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Polar codes are of great interests because they provably achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes while having an explicit construction. Most existing decoding algorithms of polar codes are based on bit-wise hard or soft decisions. In this paper, we propose symbol-decision successive cancellation (SC) and successive cancellation list (SCL) decoders for polar codes, which use symbol-wise hard or soft decisions for higher throughput or better error performance. First, we propose to use a recursive channel combination to calculate symbol-wise channel transition probabilities, which lead to symbol decisions. Our proposed recursive channel combination has lower complexity than simply combining bit-wise channel transition probabilities. The similarity between our proposed method and Arıkan's channel transformations also helps to share hardware resources between calculating bit- and symbol-wise channel transition probabilities. Second, a two-stage list pruning network is proposed to provide a trade-off between the error performance and the complexity of the symbol-decision SCL decoder. Third, since memory is a significant part of SCL decoders, we propose a pre-computation memory-saving technique to reduce memory requirement of an SCL decoder. Finally, to evaluate the throughput advantage of our symbol-decision decoders, we design an architecture based on a semi-parallel successive cancellation list decoder. In this architecture, different symbol sizes, sorting implementations, and message scheduling schemes are considered. Our synthesis results show that in terms of area efficiency, our symbol-decision SCL decoders outperform existing bit-decision and multi-bit SCL decoders. [ABSTRACT FROM PUBLISHER]

Polar codes have recently received a lot of attention because of their capacity-achieving performance and low encoding and decoding complexity. The performance of the successive cancellation decoder (SCD) of the polar codes highly depends on that of the partial-sum network (PSN) implementation. Hence, in this work, an efficient PSN architecture is proposed, based on the properties of polar codes. First, a new partial-sum updating algorithm and the corresponding PSN architecture are introduced which achieve a delay performance independent of the code length. Moreover, the area complexity is also reduced. Second, for a high-performance and area-efficient semi-parallel SCD implementation, a folded PSN architecture is presented to integrate seamlessly with the folded processing element architecture. This is achieved by using a novel folded decoding schedule. As a result, both the critical path delay and the area (excluding the memory for folding) of the semi-parallel SCD are approximately constant for a large range of code lengths. The proposed designs are implemented in both FPGA and ASIC and compared with the existing designs. Experimental result shows that for polar codes with large code length, the decoding throughput is improved by more than 1.05 times and the area is reduced by as much as 50.4%, compared with the state-of-the-art designs. [ABSTRACT FROM PUBLISHER]

In this paper, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending independent information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its throughput. The proposed scheme, called generalized dynamic-network codes (GDNC), is a generalization of the dynamic-network codes (DNC) recently proposed by Xiao and Skoglund. The design of the network codes that maximize the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. We prove that adopting a systematic generator matrix of a maximum distance separable block code over a sufficiently large finite field as the network transfer matrix is a sufficient condition for full diversity order under link failure model. The proposed generalization offers a much better tradeoff between rate and diversity order compared to the DNC. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results. [ABSTRACT FROM PUBLISHER]