In a classical wiretap channel setting, Alice communicates with Bob through a main communication channel, while her transmission also reaches an eavesdropper Eve through a wiretap channel. In this paper, we consider a general class of polar secrecy codes for wiretap channels and study their finite-length performance. In particular, bounds on the normalized mutual information security (MIS) leakage, a fundamental measure of secrecy in information-theoretic security frameworks, are presented for polar secrecy codes. The bounds are utilized to characterize the finite-length scaling behavior of polar secrecy codes, where scaling here refers to the non-asymptotic behavior of both the gap to the secrecy capacity as well as the MIS leakage. Furthermore, the bounds are shown to facilitate characterizing numerical bounds on the secrecy guarantees of polar secrecy codes in finite block lengths of practical relevance, where directly calculating the MIS leakage is in general infeasible.

Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding has become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT). To this end, schemes based on concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards. In this paper, we propose a novel mechanism for concatenating outer polar codes with inner repetition codes which we refer to as polar coded repetition. More specifically, we propose to transmit a slightly modified polar codeword by deviating from Arıkan’s standard$2 \times 2$Kernel in a certain number of polarization recursions at each repetition block. We show how this modification can improve the asymptotic achievable rate of the standard polar-repetition scheme, while ensuring that the overall encoding and decoding complexity is kept almost the same. The achievable rate is analyzed for the binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel. Moreover, we show that the finite-length performance of the polar coded repetition scheme under cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over AWGN channel is better than the uncoded polar-repetition scheme at the cost of a slight increase in decoding complexity. We also compare the proposed scheme, in terms of performance and complexity, with other low-rate solution based on polar codes in the literature.

Concatenating the state-of-the-art codes at moderate rates with repetition codes has emerged as a practical solution deployed in various standards for ultra-low-power devices such as in Internet-of-Things (IoT) networks. In this paper, we propose a novel concatenation mechanism for such applications which need to operate at very low signal-to-noise ratio (SNR) regime. In the proposed scheme, the outer code is a hybrid polar code constructed in two stages, one with a binary kernel and another also with a binary kernel but applied over a binary extension field. The inner code is a non-binary multiplicative repetition code. This particular structure inherits low-complexity decoding structures of polar codes while enabling concatenation with an inner non-binary multiplicative repetition scheme. The decoding for the proposed scheme is done using cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Simulation results demonstrate that the proposed hybrid non-binary repeated polar code provides performance gain compared to a polar-repetition scheme with comparable decoding complexity.

Concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards for ultra-low-power devices such as in Internet-of-Things (IoT) networks. In this paper, we propose a novel concatenation mechanism for such applications which need to operate at very low signal-to-noise ratio (SNR) regime. In the proposed scheme, the outer code is a hybrid polar code constructed in two stages, one with a binary kernel and another also with a binary kernel but applied over a binary extension field. The inner code is a non-binary multiplicative repetition code. This particular structure inherits low-complexity decoding structures of polar codes while enabling concatenation with an inner non-binary multiplicative repetition scheme. The decoding for the proposed scheme is done using cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over AWGN channel. Simulation results show that the proposed scheme outperforms the straightforward binary polar-repetition scheme at the cost of a negligible increase in the decoding complexity.

Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end, schemes based on concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards. In this paper, we propose a novel mechanism for concatenating outer polar codes with inner repetition codes which we refer to as polar coded repetition. More specifically, we propose to transmit a slightly modified polar codeword by deviating from Arıkan's standard 2 × 2 Kernel in a certain number of polarization recursions at each repetition block. We show how this modification can improve the asymptotic achievable rate of the polar-repetition scheme, while ensuring that the overall encoding and decoding complexity is kept almost the same. The achievable rate is analyzed for the binary erasure channels (BEC).

In this paper, we consider networks where every edge is a compound Binary Symmetric Channel whose transition probability is determined by a global network state. We first examine the setting where the sum of the transition probabilities for all edges satisfies an overall global upper bound. For networks with exactly one source and one sink we show that capacity is given by the smallest min-cut among all permitted networks states. We show that routing along with end-to-end error correction is optimal for such networks. Next, we consider networks with one source and multiple sinks with multicast demands. We give upper and lower bounds on the capacity of such networks. The coding strategy that leads to our lower bound is intriguing - it involves both end-to-end error correction across the network as well as link-by-link error correction. Finally, we give a lower bound on the capacity of networks where the transition probabilities can take any arbitrary value from a known state-space.

In this paper, we study transmission of a memoryless Laplacian source over three types of channels: additive white Laplacian noise (AWLN), additive white Gaussian noise (AWGN), and slow flat-fading Rayleigh channels under both bandwidth compression and bandwidth expansion. For this purpose, we analyze two well-known hybrid digital-analog (HDA) joint source-channel coding schemes for bandwidth compression and one for bandwidth expansion. Then we obtain achievable (absolute-error) distortion regions of the HDA schemes for the matched signal-to-noise ratio (SNR) case as well as the mismatched SNR scenario. Using numerical examples, it is shown that these schemes can achieve a distortion very close to the provided lower bound (for the AWLN channel) and to the optimum performance theoretically attainable bound (for AWGN and Rayleigh fading channels) on mean-absolute error distortion under matched SNR conditions. In addition, a non-linear analog coding scheme is analyzed, and its performance is compared to the HDA schemes for bandwidth compression under both matched and mismatched SNR scenarios. The results show that the HDA schemes outperform the non-linear analog coding over the whole CSNR region.