Optimal Decoding Performance Research Articles

Neural-Network-Assisted Polar Code Decoding Schemes

The traditional fast successive-cancellation (SC) decoding algorithm can effectively reduce the decoding steps, but the decoding adopts a sub-optimal algorithm, so it cannot improve the bit error performance. In order to improve the bit error performance while maintaining low decoding steps, we introduce a neural network subcode that can achieve optimal decoding performance and combine it with the traditional fast SC decoding algorithm. While exploring how to combine neural network node (NNN) with R1, R0, single-parity checks (SPC), and Rep, we find that the decoding failed sometimes when the NNN was not the last subcode. To solve the problem, we propose two neural network-assisted decoding schemes: a key-bit-based subcode NN-assisted decoding (KSNNAD) scheme and a last subcode NN-assisted decoding (LSNNAD) scheme. The LSNNAD scheme recognizes the last subcode as an NNN, and the NNN with nearly optimal decoding performance gives rise to some performance improvements. To further improve performance, the KSNNAD scheme recognizes the subcode with a key bit as an NNN and changes the training data and label accordingly. Computer simulation results confirm that the two schemes can effectively reduce the decoding steps, and their bit error rates (BERs) are lower than those of the successive-cancellation decoder (SCD).

Quadrature Spatial Modulation With the Fourth Order Transmit Diversity and Low-Complexity Sphere Decoding for Large-Scale MIMO Systems

A quadrature spatial modulation with the fourth order transmit diversity (FO-QSM) scheme is presented in this paper. In this scheme, two dispersion-matrix (DM) sets are assigned at the transmitter, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> DMs are activated in each set to extend the real and imaginary parts of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> QSM signals respectively, to large number of transmit antennas. The two DM sets are constructed by performing Kronecker product between two simple extension matrices and the DMs of Sezginer-Sari-Biglieri (SSB) code. The framework designs of FO-QSM and the two DM sets make FO-QSM possess the properties: 1) it guarantees the fourth order transmit diversity without requiring any parameter optimization; 2) it has higher spectral efficiency than the newly proposed generalized space-time block coded spatial modulation (GSTBC-SM) scheme. Furthermore, a repeated computation reduced sphere decoding (RCR-SD) is proposed. RCR-SD is very suitable for the schemes constructed by a large number of DMs, including FO-QSM. By sorting the index vectors, the RCR-SD detector can efficiently reduce the repeated computations in the SD searching, which significantly reduces the decoding complexity without sacrificing optimal decoding performance. Simulation results show that FO-QSM has obvious better bit error rate (BER) performance than GSTBC-SM.

Low‐complexity multiple‐signal joint decoding for overlapped x domain multiplexing signalling

By multiplexing waveform mapped with shifting and weighted symbols, overlapped x domain multiplexing (OVXDM) encoding scheme can obtain high spectral efficiency under a low signal-to-noise ratio. Though the maximum likelihood sequence detection decoders can obtain the optimal decoding performance, their computational complexities which increase exponentially with spectral efficiency in OVXDM are unbearable for practical implementations. In this study, a low-complexity multiple-signal joint decoding (MSJD) algorithm for OVXDM signalling is proposed over additive white Gaussian noise (AWGN) channel and extended to frequency selective fading (FSF) channel. Based on a novel joint information-based metric, the proposed algorithm utilises information of each transmitted symbol contained in multiple received signals, and selects the proper number of received signals for decoding to achieve performance maximisation. Moreover, theoretical analysis is provided for the proposed algorithm in both AWGN and FSF channels, which indicates the relationship between performance and number of received signals under different OVXDM encoding parameters including multiplexing waveform and overlapping fold. Simulation results confirm the superior performance of the MSJD algorithm in terms of decoding performance and computational complexity compared with the present approaches.

Unsupervised Learning for Brain-Computer Interfaces Based on Event-Related Potentials: Review and Online Comparison [Research Frontier

One of the fundamental challenges in brain-computer interfaces (BCIs) is to tune a brain signal decoder to reliably detect a user's intention. While information about the decoder can partially be transferred between subjects or sessions, optimal decoding performance can only be reached with novel data from the current session. Thus, it is preferable to learn from unlabeled data gained from the actual usage of the BCI application instead of conducting a calibration recording prior to BCI usage. We review such unsupervised machine learning methods for BCIs based on event-related potentials of the electroencephalogram. We present results of an online study with twelve healthy participants controlling a visual speller. Online performance is reported for three completely unsupervised learning methods: (1) learning from label proportions, (2) an expectation-maximization approach and (3) MIX, which combines the strengths of the two other methods. After a short ramp-up, we observed that the MIX method not only defeats its two unsupervised competitors but even performs on par with a state-of-the-art regularized linear discriminant analysis trained on the same number of data points and with full label access. With this online study, we deliver the best possible proof in BCI that an unsupervised decoding method can in practice render a supervised method unnecessary. This is possible despite skipping the calibration, without losing much performance and with the prospect of continuous improvement over a session. Thus, our findings pave the way for a transition from supervised to unsupervised learning methods in BCIs based on eventrelated potentials.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

A low-memory intensive decoding architecture for double-binary convolutional turbo code

Memory accesses take a large part of the power consumption in the iterative decoding of double-binary convolutional turbo code (DB-CTC). To deal with this, a low-memory intensive decoding architecture is proposed for DB-CTC in this paper. The new scheme is based on an improved maximum a posteriori probability algorithm, where instead of storing all of the state metrics, only a part of these state metrics is stored in the state metrics cache (SMC), and the memory size of the SMC is thus reduced by 25%. Owing to a compare-select--recalculate processing (CSRP) module in the proposed decoding architecture, the unstored state metrics are recalculated by simple operations, while maintaining near optimal decoding performance.

Sphere Decoding Complexity Exponent for Decoding Full-Rate Codes Over the Quasi-Static MIMO Channel

In the setting of quasi-static multiple-input multiple-output channels, we consider the high signal-to-noise ratio (SNR) asymptotic complexity required by the sphere decoding (SD) algorithm for decoding a large class of full-rate linear space-time codes. With SD complexity having random fluctuations induced by the random channel, noise, and codeword realizations, the introduced SD complexity exponent manages to concisely describe the computational reserves required by the SD algorithm to achieve arbitrarily close to optimal decoding performance. Bounds and exact expressions for the SD complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics. For the particular example of decoding the recently introduced threaded cyclic-division-algebra-based codes—the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff—the SD complexity exponent is shown to take a particularly concise form as a non-monotonic function of the multiplexing gain. To date, the SD complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood performance that vanishes in the high SNR limit.

Programmable processor implementations of [formula omitted]-best list sphere detector for MIMO receiver

An increasing number of standards in wireless communications have encouraged to study programmable processors as platforms for flexible receivers. A multiple-input multiple-output (MIMO) antenna system combined with orthogonal frequency division multiplexing (OFDM) technique has been introduced in many wireless communications standards, such as in the third generation long term evolution (3G LTE). The MIMO-OFDM system requires an efficient detector and a platform support for parallel processing of multiple subcarriers. A K -best list sphere detector (LSD) provides for near optimal decoding performance and a fixed throughput making it an interesting algorithm from the point of view of practical implementations. In this paper, we compare the implementations of the K -best LSD on four processor platforms: a digital signal processor (DSP), software defined radio (SDR), application-specific processor (ASP) and application-specific instruction-set processor (ASIP). The DSP is a popular very long instruction word (VLIW) device (TMS320C6455), the SDR processor employs multithreading and multiple cores (SB3500 core processor), the ASP is based on transport triggered architecture (TTA), while the ASIP is the SDR processor enhanced with a special instruction-set extension for sorting. A 2 × 2 MIMO antenna system with 64-quadrature amplitude modulation (64-QAM) is assumed. The chosen list sizes K = 8 and 16 are based on simulation results carried out in MATLAB environment with the third generation long term evolution (3G LTE) parameters. The proposed ASIP achieved a promising throughput of 32.0 Mbps, where the software defined radio (SDR) implementation on the SB3500 core processor suffers from an inefficient software sorter. The ASP, in which the minimized hardware complexity has been the goal, achieves a throughput of 7.6 Mbps. However, more essential examination is related to the symbol time, which sets strict parallel processing requirements to the programmable processors.

An efficient symbol-level combining scheme for MIMO systems with hybrid ARQ

This paper proposes a new combining scheme for multiple-input multiple-output (MIMO) systems with hybrid automatic-repeat-request (HARQ). The proposed combining scheme is proved to have the optimal decoding performance. Furthermore, the proposed combining scheme is shown to have low memory requirement and reduced complexity compared to other optimal combining schemes. Simulation results under IEEE 802.16e setting with UMTS channel models verify that the proposed combining scheme achieves the optimal decoding performance and performs much better than other suboptimal combining schemes.

Computation of posterior marginals on aggregated state models for soft source decoding

Optimum soft decoding of sources compressed with variable length codes and quasi-arithmetic codes, transmitted over noisy channels, can be performed on a bit/symbol trellis. However, the number of states of the trellis is a quadratic function of the sequence length leading to a decoding complexity which is not tractable for practical applications. The decoding complexity can be significantly reduced by using an aggregated state model, while still achieving close to optimum performance in terms of bit error rate and frame error rate. However, symbol a posteriori probabilities can not be directly derived on these models and the symbol error rate (SER) may not be minimized. This paper describes a two-step decoding algorithm that achieves close to optimal decoding performance in terms of SER on aggregated state models. A performance and complexity analysis of the proposed algorithm is given.