Information Theory (cs.IT)

Abstract: The class of k-bit delay decodable codes, source codes allowing decoding delay of at most k bits for k >= 0, can attain a shorter average codeword length than Huffman codes. This paper discusses the general properties of the class of k-bit delay decodable codes with a finite number of code tables and proves two theorems which enable us to limit the scope of code-tuples to be considered when discussing optimal k-bit delay decodable code-tuples.

Abstract: Most of the existing research on degrees-of-freedom (DoF) with imperfect channel state information at the transmitter (CSIT) assume the messages are private, which may not reflect reality as the two receivers can request the same content. To overcome this limitation, we consider hybrid private and common messages. We characterize the optimal DoF region for the two-user multiple-input multiple-output (MIMO) broadcast channel with hybrid messages and imperfect CSIT. We establish a three-step procedure for the DoF converse to exploit the utmost possible relaxation. For the DoF achievability, since the DoF region has a specific three-dimensional structure w.r.t. antenna configurations and CSIT qualities, by dividing CSIT qualities into cases, we check the existence of corner point solutions, and then design a hybrid messages-aware rate-splitting scheme to achieve them. Besides, we show that to achieve the strictly positive corner points, it is unnecessary to split the private messages into unicast and multicast parts because the allocated power for the multicast part should be zero. This implies that adding a common message can mitigate the rate-splitting complexity of private messages.

Abstract: Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined. The parameters of the related $2$-designs are also given. Moreover, we prove that the codewords with minimum Hamming weight supporting 3-designs, which gives an affirmative solution to Heng's conjecture.

Abstract: This paper addresses channel estimation for linear time-varying (LTV) wireless propagation links under the assumption of double sparsity i.e., sparsity in both the delay and the Doppler domains. Affine frequency division multiplexing (AFDM), a recently proposed waveform, is shown to be optimal (in a sense that we make explicit) for this problem. With both mathematical analysis and numerical results, the minimal pilot and guard overhead needed for achieving a target mean squared error (MSE) while performing channel estimation is shown to be the smallest when AFDM is employed instead of both conventional and recently proposed waveforms.

Abstract: We consider communication over channels whose statistics are not known in full, but can be parameterized as a finite family of memoryless channels. A typical approach to address channel uncertainty is to design codes for the worst channel in the family, resulting in the well-known compound channel capacity. Although this approach is robust, it may suffer a significant loss of performance if the capacity-achieving distribution of the worst channel attains low rates over other channels. In this work, we cope with channel uncertainty through the lens of {\em competitive analysis}. The main idea is to optimize a relative metric that compares the performance of the designed code and a clairvoyant code that has access to the true channel. To allow communication rates that adapt to the channel at use, we consider rateless codes with a fixed number of message bits and random decoding times. We propose two competitive metrics: the competitive ratio between the expected rates of the two codes, and a regret defined as the difference between the expected rates. The competitive ratio, for instance, provides a percentage guarantee on the expected rate of the designed code when compared to the rate of the clairvoyant code that knows the channel at hand. Our main results are single-letter expressions for the optimal {\em competitive-ratio} and {\em regret}, expressed as a max-min or min-max optimization. Several examples illustrate the benefits of the competitive analysis approach to code design compared to the compound channel.