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In this letter, we consider the MapReduce-type distributed system and jointly design the Map and Shuffle phases of the coded distributed computing (CDC) scheme proposed by Li, et al. By delicately setting the order of file mapping and data shuffling, we implement the Map and Shuffle phases in parallel, and thus significantly reduce the overall task latency (time cost at the Map, Shuffle, Reduce operations and codes generation). Furthermore, our scheme enables all nodes to remove their auxiliary intermediate values once these values are no longer useful in the Shuffle phase, leading to great reduction in the storage cost of the system. [ABSTRACT FROM AUTHOR]

Discrete memoryless multicast network (DM-MN) is considered in this paper. We analyze the lower bounds of noisy network coding (NNC) and distributed decode-forward (DDF) for DM-MN, and show that both NNC and DDF ignore the channel output observed at the transmitter. Motivated by this observation, new coding schemes are proposed to improve NNC and DDF by exploiting the transmitter’s observation and applying hybrid relaying strategies. We first study a special case when the transmitter’s observation is rate-limited feedback signals, and propose a scheme that strictly improves NNC when feedback rates are sufficiently large. For the relay channel with perfect relay-transmitter feedback, our achievable rate reduces to Gabbai and Bross’s rate, which is strictly larger than NNC, DDF, and all known lower bounds on the achievable rates proposed for the setup without feedback. In our scheme, both relays and receivers compress their received signals like NNC, and the relays decode independent “common” and “private” parts of the source message. The generated compression indices are sent to the transmitter through feedback, from which the transmitter reconstructs the receivers’ and relays’ inputs and can thus cooperate with the receivers and relays. We then extend our idea to DM-MN without feedback. For this case, although the transmitter observes channel output, both NNC and DDF simply ignore it, while our new scheme has the transmitter utilize its channel output to decode a set of relays’ and receivers’ compression indices, which achieves some cooperation levels between the transmitter and the receivers and relays. An enhanced relay channel is introduced to show that our scheme strictly outperforms NNC and DDF. [ABSTRACT FROM AUTHOR]

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information. [ABSTRACT FROM AUTHOR]

We consider the \(K\geq 2\) -user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk and Kailath’s scheme for point-to-point channels or Ozarow and Leung’s scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity \(C\) (which is the same with and without feedback). In the extreme case where the number of receivers \(K\to \infty \) , the largest rate achieved by linear-feedback schemes with a message point tends to 0. To contrast this negative result, we describe a scheme for rate-limited feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates \(R\) up to capacity \(C\) with an \(L\) th order exponential decay of the probability of error if the feedback rate \(R_{\text {fb}}\) is at least \((L-1)R\) for some positive integer \(L\) . [ABSTRACT FROM PUBLISHER]

In this letter, the limited feedback scheme in MIMO-Relay systems is considered. We propose a new strategy that optimizes the allocation of feedback bits between channel direction information (CDI) and phase information (PI) for multi-relay systems under the total number of feedback bits constraint. The proposed scheme eventually trades off some CDI bits for PI feedback to diminish the phase ambiguity. Simulation results show that compared to the conventional and the 1-bit PI feedback methods, the proposed scheme remarkably improves the system performance without increasing the feedback overhead. [ABSTRACT FROM PUBLISHER]