In the context of recent deep clustering studies, discriminative models dominate the literature and report the most competitive performances. These models learn a deep discriminative neural network classifier in which the labels are latent. Typically, they use multinomial logistic regression posteriors and parameter regularization, as is very common in supervised learning. It is generally acknowledged that discriminative objective functions (e.g., those based on the mutual information or the KL divergence) are more flexible than generative approaches (e.g., K-means) in the sense that they make fewer assumptions about the data distributions and, typically, yield much better unsupervised deep learning results. On the surface, several recent discriminative models may seem unrelated to K-means. This study shows that these models are, in fact, equivalent to K-means under mild conditions and common posterior models and parameter regularization. We prove that, for the commonly used logistic regression posteriors, maximizing the L2L2 regularized mutual information via an approximate alternating direction method (ADM) is equivalent to minimizing a soft and regularized K-means loss. Our theoretical analysis not only connects directly several recent state-of-the-art discriminative models to K-means, but also leads to a new soft and regularized deep K-means algorithm, which yields competitive performance on several image clustering benchmarks.

In this paper, we investigate a coding strategy devised to increase the throughput in hybrid ARQ (HARQ) transmission over a block fading channel. In our approach, the transmitter jointly encodes a variable number of bits for the each round of HARQ. The parameters (rates) of this joint coding can vary and may be based on the negative acknowledgment provided by the receiver or, on the past (outdated) information about the channel states. These new degrees of freedom allow us to improve the match between the codebook and the channel states experienced by the receiver. The results indicate that gains obtained using the proposed cross-packet coding strategy are particularly notable for the large values of the throughput. In this region, the conventional HARQ fails to offer throughput improvement even if the number of transmission rounds is increased. We implement the proposed cross-packet HARQ using turbo codes, where we show that the theoretically predicted throughput gains materialize in practice; the implementation challenges are also discussed.

In this paper, we propose a coding strategy designed to enhance the throughput of hybrid automatic repeat request (HARQ) transmissions over independent identically distributed block-fading channels with the channel state information unknown at the transmitter. We use a joint packet coding where the same channel block is logically shared among many packets. To reduce the encoding and decoding complexity, we use a two-layer coding where, first, packets are punctured, mixed, and then passed to the conventional channel encoder. We show how to optimize the puncturing rates on the basis of the empirical error-rate curves. We also discuss how the parameters of the practical turbo-codes may be modified to take advantage of the proposed HARQ scheme. Finally, simple and pragmatic rate adaptation strategies are developed. In numerical examples, our scheme is compared with the conventional incremental redundancy HARQ (IR-HARQ), which remains a strategy of choice in the region of small throughput; however, our scheme shows a notable gain of $1-2~\textrm {dB}$ in the region of high throughput, where IR-HARQ fails to provide any improvement.

In this work, we propose and optimize a new coding strategy designed to enhance the throughput of hybrid ARQ (HARQ) transmissions over i.i.d. block-fading channels where the channel state information (CSI) is unknown at the transmitter. Unlike in the conventional approach, where many blocks are exclusively assigned to carry the HARQ rounds of a single packet, we use a joint coding and the same channel block is logically shared among many packets. To reduce the complexity, we use a two-layer coding, where, first, packets are mixed on the binary level, and the resulting mixture is then passed for the conventional channel encoder. This allows us to decode packets on a block-by-block basis. Knowing the decoder error rate curves, the challenge is to find the optimal packets mixing that maximizes the total throughput. We show how to solve this problem using a dynamic programming (DP) approach, which we next apply to the off-the-shelf turbo-codes. We also discuss how the parameters of the practical turbo-encoder may be modified to take advantage of the proposed HARQ scheme. In numerical examples, our scheme is compared to the conventional incremental redundancy HARQ (IR-HARQ), and it yields a notable gain of 1 - 2dB in the region of high throughput, where IR-HARQ fails to provide any improvement.

To ensure reliable communications in randomly varying and error-prone channels, wireless systems use adaptive modulation and coding (AMC) as well as hybrid ARQ (HARQ). In order to elucidate their compatibility and interaction, we compare the throughput provided by AMC, HARQ, and their combination (AMC-HARQ) under two operational conditions: in slow- and fast block-fading channels. Considering both incremental redundancy HARQ and repetition redundancy HARQ, we optimize the rate-decision regions for AMC/HARQ and compare them in terms of attainable throughput. Under a fairly general model of the channel variation and the decoding functions, we conclude that: 1) adding HARQ on top of AMC may be counterproductive in the high average signal-to-noise ratio regime for fast fading channels and 2) HARQ is useful for slow fading channels, but it provides moderate throughput gains. We provide explanations for these results which allow us to propose paths to improve AMC-HARQ systems.

In this work, we propose and investigate a new coding strategy devised to increase the throughput of hybrid ARQ (HARQ) transmission over block fading channel. In our proposition, the transmitter jointly encodes a variable number of bits for each round of HARQ. The parameters (rates) of this joint coding can vary and may be based on the negative acknowledgment (NACK) signals provided by the receiver or, on the past (outdated) information about the channel states. The results indicate that significant gains can be obtained using the proposed coding strategy especially where the conventional HARQ fails to offer throughput improvement even if the number of transmission rounds is increased.

In this work, various channel coding schemes that can be used in hybrid automatic repeat request (HARQ) transmission protocols are investigated from an energy efficiency point of view. Conventional HARQ, where only one bit is used to inform the transmitter about the decoding success or failure, is compared to adaptive HARQ where the transmitter adapts either the length or the transmit power of the codewords using outdated channel state information (i.e., experienced by the receiver during the past transmissions). Describing the problems within a Markov decision process framework, we find optimal adaptation policies for both persistent (unlimited number of transmission) and truncated HARQ protocols. Numerical examples obtained in a Rayleigh block fading channel show that, in terms of energy efficiency, the adaptation of the codewords length provides notable gains over power adaptation and conventional HARQ.

In this work, we consider incremental redundancy (IR) hybrid automatic repeat request (HARQ), where the transmission rounds are carried over independent block-fading channels. We analyze the multipacket HARQ, where the transmitter allows two different packets to share the same channel block; this stands in contrast with the conventional HARQ, where each packet occupies the entire block. We then optimally assign resources within the block to each packet and in each transmission round. We study superposition coding and time-sharing encoding strategies, and we optimize their parameters to maximize the throughput. Besides the conventional, one-bit (ACK/NACK) signaling we also consider a multibit feedback. We formulate our problem as a Markov decision process (MDP), where the decisions concerning the encoding strategies and their parameters are taken using additional information obtained from the receiver via feedback channel. In the case of the one-bit (ACK/NACK) signaling, the partial state information Markov decision process (PSI-MDP) framework is used to obtain the optimal policies. Numerical examples obtained in a Rayleigh-fading channel indicate that, the proposed multipacket HARQ outperforms the conventional one, by more than 5 dB for high-spectral efficiencies.

In this work, we analyze hybrid ARQ (HARQ) transmission over the independent block fading channel. We consider two scenarios with respect to the message sent by the receiver via the feedback channel: i) “conventional”, one-bit feedback used to inform the transmitter about the decoding success/failure (ACK/NACK), and ii) the multi-bit feedback message, where on top of ACK/NACK, the transmitter is provided with additional information about the state of the receiver. To minimize the outage probability under long-term average and peak power constraints, we cast the problems into the dynamic programming (DP) framework and solve them for Nakagami-m fading channels. An approximate, closed-form solution for the high signal-to-noise ratio (SNR) regime is proposed using geometric programming (GP). The obtained results quantify the advantage of the multi-bit feedback over the conventional one-bit approach, and show that the power optimization can provide significant gains over conventional power-constant HARQ transmissions even in the presence of peak-power constraints.

In this work, we analyze hybrid ARQ (HARQ) protocols used over independent block fading channels. We assume that the transmitter is unaware of the channel state information (CSI) at the moment of transmission but knows the statistics of the channel. We consider two scenarios with respect to the feedback received by the transmitter: (i) “conventional”, one-bit feedback carrying the message about the decoding success/failure (ACK/NACK), and (ii) the multi-bit feedback scheme when, on top of ACK/NACK, the receiver feeds back information about the state of the decoder, which is equivalent to the CSI experienced by the receiver in the past (unsuccessful) transmissions. The feedback can then be used to allocate power across the HARQ transmission attempts (in the case of one-bit feedback) or adapt the power for each re-transmission as a function of multi-bit feedback. The objective in both cases is the minimization of the outage probability under peak and long term average power constraints. We solve the optimization problems using the dynamic programming framework. The obtained results quantify the advantage of the multi-bit feedback over the conventional approach and indicate that power optimization can provide significant gains over the conventional constant-power HARQ transmission even in the presence of peak-power constraints.