A distance-preserving mapping is a one-to-one function f from p-ary vectors of length m to q-ary vectors of length n such that any two distinct p-ary vectors are mapped to two different q-ary vectors with an equal or greater Hamming distance. A distance-increasing mapping is a special distance-preserving mapping which strictly increases the distance by at least one if the distance of two distinct input vectors is less than the length of the output vectors. A constant composition code over a k-ary alphabet has the property that the numbers of occurrences of the k symbols within a codeword are fixed for each codeword. One of the most important applications of distance-preserving mappings and distance-increasing mappings is to construct constant composition codes, of which the permutation codes are a special subclass. There are two results in this paper. First, we propose a swap-based distance-increasing mapping from binary vectors to quaternary constant composition vectors. Second, we prove that it is impossible to construct any swap-based distance-preserving mappings from binary vectors to ternary constant composition vectors under the swap model that we defined.

Constant composition codes arise from applications in powerline communication and balanced scheduling in frequency hopping. Binary constant weight codes and permutation codes are special types of constant composition codes. In ISIT 2009, Chang and Wu proposed a method to construct constant composition codes through distance-increasing mappings from binary vectors to quaternary constant composition vectors. But they did not touch the decoding problem. In this paper, we present efficient decoding algorithms for the constant composition codes generated from distance-increasing (or distance-preserving) mappings.

A distance-preserving mapping is a one-to-one function f from p-ary vectors of length m to q-ary vectors of length n such that any two distinct p-ary vectors are mapped to two different q-ary vectors with an equal or greater Hamming distance. A special distance-preserving mapping called a distance-increasing mapping is a mapping which increases the distance at least one if the distance of two distinct input strings are not equal to the output length. A constant composition vector is a vector under the restriction that each alphabet symbol occurs a given number of times. In this paper, we propose a distance-increasing mapping from binary vectors to constant composition quaternary vectors. We also give an optimal impossibility result for constructing distance-preserving mapping from binary vectors to constant composition ternary vectors in the so-called swapping model.

Permutation arrays have found applications in powerline communication. One construction method for permutation arrays is to map good codes to permutations using a distance-preserving mappings (DPM). DPMs are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of some fixed length (the same or longer) such that every two distinct vectors are mapped to permutations with the same or larger Hamming distance than that of the vectors. A DPM is called distance increasing (DIM) if the distances are strictly increased (except when the two vectors are equal). In this correspondence, we propose constructions of DPMs and DIMs from ternary vectors. The constructed DPMs and DIMs improve many lower bounds on the maximal size of permutation arrays.

In this correspondence, for any k /spl ges/ 2, we first propose two constructions of (n,k) distance-increasing mappings (DIMs) from the set of binary vectors of length n to the set of permutations of the same length that strictly increase the Hamming distance by at least k except when it is obviously not possible. Next, we prove that for any k /spl ges/ 2, there is a smallest positive integer n/sub k/ such that an (n,k) DIM can be constructed for any n /spl ges/ n/sub k/. An explicit upper bound on n/sub k/ is also given.

Mappings from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase Hamming distances except when that is obviously not possible are useful for the construction of permutation codes. In this correspondence, we propose recursive and explicit constructions of such mappings. Some comparisons show that the new mappings have better distance expansion distributions than other known distance-preserving mappings (DPMs). We also give some examples to illustrate the applications of these mappings to permutation arrays (PAs).

In this paper, we propose a new approach to establishing application layer conference trees for multimedia multipoint conferences on the Internet using the Megaco/H.248 protocol, a Voice over IP (VoIP) media gateway control protocol. In existing VoIP protocols (and also legacy telephone networks), a multipoint conference takes place through an MCU, and forms a star topology centered at the MCU. This paper suggests to establishing shared, cost effective conference trees for VoIP conferences. Each tree is rooted at the conference initiator, who initiates the conference, and spans over all the conference members. Tree branches grow or are trimmed dynamically and adaptively, in a way to avoid the growth of a skewed tree. We develop a simplified analytical model and conduct simulations to evaluate the performance of the proposed approach. The results show that our approach enjoys the advantage of lower join latency and better bandwidth efficiency compared to the traditional MCU approach, and is cost effective compared to a near optimal Steiner tree.

Mappings of the set of binary vectors of a fixed length to the set of permutations of the same length are useful for the construction of permutation codes. In this article, several explicit constructions of such mappings preserving or increasing the Hamming distance are given. Some applications are given to illustrate the usefulness of the construction. In particular, a new lower bound on the maximal size of permutation arrays (PAs) is given.

In this paper, we propose a new approach to estab- lishing application layer conference trees for multimedia multi- point conferences on the Internet using the Megaco/H.248 protocol, a Voice over IP (VoIP) media gateway control protocol. In existing VoIP protocols (and also legacy telephone networks), a multipoint conference takes place through an MCU, and forms a star topology centered at the MCU. This paper suggests to establishing shared, cost effective conference trees for VoIP conferences. Each tree is rooted at the conference initiator, who initiates the conference, and spans over all the conference members. Tree branches grow or are trimmed dynamically and adaptively, in a way to avoid the growth of a skewed tree. We develop a simplified analytical model and con- duct simulations to evaluate the performance of the proposed ap- proach. The results show that our approach enjoys the advantage of lower join latency and better bandwidth efficiency compared to the traditional MCU approach, and is cost effective compared to a near optimal Steiner tree.