Approximately Optimal Wireless Broadcasting

Abstract

We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the potential aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as well as the superposition of transmitted signals plus independent Gaussian noise at the received signal at any radio. We propose a scheme that can achieve rate tuples within a constant gap away from the cut-set bound, where the constant is independent of channel coefficients and power constraints. First, for a deterministic broadcast network, we propose a new coding scheme, constructed by adopting a "receiver-centric" viewpoint, that uses quantize-and-forward relaying as an inner code concatenated with an outer Marton code for the induced deterministic broadcast channel. This scheme is shown to achieve the cut-set bound evaluated with product form distributions. This result is then lifted to the Gaussian network by using a deterministic network called the discrete superposition network as a formal quantization interface. This two-stage construction circumvents the difficulty involved in working with a vector nonlinear non-Gaussian broadcast channel that arises if we construct a similar scheme directly for the Gaussian network.Index Terms-Broadcast network, broadcast-relay channels, capacity, Marton code, multiuser channels, network information theory, wireless networks.

Distributed decode-forward for multicast

“…This operational reciprocity in the roles of source and destination for multiple access and broadcast has been well noted by Kannan, Raja, and Viswanath [15], which was the key intuition for their coding scheme that parallels the quantize-map-forward scheme by Avestimehr, Diggavi, and Tse [6]. Compared to these nested multiletter schemes [6], [15], however, NNC and DDF provide a more conclusive example on the duality between multiple access and broadcast-NNC achieves the capacity region of the (single-hop) multiple access channel, while 1 For general deterministic multicast networks, DDF performs better than NNC in general, due to input pmfs of the form p(x 1 |x N 2 ) N k=1 p(x k ) instead of product pmfs used in NNC.…”

“…For deterministic networks, Theorem 2 simplifies to the same rate expression as the cutset outer bound [15,Eq. (9)] except that input pmfs are of the form p(x 1 |x N 2 )( n k=2 p(x k )).…”

“…Compared to these nested multiletter schemes [6], [15], however, NNC and DDF provide a more conclusive example on the duality between multiple access and broadcast-NNC achieves the capacity region of the (single-hop) multiple access channel, while 1 For general deterministic multicast networks, DDF performs better than NNC in general, due to input pmfs of the form p(x 1 |x N 2 ) N k=1 p(x k ) instead of product pmfs used in NNC.…”

“…As in [13], [12], the coding scheme uses multicoding as a basis for coordination among distributed nodes. To some extent, the idea of "pruning" superletter codewords by Anand and Kumar [14] for multicast and extended by Kannan, Raja, and Viswanath [15] to broadcast is also reminiscent of multicoding. By encoding the message with compatible codewords via multicoding, the source can coordinate and control the transmission over the entire network, which results in a scalable performance.…”

“…By encoding the message with compatible codewords via multicoding, the source can coordinate and control the transmission over the entire network, which results in a scalable performance. With streamlined operations and singleletter achievable rates for general broadcast networks, the proposed scheme can be viewed as an extension and refinement of the coding scheme of Kannan et al [15].…”