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Register a new userCurves on Flat Tori and Analog Source-Channel Codes
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Added by
Antonio Campello
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. We propose a constructive scheme based on a set of curves on the surface of a N-dimensional sphere. Our approach shows that the design of good codes for this communication problem is related to geometrical properties of spherical codes and projections of N-dimensional rectangular lattices. Theoretical comparisons with some previous works in terms of the mean square error as a function of the channel SNR as well as simulations are provided.
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A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific hyperbox in R^L in each layer. Group structure and homogeneity, useful for efficient storage and decoding, are inherited from the underlying lattice codebook. A systematic method for constructing such codes are presented and, as an example, the Leech lattice is used to construct a spherical code in R^{48}. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.
We exploit the redundancy of the language-based source to help polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after every few bits are decoded. This path-pruning technique based on joint decoding has advantages over stand-alone polar list decoding in that most decoding errors in early stages are corrected. In order to facilitate the joint decoding, we first propose a construction of dynamic dictionary using a trie and show an efficient way to trace the dictionary during decoding. Then we propose a joint decoding scheme of polar codes taking into account both information from the channel and the source. The proposed scheme has the same decoding complexity as the list decoding of polar codes. A list-size adaptive joint decoding is further implemented to largely reduce the decoding complexity. We conclude by simulation that the joint decoding schemes outperform stand-alone polar codes with CRC-aided successive cancellation list decoding by over 0.6 dB.
In this paper, we show some applications of algebraic curves to the construction of kernels of polar codes over a discrete memoryless channel which is symmetric w.r.t the field operations. We will also study the minimum distance of the polar codes proposed, their duals and the exponents of the matrices used for defining them. All the restrictions that we make to our curves will be accomplished by the so-called Castle Curves.
In this paper, we perform a threshold analysis of braided convolutional codes (BCCs) on the additive white Gaussian noise (AWGN) channel. The decoding thresholds are estimated by Monte-Carlo density evolution (MC-DE) techniques and compared with approximate thresholds from an erasure channel prediction. The results show that, with spatial coupling, the predicted thresholds are very accurate and quickly approach capacity if the coupling memory is increased. For uncoupled ensembles with random puncturing, the prediction can be improved with help of the AWGN threshold of the unpunctured ensemble.
Zero-error single-channel source coding has been studied extensively over the past decades. Its natural multi-channel generalization is however not well investigated. While the special case with multiple symmetric-alphabet channels was studied a decade ago, codes in such setting have no advantage over single-channel codes in data compression, making them worthless in most applications. With essentially no development since the last decade, in this paper, we break the stalemate by showing that it is possible to beat single-channel source codes in terms of compression assuming asymmetric-alphabet channels. We present the multi-channel analog of several classical results in single-channel source coding, such as that a multi-channel Huffman code is an optimal tree-decodable code. We also show some evidences that finding an efficient construction of multi-channel Huffman codes may be hard. Nevertheless, we propose a suboptimal code construction whose redundancy is guaranteed to be no larger than that of an optimal single-channel source code.
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