Sequences having better autocorrelation properties play a crucial role in enhancing the performance of active sensing systems. Hence, sequences with good are very much demand. In this paper, we addressed problem designing unimodular sequence side-lobe levels. We formulated it as constrained optimization comprising Integrated Side-lobe Level (ISL) metric and then proposed an effective algorithm ...

We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning random walks, percolation, spanning forests, and amenability from the known context of unimodular quasi-transitive graphs to the more general context of unimodu...

Bhatwadekar and Raja Sridharan have constructed a homomorphism from an orbit set of unimodular rows to an Euler class group. We show under weaker assumptions that a generalization of its kernel is a subgroup. Our tool is a partially defined operation on the set of unimodular matrices with two rows. 1 The exact sequence Consider a commutative noetherian Q-algebra A of dimension d. Let n = d + 1....

Given a set B of finite rooted graphs and a radius r as an input, we prove that it is undecidable to determine whether there exists a sequence (Gi) of finite bounded degree graphs such that the rooted r-radius neighbourhood of a random node of Gi is isomorphic to a rooted graph in B with probability tending to 1. Our proof implies a similar result for the case where the sequence (Gi) is replace...

It is shown that if there is an extremal even unimodular lattice in dimension 72, then there is an optimal odd unimodular lattice in that dimension. Hence, the first example of an optimal odd unimodular lattice in dimension 72 is constructed from the extremal even unimodular lattice which has been recently found by G. Nebe.

A recursive construction is provided for sequence sets which possess good Hamming Distance and low Peak-to-Average Power Ratio (PAR) under any Local Unitary Unimodular Transform (including all one and multi-dimensional Discrete Fourier Transforms). An important instance of the construction identifies an iteration and specialisation of the Maiorana-McFarland (MM) construction.

We use the property of unimodular functions to perform approximate inference with dual decomposition in binary labeled graphs. Exact inference is possible for a subclass of binary labeled graphs that have unimodular functions. We call such graphs unimodular graphs. These are graphs where the submodular and nonsubmodular edges follow a specific pattern– essentially that an isomorphism or ”flippi...

The integrated design for both radar and anonymous communication has drawn more attention recently since wireless communication system appeals to enhance security and reliability. Given the frequency hopping (FH) communication system, an effective way to realize integrated design is to meet the spectrum compatibility between these two systems. The paper deals with a unimodular sequence design t...