Variable-rate linear network codes are investigated in this paper, which are referred to as linear network codes that can support a demanded range of transmission rates on a common netowrk. A new kind of linear network code, called as strict linear broadcast, is defined. Compared with general linear broadcast, it imposes more rigid constraints on the global encoding kernels, but does not require larger finite field size for construction. Then, an efficient scheme is proposed to construct variable-rate linear broadcasts based on the strict linear broadcast. Instead of construcing a fix-rate linear broadcast for each demanded transmission rate, this scheme implements variable-rate linear broadcasts with a single-rate strict linear broadcast. Every node in the network, including the source node, needs to store only one local encoding kernel. When transmission rate varies, the coding operations performed on every network node remain unchanged. Thus, small storage space and no kernel-swithching operations are required on any network code. Furthermore, by combining the strict linear broadcast with a special source-data packetization strategy, a hierarchical broadcast scheme is proposed. With this scheme, multi-rate service can be provided by a single-rate strict linear broadcast to heterogeneous receivers, even at variable transmission rate. Thus, the variable-rate linear broadcasts constructed in this paper are also applicable to the network with heterogeneous receivers.

Generalized approximate message passing (GAMP) can be applied to compressive phase retrieval (CPR) with excellent phase-transition behavior. In this paper, we introduced the cartoon-texture model into the denoising-based phase retrieval GAMP(D-prGAMP), and proposed a cartoon-texture model based D-prGAMP (C-T D-prGAMP) algorithm. Then, based on experiments and analyses on the variations of the performance of D-PrGAMP algorithms with iterations, we proposed a 2-stage D-prGAMP algorithm, which makes tradeoffs between the C-T D-prGAMP algorithm and general D-prGAMP algorithms. Finally, facing the non-convergence issues of D-prGAMP, we incorporated adaptive damping to 2-stage D-prGAMP, and proposed the adaptively damped 2-stage D-prGAMP (2-stage ADD-prGAMP) algorithm. Simulation results show that, runtime of 2-stage D-prGAMP is relatively equivalent to that of BM3D-prGAMP, but 2-stage D-prGAMP can achieve higher image reconstruction quality than BM3D-prGAMP. 2-stage ADD-prGAMP spends more reconstruction time than 2-stage D-prGAMP and BM3D-prGAMP. But, 2-stage ADD-prGAMP can achieve PSNRs 0.2∼3dB higher than those of 2-stage D-prGAMP and 0.3∼3.1dB higher than those of BM3D-prGAMP.

Deep learning is playing an increasingly important role in signal processing field due to its excellent performance on many inference problems. Parametric bilinear generalized approximate message passing (P-BiG-AMP) is a new approximate message passing based approach to a general class of structure-matrix bilinear estimation problems. In this letter, we propose a novel feed-forward neural network architecture to realize P-BiG-AMP methodology with deep learning for the inference problem of compressive sensing under matrix uncertainty. Linear transforms utilized in the recovery process and parameters involved in the input and output channels of measurement are jointly learned from training data. Simulation results show that the trained P-BiG-AMP network can achieve higher reconstruction performance than the P-BiG-AMP algorithm with parameters tuned via the expectation-maximization method.

In cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing. However, the problem becomes quite challenging in wideband spectrum sensing due to high sampling pressure, limited power and computing resources, and serious channel fading. To overcome these challenges, this paper proposes a distributed collaborative spectrum sensing scheme based on 1-bit compressive sensing (CS). Each secondary user (SU) performs local 1-bit CS and obtains support estimate information from the signal reconstruction. To utilize joint sparsity and achieve spatial diversity, the support estimate information among the network is fused via the average consensus technique based on distributed computation and one-hop communications. Then the fused result on support estimate is used as priori information to guide the next local signal reconstruction, which is implemented via our proposed weighted binary iterative hard thresholding (BIHT) algorithm. The local signal reconstruction and the distributed fusion of support information are alternately carried out until reliable spectrum detection is achieved. Simulations testify the effectiveness of our proposed scheme in distributed CR networks.

Generalized approximate message passing (GAMP) is introduced into distributed compressed sensing (DCS) to reconstruct jointly sparse signals under the mixed support-set model. A GAMP algorithm with known support-set is presented and the matching pursuit generalized approximate message passing (MPGAMP) algorithm is modified. Then, a new joint recovery algorithm, referred to as the joint MPGAMP algorithm, is proposed. It sets up the jointly shared support-set of the signal ensemble with the support exploration ability of matching pursuit and recovers the signals' amplitudes on the support-set with the good reconstruction performance of GAMP. Numerical investigation shows that the joint MPGAMP algorithm provides performance improvements in DCS reconstruction compared to joint orthogonal matching pursuit, joint look ahead orthogonal matching pursuit and regular MPGAMP.