It is shown that efficient reversible variable length codes (RVLCs) with numerous codewords can be obtained if suboptimal RVLCs for the average distributions of monotone sources with relatively small alphabet sizes are multiplied by some fixed-length codes. Employing these RVLCs, the best known upper bounds on the average redundancy of optimal RVLC are almost halved. In particular, it is proved that the average redundancy of optimal RVLC for sources withnsymbols is less than 11/n+0.11345 bits forn> 32. Some other upper bounds are also derived which are either suboptimal in some sense for smallnor easily computable for largenor descriptive of asymptotic behavior. Moreover, we prove that the penalty of using optimal RVLC instead of Huffman code is less than 0.0848 bits for almost all sources with sufficiently large alphabet size. These results provide stronger evidence that, overall, the cost of benefiting from the desired properties of RVLC is not significant in terms of the redundancy.

This paper proposes a compressive pulse-Doppler radar that works through one-bit quantization of the received noisy signal. The one-bit quantization is performed by comparing the signal with a time-varying reference level. Considering the sparsity of the targets in the range-Doppler domain, the problem is dealt with by a sparse recovery method. The proposed method leads to an optimization problem that can be tackled by a convex approximation. Numerical examples show that the proposed method has a promising performance in the detection/estimation of the target parameters. Moreover, it is seen that in low signal to noise ratio, increasing the sampling rate at the receiver side is a compensating factor that effectively improves the performance.

For each alphabet size up to 30, a symmetric reversible variable length code (RVLC) is determined which is most likely to be optimal in average codeword length. It is shown that these codes are optimal for more than half of all the possible sources.

In this paper, the difference between the redundancy of the optimal asymmetric/symmetric fix-free code, and that of the optimal prefix-free code is considered as the penalty of benefiting from the desired properties of fix-free codes. This penalty is studied from different perspectives. In particular, it is shown that the average penalty of asymmetric fix-free codes is less than 0.21 bit per symbol. Moreover, it is proved that when the source alphabet size is sufficiently large, for almost all sources, the penalty is less than or equal to 0.182 bit per symbol. Regarding symmetric fix-free codes, it is shown that the average penalty tends to infinity as the source alphabet size increases.

Dominant codelength sequences for reversible variable length codes (RVLCs) have been recently introduced and studied as a means to looking into optimal RVLCs. However, obtaining the dominant sequences for RVLCs is computationally challenging. In this paper, we consider a special subset of all RVLCs, namely, the sequentially-constructible (SC) RVLCs, for which the dominant sequences can be obtained with less computational complexity. Of course, this time saving is achieved at the cost of losing the optimality. However, it is shown that the dominant sequences for SC RVLCs provide acceptable performance in terms of the redundancy. Specifically, it is seen that the worst case penalty in using the optimal SC RVLCs with respect to the optimal RVLCs is at most 2/9 bit per symbol for alphabet size of up to 16. While obtaining the dominant sequences of SC RVLCs is relatively faster, it will still become challenging as the search space of the relevant branch-and-bound algorithm gets larger, when the source alphabet size increases. In order to further reduce the time complexity, we propose an alternative approach to a table of SC RVL codelength sequences, which avoids the branch-and-bound algorithm. It is shown that the codes obtained by this approach perform almost as well as the SC dominant sequences. Specifically, for an alphabet size of up to 21, the redundancy of this approach is, at most, 2/19 bit more than the optimal SC RVLCs.

In this paper, we investigate a cooperative spectrum sensing scheme in which the local sensors at the secondary users perform an M-level quantization on the local decision statistic, and the quantized data are reported through erroneous channels, to be fused under Neyman-Pearson (N-P) criterion. The local quantization can be as fine as the bandwidth limitations permit; thus, the idea behind our effort is to smooth up the path towards the challenge of cooperative spectrum sensing under bandwidth constraints. We initially aim at formulating the N-P fusion rule with M-level quantization of the decision statistic. In this vein, we derive the required randomized test for the N-P fusion that represents the total performance of our spectrum sensing scheme. We further introduce a tight lower bound for the optimal performance of the primary user signal detection. An analytical procedure towards the bound and its relevant quantization setup at the local sensors are proposed and examined through case studies. The proposed near optimal bound gets closer to the optimal performance as the channel probability of error decreases, such that for ideal channels, it is seen to provide the exact optimal performance.

We consider a cooperative spectrum sensing scenario where the local sensors at the secondary users are viewed as one-level quantizers, and the quantized data are to be fused under Neyman-Pearson (N-P) criterion. We demonstrate how the N-P fusion results in a randomized test, which represents the total performance of our spectrum sensing scheme. We further introduce an upper performance bound for the overall primary user signal detection. An analytical procedure towards the upper bound and its relevant quantization setup at the local sensors are proposed and examined through simulations.

This work presents a new perspective to the relationship between the composite binary hypothesis test and the estimation of its unknown parameters, i.e. the Uniformly Most Powerful (UMP) test and the Minimum Variance and Unbiased Estimator(MVUE). We show that for the one-sided binary composite hypothesis test, if the UMP test exists, it is nothing but comparing the MVUE for the unknown parameter with a threshold. The paper tries to make a link between the Cramer Rao Bound (CRB) in estimation theory and the UMP performance bound in detection theory. In addition to the intrinsic theoretical interest of such relationship discussed in the paper, it leads us to proposing a novel detection method. For such problems in which the UMP test does not exist, we suggest using a good estimator of the unknown parameter as the decision statistic. The simulation results confirm the idea that the closer we get to the CRB in estimating the unknown parameter, the more we get near to the UMP performance bound in detection.