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Register a new userBinary CEO Problem under Log-Loss with BSC Test-Channel Model
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Added by
Mahdi Nangir
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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In this paper, we propose an efficient coding scheme for the two-link binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. The exact rate-distortion bound for a two-link binary CEO problem under the logarithmic loss has been obtained by Courtade and Weissman. We propose an encoding scheme based on compound LDGM-LDPC codes to achieve the theoretical bounds. In the proposed encoding, a binary quantizer using LDGM codes and a syndrome-coding employing LDPC codes are applied. An iterative joint decoding is also designed as a fusion center. The proposed CEO decoder is based on the sum-product algorithm and a soft estimator.
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An $l$-link binary CEO problem is considered in this paper. We present a practical encoding and decoding scheme for this problem employing the graph-based codes. A successive coding scheme is proposed for converting an $l$-link binary CEO problem to the $(2l-1)$ single binary Wyner-Ziv (WZ) problems. By using the compound LDGM-LDPC codes, the theoretical bound of each binary WZ is asymptotically achievable. Our proposed decoder successively decodes the received data by employing the well-known Sum-Product (SP) algorithm and leverages them to reconstruct the source. The sum-rate distortion performance of our proposed coding scheme is compared with the theoretical bounds under the logarithmic loss (log-loss) criterion.
The $L$-link binary Chief Executive Officer (CEO) problem under logarithmic loss is investigated in this paper. A quantization splitting technique is applied to convert the problem under consideration to a $(2L-1)$-step successive Wyner-Ziv (WZ) problem, for which a practical coding scheme is proposed. In the proposed scheme, low-density generator-matrix (LDGM) codes are used for binary quantization while low-density parity-check (LDPC) codes are used for syndrome generation; the decoder performs successive decoding based on the received syndromes and produces a soft reconstruction of the remote source. The simulation results indicate that the rate-distortion performance of the proposed scheme can approach the theoretical inner bound based on binary-symmetric test-channel models.
In this paper, we propose an efficient coding scheme for the binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. Courtade and Weissman obtained the exact rate-distortion bound for a two-link binary CEO problem under this criterion. We find the optimal test-channel model and its parameters for the encoder of each link by using the given bound. Furthermore, an efficient encoding scheme based on compound LDGM-LDPC codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome-decoding employing LDPC codes are applied. An iterative decoding is also presented as a fusion center to reconstruct the observation bits. The proposed decoder consists of a sum-product algorithm with a side information from other decoder and a soft estimator. The output of the CEO decoder is the probability of source bits conditional to the received sequences of both links. This method outperforms the majority-based estimation of the source bits utilized in the prior studies of the binary CEO problem. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.
We show that Reed-Muller codes achieve capacity under maximum a posteriori bit decoding for transmission over the binary erasure channel for all rates $0 < R < 1$. The proof is generic and applies to other codes with sufficient amount of symmetry as well. The main idea is to combine the following observations: (i) monotone functions experience a sharp threshold behavior, (ii) the extrinsic information transfer (EXIT) functions are monotone, (iii) Reed--Muller codes are 2-transitive and thus the EXIT functions associated with their codeword bits are all equal, and (iv) therefore the Area Theorem for the average EXIT functions implies that RM codes threshold is at channel capacity.
We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the skeleton sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the stochastic binary symmetric channel, we show that the scheme is nearly optimal in a strong sense for certain parameters.
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