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Abstract-We characterize the best achievable performance of lossy compression algorithms operating on arbitrary random sources, and with respect to general distortion measures. Direct and converse coding theorems are given for variable-rate codes operating at a fixed distortion level, emphasizing: a) nonasymptotic results, b) optimal or near-optimal redundancy bounds, and c) results with probability one. This development is based in part on the observation that there is a precise correspondence between compression algorithms and probability measures on the reproduction alphabet. This is analogous to the Kraft inequality in lossless data compression. In the case of stationary ergodic sources our results reduce to the classical coding theorems. As an application of these general results, we examine the performance of codes based on mixture codebooks for discrete memoryless sources. A mixture codebook (or Bayesian codebook) is a random codebook generated from a mixture over some class of reproduction distributions. We demonstrate the existence of universal mixture codebooks, and show that it is possible to universally encode memoryless sources with redundancy of approximately ( 2) log bits, where is the dimension of the simplex of probability distributions on the reproduction alphabet.

Abstract-We characterize the best achievable performance of lossy compression algorithms operating on arbitrary random sources, and with respect to general distortion measures. Direct and converse coding theorems are given for variable-rate codes operating at a fixed distortion level, emphasizing: a) nonasymptotic results, b) optimal or near-optimal redundancy bounds, and c) results with probability one. This development is based in part on the observation that there is a precise correspondence between compression algorithms and probability measures on the reproduction alphabet. This is analogous to the Kraft inequality in lossless data compression. In the case of stationary ergodic sources our results reduce to the classical coding theorems. As an application of these general results, we examine the performance of codes based on mixture codebooks for discrete memoryless sources. A mixture codebook (or Bayesian codebook) is a random codebook generated from a mixture over some class of reproduction distributions. We demonstrate the existence of universal mixture codebooks, and show that it is possible to universally encode memoryless sources with redundancy of approximately ( 2) log bits, where is the dimension of the simplex of probability distributions on the reproduction alphabet.

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We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain , the number of users , and the number of received signal samples all go to infinity, while keeping the ratios and fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the function.

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Federated learning (FL) is a promising distributed framework for collaborative artificial intelligence model training while protecting user privacy. A bootstrapping component that has attracted significant research attention is the design of incentive mechanism to stimulate user collaboration in FL. The majority of works adopt a broker-centric approach to help the central operator to attract participants and further obtain a well-trained model. Few works consider forging participant-centric collaboration among participants to pursue an FL model for their common interests, which induces dramatic differences in incentive mechanism design from the broker-centric FL. To coordinate the selfish and heterogeneous participants, we propose a novel analytic framework for incentivizing effective and efficient collaborations for participant-centric FL. Specifically, we respectively propose two novel game models for contribution-oblivious FL (COFL) and contribution-aware FL (CAFL), where the latter one implements a minimum contribution threshold mechanism. We further analyze the uniqueness and existence for Nash equilibrium of both COFL and CAFL games and design efficient algorithms to achieve equilibrium solutions. Extensive performance evaluations show that there exists free-riding phenomenon in COFL, which can be greatly alleviated through the adoption of CAFL model with the optimized minimum threshold.

Multiple-access interference (MAI) in a code-division multiple-access (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. In this paper, we study the behavior of the output MAI of the minimum mean-square error (MMSE) receiver employed in the uplink of a direct-sequence (DS)-CDMA system. We focus on imperfect power-controlled systems with random spreading, and establish that in a synchronous system 1) the output MAI of the MMSE receiver is asymptotically Gaussian, and 2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of single-user Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signal-to-interference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system.