Parallel concatenated convolutional codes from linear systems theory viewpoint

The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input–state–output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances

Analysis of control properties of concatenated convolutional codes

In this paper we consider two models of concatenated convolutional codes from the perspective of linear systems theory. We present an input-state-output representation of these models and we study the conditions for control properties for concatenated convolutional codes.Postprint (published version

Weight-2 input sequences of 1/n convolutional codes from linear systems point of view

Convolutional codes form an important class of codes that have memory. One natural way to study these codes is by means of input state output representations. In this paper we study the minimum (Hamming) weight among codewords produced by input sequences of weight two. In this paper, we consider rate 1/n and use the linear system setting called (A,B,C,D) input-state-space representations of convolutional codes for our analysis. Previous results on this area were recently derived assuming that the matrix A, in the input-state-output representation, is nonsingular. This work completes this thread of research by treating the nontrivial case in which A is singular. Codewords generated by weight-2 inputs are relevant to determine the effective free distance of Turbo codes.The research of the second author was supported by Spanish I+D+i project PID2019-108668GB-I00 of MCIN/AEI/10.13039/501100011033

1/n Turbo codes from linear system point of view

The performance of turbo codes at the error floor region is largely determined by the effective free distance, which corresponds to the minimum Hamming weight among all codeword sequences generated by input sequences of weight two. In this paper, we study turbo codes of dimension one obtained from the concatenation of two equal codes and present an upper bound on the effective free distance of a turbo code with these parameters defined over any finite field. We do that making use of the so-called (A, B, C, D) state-space representations of convolutional codes and restrict to the case where A is invertible. A particular construction, from a linear systems point of view, of a recursive systematic convolutional code of rate 1/n so that the effective free distance of the corresponding turbo code attains this upper bound is also presented.D. Napp was partially supported by the the Universitat d’Alacant (Grant No. VIGROB-287) and Generalitat Valenciana (Grant No. AICO/2017/128). V. Herranz and C. Perea were supported by the Ministerio de Economa, Industria y Competitividad within project TIN2016-80565-R

Orthogonal Multiple Access with Correlated Sources: Feasible Region and Pragmatic Schemes

In this paper, we consider orthogonal multiple access coding schemes, where correlated sources are encoded in a distributed fashion and transmitted, through additive white Gaussian noise (AWGN) channels, to an access point (AP). At the AP, component decoders, associated with the source encoders, iteratively exchange soft information by taking into account the source correlation. The first goal of this paper is to investigate the ultimate achievable performance limits in terms of a multi-dimensional feasible region in the space of channel parameters, deriving insights on the impact of the number of sources. The second goal is the design of pragmatic schemes, where the sources use "off-the-shelf" channel codes. In order to analyze the performance of given coding schemes, we propose an extrinsic information transfer (EXIT)-based approach, which allows to determine the corresponding multi-dimensional feasible regions. On the basis of the proposed analytical framework, the performance of pragmatic coded schemes, based on serially concatenated convolutional codes (SCCCs), is discussed

On the error statistics of turbo decoding for hybrid concatenated codes design

In this paper we propose a model for the generation of error patterns at the output of a turbo decoder using a Context Tree based modelling technique. This model can be used not only to generate the decoder error pattern behaviour with little effort, avoiding simulations, but also to investigate \u2013 with no need of performing neither a turbo code distance spectrum analysis, nor the probabilistic characterization of log-likelihood ratios or of the extrinsic information at a turbo decoder output \u2013 the performance of hybrid concatenated coding (HCC) schemes having a turbo code as component code. These coding schemes combine the features of parallel and serially concatenated codes and thus offer more freedom in code design. It has been demonstrated, in fact, that HCCs can perform closer to capacity than serially concatenated codes while still maintaining a minimum distance that grows linearly with block length

Convolutional codes under linear systems point of view. Analysis of output-controllability

In this work we make a detailed look at the algebraic structure of convolutional codes using techniques of linear systems theory. In particular we study the input-state-output representation of a convolutional code. We examine the output-controllability property and we give conditions for this property. At the end of the paper is presented a brief introduction to the analysis of output controllability for parallel concatenated codes.Peer ReviewedPostprint (published version

Generative Model with Coordinate Metric Learning for Object Recognition Based on 3D Models

Given large amount of real photos for training, Convolutional neural network shows excellent performance on object recognition tasks. However, the process of collecting data is so tedious and the background are also limited which makes it hard to establish a perfect database. In this paper, our generative model trained with synthetic images rendered from 3D models reduces the workload of data collection and limitation of conditions. Our structure is composed of two sub-networks: semantic foreground object reconstruction network based on Bayesian inference and classification network based on multi-triplet cost function for avoiding over-fitting problem on monotone surface and fully utilizing pose information by establishing sphere-like distribution of descriptors in each category which is helpful for recognition on regular photos according to poses, lighting condition, background and category information of rendered images. Firstly, our conjugate structure called generative model with metric learning utilizing additional foreground object channels generated from Bayesian rendering as the joint of two sub-networks. Multi-triplet cost function based on poses for object recognition are used for metric learning which makes it possible training a category classifier purely based on synthetic data. Secondly, we design a coordinate training strategy with the help of adaptive noises acting as corruption on input images to help both sub-networks benefit from each other and avoid inharmonious parameter tuning due to different convergence speed of two sub-networks. Our structure achieves the state of the art accuracy of over 50\% on ShapeNet database with data migration obstacle from synthetic images to real photos. This pipeline makes it applicable to do recognition on real images only based on 3D models.Comment: 14 page

Iterative decoding for magnetic recording channels.

The success of turbo codes indicates that performance close to the Shannon limit may be achieved by iterative decoding. This has in turn stimulated interest in the performance of iterative detection for partial-response channels, which has been an active research area since 1999. In this dissertation, the performance of serially concatenated recording systems is investigated by computer simulations as well as experimentally. The experimental results show that the iterative detection algorithm is not sensitive to channel nonlinearities and the turbo coded partial-response channel is substantially better than partial-response maximum-likelihood channels. The classical iterative decoding algorithm was originally designed for additive white Gaussian noise channels. This dissertation shows that the performance of iterative detection can be significantly improved by considering the noise correlation of the magnetic recording channel. The idea is to iteratively estimate the correlated noise sequence at each iteration. To take advantage of the noise estimate, two prediction techniques were proposed, and the corresponding systems were named noise predictive turbo systems. These noise predictive turbo systems can be generalized to other detector architectures for magnetic recording channels straightforwardly