Network coded modulation for two-way relaying

Network coding compresses multiple traffic flows with the aid low-complexity algebraic operations, hence holds the potential of significantly improving both the power and bandwidth efficiency of wireless networks. In this contribution, the novel concept of Network Coded Modulation (NCM) is proposed for jointly performing network coding and modulation in bi-directional/duplex relaying. Each receiver is colocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. As in classic coded modulation, the Euclidian distance between the symbols is maximized, hence the Symbol Error Ratio (SER) is minimized. Specifically, we conceive NCM methods for PSK, PAM and QAM based on modulo addition of the normalized phase or amplitude. Furthermore, we propose low complexity decoding algorithms based on the corresponding conditional minimum distance criteria. Our performance analysis and simulations demonstrate that NCM relying on PSK is capable of achieving a SER at both receivers of the NCM scheme as if the relay transmitted exclusively to a single receiver only. By contrast, when our NCM concept is combined with PAM/QAM, an SNR loss (<1.25dB) is imposed at one of the receivers, usually at the one having a lower data rate in a realistic different rate scenario. Finally, we will demonstrate that the proposed NCM is compatible with existing physical layer designs

Cross-Sender Bit-Mixing Coding

Scheduling to avoid packet collisions is a long-standing challenge in networking, and has become even trickier in wireless networks with multiple senders and multiple receivers. In fact, researchers have proved that even {\em perfect} scheduling can only achieve $\mathbf{R} = O(\frac{1}{\ln N})$. Here $N$ is the number of nodes in the network, and $\mathbf{R}$ is the {\em medium utilization rate}. Ideally, one would hope to achieve $\mathbf{R} = \Theta(1)$, while avoiding all the complexities in scheduling. To this end, this paper proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely on scheduling. Instead, users transmit simultaneously on suitably-chosen slots, and the amount of overlap in different user's slots is controlled via coding. We prove that in all possible network topologies, using BMC enables us to achieve $\mathbf{R}=\Theta(1)$. We also prove that the space and time complexities of BMC encoding/decoding are all low-order polynomials.Comment: Published in the International Conference on Information Processing in Sensor Networks (IPSN), 201

A New Class of Multiple-rate Codes Based on Block Markov Superposition Transmission

Hadamard transform~(HT) as over the binary field provides a natural way to implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the code length $N=2^p$ is fixed but the code dimension $K$ can be varied from $1$ to $N-1$ by adjusting the set of frozen bits. The HT-coset codes, including Reed-Muller~(RM) codes and polar codes as typical examples, can share a pair of encoder and decoder with implementation complexity of order $O(N \log N)$. However, to guarantee that all codes with designated rates perform well, HT-coset coding usually requires a sufficiently large code length, which in turn causes difficulties in the determination of which bits are better for being frozen. In this paper, we propose to transmit short HT-coset codes in the so-called block Markov superposition transmission~(BMST) manner. At the transmitter, signals are spatially coupled via superposition, resulting in long codes. At the receiver, these coupled signals are recovered by a sliding-window iterative soft successive cancellation decoding algorithm. Most importantly, the performance around or below the bit-error-rate~(BER) of $10^{-5}$ can be predicted by a simple genie-aided lower bound. Both these bounds and simulation results show that the BMST of short HT-coset codes performs well~(within one dB away from the corresponding Shannon limits) in a wide range of code rates

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Throughput-based Design for Polar Coded-Modulation

Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive modulation and coding, the throughput is a more important performance metric than the error rate. Polar codes, a new class of FEC codes with simple rate matching, can be optimized efficiently for maximization of the throughput. In this paper, we aim to design HARQ schemes using multilevel polar coded-modulation (MLPCM). Thus, we first develop a method to determine a set-partitioning based bit-to-symbol mapping for high order QAM constellations. We simplify the LLR estimation of set-partitioned QAM constellations for a multistage decoder, and we introduce a set of algorithms to design throughput-maximizing MLPCM for the successive cancellation decoding (SCD). These codes are specifically useful for non-combining (NC) and Chase-combining (CC) HARQ protocols. Furthermore, since optimized codes for SCD are not optimal for SC list decoders (SCLD), we propose a rate matching algorithm to find the best rate for SCLD while using the polar codes optimized for SCD. The resulting codes provide throughput close to the capacity with low decoding complexity when used with NC or CC HARQ

Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe

Performance Analysis and Enhancement of Multiband OFDM for UWB Communications

In this paper, we analyze the frequency-hopping orthogonal frequency-division multiplexing (OFDM) system known as Multiband OFDM for high-rate wireless personal area networks (WPANs) based on ultra-wideband (UWB) transmission. Besides considering the standard, we also propose and study system performance enhancements through the application of Turbo and Repeat-Accumulate (RA) codes, as well as OFDM bit-loading. Our methodology consists of (a) a study of the channel model developed under IEEE 802.15 for UWB from a frequency-domain perspective suited for OFDM transmission, (b) development and quantification of appropriate information-theoretic performance measures, (c) comparison of these measures with simulation results for the Multiband OFDM standard proposal as well as our proposed extensions, and (d) the consideration of the influence of practical, imperfect channel estimation on the performance. We find that the current Multiband OFDM standard sufficiently exploits the frequency selectivity of the UWB channel, and that the system performs in the vicinity of the channel cutoff rate. Turbo codes and a reduced-complexity clustered bit-loading algorithm improve the system power efficiency by over 6 dB at a data rate of 480 Mbps.Comment: 32 pages, 10 figures, 1 table. Submitted to the IEEE Transactions on Wireless Communications (Sep. 28, 2005). Minor revisions based on reviewers' comments (June 23, 2006

Improved Decoding of Staircase Codes: The Soft-aided Bit-marking (SABM) Algorithm

Staircase codes (SCCs) are typically decoded using iterative bounded-distance decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is proposed, which partially uses soft information from the channel. The proposed algorithm is based on marking certain number of highly reliable and highly unreliable bits. These marked bits are used to improve the miscorrection-detection capability of the SCC decoder and the error-correcting capability of BDD. For SCCs with $2$-error-correcting Bose-Chaudhuri-Hocquenghem component codes, our algorithm improves upon standard SCC decoding by up to $0.30$~dB at a bit-error rate (BER) of $10^{-7}$. The proposed algorithm is shown to achieve almost half of the gain achievable by an idealized decoder with this structure. A complexity analysis based on the number of additional calls to the component BDD decoder shows that the relative complexity increase is only around $4\%$ at a BER of $10^{-4}$. This additional complexity is shown to decrease as the channel quality improves. Our algorithm is also extended (with minor modifications) to product codes. The simulation results show that in this case, the algorithm offers gains of up to $0.44$~dB at a BER of $10^{-8}$.Comment: 10 pages, 12 figure