# wireless communication

**Energy-Efficient Data Acquisition in Wireless Sensor Networks Using Compressive Sensing **

We studied the problem of data acquisition in wireless sensor networks (WSNs). A recently revitalized technique called compressive sensing (CS) has presented a new method to capture sparse signals at a rate below Nyquist. There are drawbacks to directly applying the existing CS algorithm to WSNs, which are mainly due to the fact that CS requires a large number of inter-communications for generating each projection.

To mitigate these drawbacks, we propose compressive distributed sensing using random walk (CDS(RW)), an algorithm for CS in WSNs that uses rateless coding. Our proposed algorithm is independent of routing algorithms and network topologies. CDS(RW) collects sufficient number of sensor readings while combining them together without significantly increasing the inter-communication cost. We model the CS problem with code design for a set of parallel channels which helps us to design the rateless code degree distribution. This model provides the advantage of using non-uniform and unequal error protection codes.

**An Energy-Efficient and Rate-Optimal Multicast Protocol for Wireless Networks **

In wireless networks, multicast is an elementary service that is used in many applications. We proposed a new algorithm for constructing a multicast subgraph and a distributed source coding-based Multicast (DSCM) protocol for multihop wireless networks with emphasis on reliability, rate optimality, and energy efficiency.

DSCM is based on local knowledge of the network, i.e., each node knows its neighbors and the location of the destination nodes. The multicast subgraph algorithm constructs two edge-disjoint paths to each destination in order to form a multicast subgraph. However, it attempts to minimize the cost and maximize the use of common paths for delivering information to multiple destination nodes. DSCM is then applied to this multicast subgraph. DSCM uses rateless error correcting codes to provide reliability and rate optimality, and distributed source coding to ensure the energy efficiency. We compare our scheme with present energy-efficient methods such as Network Coding (NC) and Multicast Incremental Power (MIP). The simulation results reveal that DSCM performs close to these algorithms. However, NC and MIP, unlike the proposed algorithm, assume full knowledge of the network topology and have much higher decoding complexity in comparison with DSCM.

**Distributed Source Coding using Finite-Length Rate-Compatible LDPC Codes: The Entire Slepian-Wolf Rate Region **

We proposed a technique to reduce the transmission power usage in the wireless sensor networks (WSNs) exploiting the spatial correlations between sensor readings in a network. Each node compresses its data without communicating with other nodes and sends the compressed data to the base station. Such a system requires distributed source coding (DSC), since the encoders are distributed and the signals are compressed independently.

The base station collects the compressed sensor readings and recovers the original signals error free. The following three points are significance of our work: First, we studied the DSC of applications with finite-length sequences. DSC using finite-length channel codes introduces new challenges, since the assumption of capacity-approaching channel code is not valid anymore. We model the distributed source coding problem with code design for a set of parallel channels. This model; for short-length sequences; provides the advantage of using non-uniform, rate adaptive and unequal error protection codes. Second, we investigated the DSC of correlated sources when there is no prior knowledge about the correlation parameter at the time of code design. We show how method of distributed source coding at arbitrary rates can also be applied when the correlation parameter is unknown in advance. Third, our work focused on DSC based on sending parity bits. This is a substantial diversion over the other possible method, which is based on syndromes. If the wireless channel is ideal, both syndrome and parity methods can be used. However, in applications where wireless channels is not error free, the syndrome-based method cannot be applied for distributed source coding.

**2-D Wavelet Codes for Correcting 2-D Burst Errors **

There are many data transmission and storage systems with two-dimensional (2-D) data structures that suffer from 2-D bursts of error and erasures. 2-D codes can be used to combat such errors and erasures. We introduced two-dimensional wavelet codes (TDWCs).

The synthesis bank of a two-channel two-variable filter bank over the finite field is used to design a two-dimensional (2-D) code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we studied the encoder of half-rate TDWCs and show that these linear codes are lattice cyclic. It is proven that any 2-D lattice-cyclic code can also be generated by a 2-D wavelet transform. Second, we introduced a methodology to design TDWCs over binary erasure channels. These codes have simple and efficient maximum likelihood (ML) decoding for burst erasures. We showed that half-rate TDWCs of dimensions N1 × N2 can recover burst erasures of size up to N1 × N2/2 and N1/2 × N2 using our proposed simple decoding technique. Finally, we presented examples of TDWCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N1N2/2.