A new coding scheme for multicasting multiple sources over a general noisy network is presented. The scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover-EI Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The key idea is to use block Markov message repetition coding and simultaneous decoding. Instead of sending multiple independent messages over several blocks and decoding them sequentially as in previous relaying schemes, the same mes sage is sent multiple times using independent codebooks and the decoder performs joint typicality decoding on the received signals from all the blocks without explicitly decoding the compression indices. New results on semideterministic relay networks and Gaussian networks demonstrate the potential of noisy network coding as a robust and scalable scheme for communication over wireless networks.
Abstract-Hybrid analog-digital coding has been used for several communication scenarios, such as joint source-channel coding of Gaussian sources over Gaussian channels and relay communication over Gaussian networks. In this paper, a generalized hybrid coding technique is proposed for communication over discrete memoryless and Gaussian systems, and its utility is demonstrated via three examples-lossy joint source-channel coding over multiple access channels, channel coding over two-way relay channels, and channel coding over diamond networks. The corresponding coding schemes recover and extend several existing results in the literature.
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Abstract-A new approach to joint source-channel coding is presented in the context of communicating correlated sources over multiple access channels. Similar to the separation architecture, the joint source-channel coding system architecture in this approach is modular, whereby the source encoding and channel decoding operations are decoupled. However, unlike the separation architecture, the same codeword is used for both source coding and channel coding, which allows the resulting coding scheme to achieve the performance of the best known schemes despite its simplicity. In particular, it recovers as special cases previous results on lossless communication of correlated sources over multiple access channels by Cover, El Gamal, and Salehi, distributed lossy source coding by Berger and Tung, and lossy communication of the bivariate Gaussian source over the Gaussian multiple access channel by Lapidoth and Tinguely. The proof of achievability involves a new technique for analyzing the probability of decoding error when the message index depends on the codebook itself. Applications of the new joint source-channel coding system architecture in other settings are also discussed. I. PROBLEM STATEMENT AND THE MAIN RESULTConsider the problem of communicating a pair of correlated discrete memoryless sources (2-DMS) (S 1 , S 2 ) over a discrete memoryless multiple access channel (DM-MAC) (X 1 × X 2 , p(y|x 1 , x 2 ), Y) as depicted in Fig. 1. Here each sender j = 1, 2 wishes to communicate its source S j to a common receiver so the sources can be reconstructed with desired distortions. We will consider the block coding setting in which the source sequences S n 1 = (S 11 , . . . , S 1n ) and S n 2 = (S 21 , . . . , S 2n ) are communicated by n transmissions over the channel. Formally, a (|S 1 | n , |S 2 | n , n) joint source-channel code consists of• two encoders, where encoder j = 1, 2 assigns a sequence x n j (s n j ) ∈ X n j to each sequence s n j ∈ S n j , and • a decoder that assigns an estimate (ŝ D 2 ) is said to be achievable for communication of the 2-DMS (S 1 , S 2 ) over the DM-MAC p(y|x 1 , x 2 ) if there exists a sequence of (|S 1 | n , |S 2 | n , n) joint source-channel codes such thatThe optimal distortion region D * is the closure of the set of all achievable distortion pairs (D 1 , D 2 ).A computable characterization of the optimal distortion region is not known in general. This paper establishes the following inner bound on the optimal distortion region. For simplicity, we will assume that the sources S 1 and S 2 have no common part in the sense of Gács-Körner [1] and Witsenhausen [2].for some pmf p(s 1 , s 2 )p(q)p(u 1 , x 1 |s 1 , q)p(u 2 , x 2 |s 2 , q) and functionsŝ 1 (u 1 , u 2 , y, q) andŝ 2 (u 1 , u 2 , y, q) such thatHere and throughout, we use notation in [3]. As we will see in Section II, Theorem 1 includes previous results on lossless communication of a 2-DMS over a DM-MAC by Cover, El Gamal, and Salehi [4], distributed lossy source coding of a 2-DMS by Berger [5] and Tung [6], and lossy commun...
Abstract-A new coding scheme for multicasting a message over a general relay network is presented that extends both network coding for graphical networks by Ahlswede, Cai, Li, and Yeung, and partial decode-forward for relay channels by Cover and El Gamal. For the N -node Gaussian multicast network, the scheme achieves within 0.5N bits from the capacity, improving upon the best known capacity gap results. The key idea is to use multicoding at the source as in Marton coding for broadcast channels. Instead of recovering a specific part of the message as in the original partial decode-forward scheme, a relay in the proposed distributed decode-forward scheme recovers an auxiliary index that implicitly carries some information about the message and forwards it in block Markov coding. This scheme can be adapted to broadcasting multiple messages over a general relay network, extending and refining a recent result by Kannan, Raja, and Viswanath.
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