440 research outputs found
Decoding of Convolutional Codes over the Erasure Channel
In this paper we study the decoding capabilities of convolutional codes over
the erasure channel. Of special interest will be maximum distance profile (MDP)
convolutional codes. These are codes which have a maximum possible column
distance increase. We show how this strong minimum distance condition of MDP
convolutional codes help us to solve error situations that maximum distance
separable (MDS) block codes fail to solve. Towards this goal, we define two
subclasses of MDP codes: reverse-MDP convolutional codes and complete-MDP
convolutional codes. Reverse-MDP codes have the capability to recover a maximum
number of erasures using an algorithm which runs backward in time. Complete-MDP
convolutional codes are both MDP and reverse-MDP codes. They are capable to
recover the state of the decoder under the mildest condition. We show that
complete-MDP convolutional codes perform in certain sense better than MDS block
codes of the same rate over the erasure channel.Comment: 18 pages, 3 figures, to appear on IEEE Transactions on Information
Theor
Complete j-MDP convolutional codes
Maximum distance profile (MDP) convolutional codes have been proven to be
very suitable for transmission over an erasure channel. In addition, the
subclass of complete MDP convolutional codes has the ability to restart
decoding after a burst of erasures. However, there is a lack of constructions
of these codes over fields of small size. In this paper, we introduce the
notion of complete j-MDP convolutional codes, which are a generalization of
complete MDP convolutional codes, and describe their decoding properties. In
particular, we present a decoding algorithm for decoding erasures within a
given time delay T and show that complete T-MDP convolutional codes are optimal
for this algorithm. Moreover, using a computer search with the MAPLE software,
we determine the minimal binary and non-binary field size for the existence of
(2,1,2) complete j-MDP convolutional codes and provide corresponding
constructions. We give a description of all (2,1,2) complete MDP convolutional
codes over the smallest possible fields, namely F_13 and F_16 and we also give
constructions for (2,1,3) complete 4-MDP convolutional codes over F_128
obtained by a randomized computer search.Comment: 2
Weighted Reed-Solomon convolutional codes
In this paper we present a concrete algebraic construction of a novel class
of convolutional codes. These codes are built upon generalized Vandermonde
matrices and therefore can be seen as a natural extension of Reed-Solomon block
codes to the context of convolutional codes. For this reason we call them
weighted Reed-Solomon (WRS) convolutional codes. We show that under some
constraints on the defining parameters these codes are Maximum Distance Profile
(MDP), which means that they have the maximal possible growth in their column
distance profile. We study the size of the field needed to obtain WRS
convolutional codes which are MDP and compare it with the existing general
constructions of MDP convolutional codes in the literature, showing that in
many cases WRS convolutional codes require significantly smaller fields.Comment: 30 page
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Towards Informed Exploration for Deep Reinforcement Learning
In this thesis, we discuss various techniques for improving exploration for deep reinforcement learning. We begin with a brief review of reinforcement learning (RL) and the fundamental v.s. exploitation trade-off. Then we review how deep RL has improved upon classical and summarize six categories of the latest exploration methods for deep RL, in the order increasing usage of prior information. We then explore representative works in three categories discuss their strengths and weaknesses. The first category, represented by Soft Q-learning, uses regularization to encourage exploration. The second category, represented by count-based via hashing, maps states to hash codes for counting and assigns higher exploration to less-encountered states. The third category utilizes hierarchy and is represented by modular architecture for RL agents to play StarCraft II. Finally, we conclude that exploration by prior knowledge is a promising research direction and suggest topics of potentially impact
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
Descodificação através de Machine Learning
In recent years, machine learning has become one of the most rapidly expanding
technologies in a variety of technological fields. In general, it allows a computer
to learn from data without being expressly designed for a particular purpose. This
thesis investigates the application of decoding methods inspired by machine learning
to linear block codes, such as Reed-Muller (RM) codes.Recentemente, o Machine Learning tornou-se uma das tecnologias em mais rápida
expansão numa variedade de campos tecnológicos. Em geral, permite que um
computador aprenda com os dados sem ser expressamente concebido para um fim
específico. Esta dissertação investiga a aplicação de métodos de descodificação
inspirados no Machine Learning a códigos de blocos lineares, tais como os códigos
de Reed-Muller
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