal loading-based method is proposed to optimize the waveform covariance matrix for maximizing the worst-case output signal-interference-noise ratio (SINR) over the convex uncertainty set such that the worst-case detection performance of MIMO-STAP can be maximized. The resultant nonlinear optimization problem is reformulated as a semidefinite programming problem, which can be solved very efficiently. Numerical examples show that the worst-case output SINR of MIMO-STAP can be improved considerably by the proposed method compared to that of uncorrelated waveforms.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.

We consider an Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at the related sink nodes have full rank. ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved. We show that this method performs no worse than block linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.