Abstract-Traditional approaches to transmit information reliably over an error-prone network employ either Forward Error Correction (FEC) or retransmission techniques. In this paper we consider an application of network coding to increase the bandwidth efficiency of reliable broadcast in a wireless network. In particular, we propose two schemes which employ network coding to reduce the number of retransmissions as a result of packet losses. Our proposed schemes combine different lost packets from different receivers in such a way that multiple receivers are able to recover their lost packets with one transmission by the source. The advantages of the proposed schemes over the traditional wireless broadcast are shown through simulations and theoretical analysis. Specifically, we provide a few results on the retransmission overhead of the proposed schemes under different channel conditions.

No abstract

Earlier authors have used quotient rings of Gaussian and Eisenstein-Jacobi integers to construct interconnection networks with good topological properties. In this paper, we present a unified study of these two types of networks. Our results include decomposing the edges into disjoint Hamiltonian cycles, a simplification of the calculation of the Eisenstein-Jacobi distance, a distribution of the distances between Eisenstein-Jacobi nodes, and shortest path routing algorithms. In particular, the known Gaussian routing algorithm is simplified.Index Terms-Interconnection network, Gaussian integers, Eisenstein-Jacobi integers, routing in networks, diameter of a network.

An m-ary block code, m = 2, 3, 4, . . ., of length n ∈ II N is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to (m − 1)n/2 . This paper presents a tight generalization of Knuth's complementation method with parallel (hence, fast) decoding scheme. Let n w m indicate the number of m-ary words of length n and weight w ∈ {0, 1, . . . , (m − 1)n}. A simple implementation of the scheme uses (m − 1)k + m mod 2 balancing functions to make a k ∈ II N digit information word to be balanced. So, r ∈ II N check digits can be used to balance k ≤ r (m−1)r/2 m − m mod 2 /(m − 1) information digits. A refined implementation of the parallel decoding scheme uses r check digits to balance k ≤ (m r − 1)/(m − 1) information digits.Index Terms-m-ary alphabet, balanced codes, Knuth's complementation method, parallel decoding scheme, unidirectional error detection, optical and magnetic recording.

No abstract