Abstract-During the last two decades, wireless communication has been revolutionized by near-capacity Error-Correcting Codes (ECCs), such as Turbo Codes (TCs), which offer a lower Bit Error Ratio (BER) than their predecessors, without requiring an increased transmission Energy Consumption (EC). Hence, TCs have found widespread employment in spectrum-constrained wireless communication applications, such as cellular telephony, Wireless Local Area Network (WLAN) and broadcast systems. Recently however, TCs have also been considered for energyconstrained wireless communication applications, such as Wireless Sensor Networks (WSNs) and the 'Internet of Things' (IoT). In these applications, TCs may also be employed for reducing the required transmission EC, instead of improving the BER. However, TCs have relatively high computational complexities and hence the associated signal-processing-related ECs are not insignificant. Therefore, when parameterizing TCs for employment in energy-constrained applications, both the processing EC and the transmission EC must be jointly considered. In this tutorial, we investigate holistic design methodologies conceived for this purpose. We commence by introducing turbo coding in detail, highlighting the various parameters of TCs and characterizing their impact on the encoded bit rate, on the Radio Frequency (RF) bandwidth requirement, on the transmission EC and on the BER. Following this, energy-efficient TC decoder ApplicationSpecific Integrated Circuit (ASIC) architecture designs are exemplified and the processing EC is characterized as a function of the TC parameters. Finally, the TC parameters are selected in order to minimize the sum of the processing EC and the transmission EC.
Abstract-Multimedia encoders typically generate symbols having a wide range of legitimate values. In practical mobile wireless scenarios, the transmission of these symbols is required to be bandwidth efficient and error resilient, motivating both source coding and channel coding. However, Separate Source and Channel Coding (SSCC) schemes are typically unable to exploit the residual redundancy in the source symbols, which cannot be totally reduced by finite-delay, finite-complexity schemes, hence resulting in a capacity loss. Until recently, none of the existing Joint Source and Channel Codes (JSCCs) were suitable for this application, since their decoding complexity increases rapidly with the size of the symbol alphabet. Motivated by this, we proposed a novel JSCC referred to as the Unary Error Correction (UEC) code, which is capable of exploiting all residual redundancy and eliminating any capacity loss, while imposing only a moderate decoding complexity. In this paper, we show that the operation of the UEC decoder can be dynamically adapted, in order to strike an attractive trade-off between its decoding complexity and its error correction capability. Furthermore, we conceive the corresponding Three Dimensional (3D) EXtrinsic Information Transfer (EXIT) charts for controlling this dynamic adaptation, as well as the decoder activation order, when the UEC code is serially concatenated with a turbo code. In this way, we expedite the iterative decoding convergence, facilitating a gain of up to 1.2 dB compared to both SSCC and to its non-adaptive UEC benchmarkers, while maintaining the same transmission bandwidth, duration, energy and decoding complexity.
In order to meet the latency requirements of the Ultra-Reliable Low Latency Communication (URLLC) mode of the 3GPP Long Term Evolution (LTE) mobile communication standard, this paper proposes a novel turbo decoding algorithm that supports an arbitrarily-high degree of parallel processing, facilitating significantly higher processing throughputs and substantially lower processing latencies than the state-of-the-art (SOTA) LTE turbo decoder. As in conventional turbo decoding algorithms, the proposed Arbitrarily Parallel Turbo Decoder (APTD) decomposes each frame of information bits into a sequence of windows, where the bits within different windows are processed simultaneously using forward and backward recursions in a serial manner. However, in contrast to conventional turbo decoding algorithms, the APTD does not require the different windows to be composed of an identical number of bits, which allows the use of an arbitrary number of windows and hence an arbitrary degree of parallelism, when decoding information bits of an arbitrary frame length. Furthermore, conventional turbo decoding algorithms alternate between simultaneously processing the windows in the upper decoder and those in the lower decoder. By contrast, the APTD processes the odd-indexed windows in the upper decoder at the same time as the even-indexed windows in the lower decoder and alternates between this and the reversed arrangement, hence further improving the decoding throughput and latency. Furthermore, the APTD achieves a reduced hardware resource requirement by calculating the extrinsic information based only on the outputs of the forward recursions, rather than based on both the forward and backward recursions of conventional turbo decoding algorithms. We demonstrate that the proposed APTD achieves superior latency, throughput and computational efficiency than the SOTA LTE turbo decoder at all frame lengths, but particularly at the short frame lengths that are typically used in URLLC approaches. For example, at a frame length of N = 504 bits, the proposed APTD achieves an FER of 10 −5 at the same E b /N0 as I = 8 iterations of a conventional turbo decoder, but with a computational efficiency that is 6 times higher than that of the SOTA turbo decoder, while achieving a latency and throughput that are 0.7 and 1.4 times those of the SOTA decoder, respectively.
Unary error correction (UEC) codes have recently been proposed for the joint source and channel coding of symbol values that are selected from a set having an infinite cardinality. However, the original UEC scheme requires the knowledge of the source probability distribution, in order to achieve nearcapacity operation. This limits the applicability of the UEC scheme, since the source probability distribution is typically non-stationary and is unknown in practice. In this paper, we propose a dynamic version of the UEC scheme, which can learn the unknown source statistics and gradually improve its decoding performance during a transient phase, then dynamically adapt to the non-stationary statistics and maintain reliable nearcapacity operation during a steady-state phase, at the cost of only a moderate memory requirement at the decoder. Based on the same learning technique, we also propose two separate source and channel coding benchmarkers, namely, a learning-aided Elias gamma-convolutional code (CC) scheme and a learningaided arithmetic-CC scheme. The simulation results reveal that our proposed learning-aided UEC scheme outperforms the benchmarkers by up to 0.85 dB, without requiring any additional decoding complexity or any additional transmission-energy, -bandwidth, or -duration.
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