Channel Coding at Low Capacity

Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of mobile networks. Such scenarios require efficient and reliable transmission of information over channels with an extremely small capacity. Within these constraints, the performance of state-of-the-art coding techniques is far from optimal in terms of either rate or complexity. Moreover, the current non-asymptotic laws of optimal channel coding provide inaccurate predictions for coding in the low-capacity regime. In this paper, we provide the first comprehensive study of channel coding in the low-capacity regime. We will investigate the fundamental non-asymptotic limits for channel coding as well as challenges that must be overcome for efficient code design in low-capacity scenarios.Comment: 39 pages, 5 figure

Polar Coding for the Cognitive Interference Channel with Confidential Messages

In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple point-to-point polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder

Iteratively Decoded Irregular Variable Length Coding and Sphere-Packing Modulation-Aided Differential Space-Time Spreading

In this paper we consider serially concatenated and iteratively decoded Irregular Variable Length Coding (IrVLC) combined with precoded Differential Space-Time Spreading (DSTS) aided multidimensional Sphere Packing (SP) modulation designed for near-capacity joint source and channel coding. The IrVLC scheme comprises a number of component Variable Length Coding (VLC) codebooks having different coding rates for the sake of encoding particular fractions of the input source symbol stream. The relative length of these source-stream fractions can be chosen with the aid of EXtrinsic Information Transfer (EXIT) charts in order to shape the EXIT curve of the IrVLC codec, so that an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. These schemes are shown to be capable of operating within 0.9 dB of the DSTS-SP channel’s capacity bound using an average interleaver length of 113, 100 bits and an effective bandwidth efficiency of 1 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based benchmarker scheme was found to be capable of operating at 1.4 dB from the capacity bound, which is about 1.56 times the corresponding discrepancy of the proposed IrVLC-aided scheme

Entanglement-assisted zero-error source-channel coding

We study the use of quantum entanglement in the zero-error source-channel coding problem. Here, Alice and Bob are connected by a noisy classical one-way channel, and are given correlated inputs from a random source. Their goal is for Bob to learn Alice's input while using the channel as little as possible. In the zero-error regime, the optimal rates of source codes and channel codes are given by graph parameters known as the Witsenhausen rate and Shannon capacity, respectively. The Lov\'asz theta number, a graph parameter defined by a semidefinite program, gives the best efficiently-computable upper bound on the Shannon capacity and it also upper bounds its entanglement-assisted counterpart. At the same time it was recently shown that the Shannon capacity can be increased if Alice and Bob may use entanglement. Here we partially extend these results to the source-coding problem and to the more general source-channel coding problem. We prove a lower bound on the rate of entanglement-assisted source-codes in terms Szegedy's number (a strengthening of the theta number). This result implies that the theta number lower bounds the entangled variant of the Witsenhausen rate. We also show that entanglement can allow for an unbounded improvement of the asymptotic rate of both classical source codes and classical source-channel codes. Our separation results use low-degree polynomials due to Barrington, Beigel and Rudich, Hadamard matrices due to Xia and Liu and a new application of remote state preparation.Comment: Title has been changed. Previous title was 'Zero-error source-channel coding with entanglement'. Corrected an error in Lemma 1.

Capacity Gain from Two-Transmitter and Two-Receiver Cooperation

Capacity improvement from transmitter and receiver cooperation is investigated in a two-transmitter, two-receiver network with phase fading and full channel state information available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal transmitter cooperation channel, then encoding jointly with dirty paper coding. The receivers cooperate by using Wyner-Ziv compress-and-forward over an analogous orthogonal receiver cooperation channel. To account for the cost of cooperation, the allocation of network power and bandwidth among the data and cooperation channels is studied. It is shown that transmitter cooperation outperforms receiver cooperation and improves capacity over non-cooperative transmission under most operating conditions when the cooperation channel is strong. However, a weak cooperation channel limits the transmitter cooperation rate; in this case receiver cooperation is more advantageous. Transmitter-and-receiver cooperation offers sizable additional capacity gain over transmitter-only cooperation at low SNR, whereas at high SNR transmitter cooperation alone captures most of the cooperative capacity improvement.Comment: Accepted for publication in IEEE Transactions on Information Theor