We consider a system in which random status updates arrive at a source node, and should be transmitted through a wireless network to the intended destination node. The status updates are samples of a random process, transmitted as packets, containing the time stamp to identify the moment the sample was generated. The time it takes to successfully transmit a packet to the destination is modeled as an exponentially distributed service time. The status update age at the receiver is the time elapsed since the last received update was generated. In this paper, we analyze the age in the case that the source node has the capability to manage the arriving samples and decide which packets will be transmitted to the destination. In addition to the average age, we investigate the average of a new metric, called peak age, which provides information about the maximum value of the Age, achieved immediately before receiving an update.

Age of information with packet management

Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector x observed through a linear transform A. In the case of large i.i.d. zero-mean Gaussian A, the methods exhibit fast convergence with precise analytic characterizations on the algorithm behavior. However, the convergence of AMP under general transforms A is not fully understood. In this paper, we provide sufficient conditions for the convergence of a damped version of the generalized AMP (GAMP) algorithm in the case of quadratic cost functions (i.e., Gaussian likelihood and prior). It is shown that, with sufficient damping, the algorithm is guaranteed to converge, although the amount of damping grows with peak-to-average ratio of the squared singular values of the transforms A. This result explains the good performance of AMP on i.i.d. Gaussian transforms A, but also their difficulties with ill-conditioned or non-zero-mean transforms A. A related sufficient condition is then derived for the local stability of the damped GAMP method under general cost functions, assuming certain strict convexity conditions.

On the Convergence of Approximate Message Passing With Arbitrary Matrices

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan \textit{et al}, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from $2$ erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

Codes with Locality for Two Erasures

Fiber's nonlinearity fundamentally bounds the achievable information rates in fiber-optic communication systems. In a wavelength-division multiplexed system it induces a nonlinear interference between adjacent channels, an interference that was recently shown to have a strong dependance on the input distribution. In this work we show that a ball shaped input constellation may significantly reduce the nonlinear effects. We study the shaping gains in the fiber-optic channel and show that in certain scenarios the maximum gains may be higher than the 1.53dB ultimate shaping gain in linear additive white Gaussian noise channels. Furthermore, the maximum gain is achieved with a finite-dimensional ball shaping region.

On shaping gain in the nonlinear fiber-optic channel

Puncturing is widely used to generate rate-compatible codes. However, for punctured polar codes, some puncturing patterns may greatly affect the split bit channels and cause considerable performance loss. In this paper, we aim to investigate how the split bit channels are affected by various puncturing patterns, and then evaluate the performances of these patterns. We propose a search algorithm to design good punctured polar codes, and prove that designing the optimal puncturing pattern for output bits is equivalent to finding the optimal puncturing pattern for frozen bits. We also propose a heuristic approach based on the idea of polarization to select the position of each punctured output bit, and simulations show that the puncturing pattern designed this way almost achieves the same performance as the optimal one selected by exhaustive search.

On the puncturing patterns for punctured polar codes

国際会議参加報告:2014 IEEE International Symposium on Information Theory

This study focuses on delayed bit-interleaved coded modulation (DBICM) for a two-dimensional signal constellation and shows that the capacity of DBICM is identical to the coded modulation capacity with less delay than before. An appropriate bit-labeling scheme based on Gray labeling for each signal point is also considered to prevent the performance degradation of DBICM. The results of the numerical calculations and simulations indicate that the proposed method improves performance.

Gou Hosoya

Papers

国際会議参加報告:2014 IEEE International Symposium on Information Theory

Reduction of Delay for Delayed Bit-Interleaved Coded Modulation