Many memory cell technologies are being considered as possible replacements for DRAM and Flash technologies, both of which are nearing their scaling limits. While these new cells (PCM, STT-RAM, FeRAM, etc.) promise high density, better scaling, and non-volatility, they introduce new challenges. Solutions at the architecture level can help address some of these problems; e.g., prior research has proposed wear-leveling and hard error tolerance mechanisms to overcome the limited write endurance of PCM cells. In this paper, we focus on the soft error problem in PCM, a topic that has received little attention in the architecture community. Soft errors in DRAM memories are typically addressed by having SECDED support and a scrub mechanism. The scrub mechanism scans the memory looking for a single-bit error and corrects it before the line experiences a second uncorrectable error. However, PCM (and other emerging memories) are prone to new sources of soft errors. In particular, multi-level cell (MLC) PCM devices will suffer from resistance drift, that increases the soft error rate and incurs high overheads for the scrub mechanism. This paper is the first to study the design of architectural scrub mechanisms, especially when tailored to the drift phenomenon in MLC PCM. Many of our solutions will also apply to other soft-error prone emerging memories. We first show that scrub overheads can be reduced with support for strong ECC codes and a lightweight error detection operation. We then design different scrub algorithms that can adaptively trade-off soft and hard errors. Using an approach that combines all proposed solutions, our scrub mechanism yields a 96.5% reduction in uncorrectable errors, a 24.4 × decrease in scrub-related writes, and a 37.8% reduction in scrub energy, relative to a basic scrub algorithm used in modern DRAM systems.

Efficient scrub mechanisms for error-prone emerging memories

Polar codes have emerged as important channel codes because of their capacity-achieving property. For low-complexity polar decoding, hardware architectures for successive cancellation (SC) algorithm have been investigated in prior works. However, belief propagation (BP)-based architectures have not been explored in detail. This paper begins with a review of min-sum (MS) approximated BP algorithm, and then proposes a scaled MS (SMS) algorithm with improved decoding performance. Then, in order to solve long critical path problem in the SMS algorithm, we propose an efficient critical path reduction approach. Due to its generality, this optimization method can be applied to both of SMS and MS algorithms. Compared with the state-of-the-art MS decoder, the proposed (1024, 512) SMS design can lead to 0.5dB extra decoding gain with the same hardware performance. Besides, the proposed optimized MS architecture can also achieve more than 30% and 80% increase in throughput and hardware efficiency, respectively.

Architecture optimizations for BP polar decoders

In this paper, we present an improvement and a new implementation of a simplified decoding algorithm for non-binary low density parity-check codes (NB-LDPC) in Galois fields GF(q). The base algorithm that we use is the Extended Min-Sum (EMS) algorithm, which has been widely studied in the recent literature, and has been shown to approach the performance of the belief propagation (BP) algorithm, with limited complexity. In our work, we propose a new way to compute modified configuration sets, using a trellis representation of incoming messages to check nodes. We call our modification of the EMS algorithm trellis-EMS (T-EMS). In the T-EMS, the algorithm operates directly on the deviation space by considering a trellis built from differential messages, which serves as a new reliability measure to sort the configurations. We show that this new trellis representation reduces the computational complexity, without any performance degradation. In addition, we show that our modifications of the algorithm allows to greatly reduce the decoding latency, by using a larger degree of hardware parallelization.

Trellis-Based Extended Min-Sum Algorithm for Non-Binary LDPC Codes and its Hardware Structure

Polar codes have become one of the most favorable capacity achieving error correction codes (ECC) along with their simple encoding method. However, among the very few prior successive cancellation (SC) polar decoder designs, the required long code length makes the decoding latency high. In this paper, conventional decoding algorithm is transformed with look-ahead techniques. This reduces the decoding latency by 50%. With pipelining and parallel processing schemes, a parallel SC polar decoder is proposed. Sub-structure sharing approach is employed to design the merged processing element (PE). Moreover, inspired by the real FFT architecture, this paper presents a novel input generating circuit (ICG) block that can generate additional input signals for merged PEs on-the-fly. Gate-level analysis has demonstrated that the proposed design shows advantages of 50% decoding latency and twice throughput over the conventional one with similar hardware cost.

Reduced-latency SC polar decoder architectures

Automatic repeat request (ARQ) schemes, and in particular hybrid-ARQ (HARQ) schemes, which jointly adopt forward error correction (FEC) and ARQ, are essential to provide reliable data transmission in wireless communications systems. However, the feedback from the receiver to the transmitter and the retransmission process used in ARQ incurs significant cost in terms of power efficiency, throughput, computational power and delay. Unfortunately, such drawbacks can limit their applications to several current and emerging technologies. More specifically, the increasing number of wireless users has create spectrum scarcity, relying on small-size batteries create power constraints, deployment of real-time applications boost the demand for ultra-low delay networks, and the ultra-small low-cost Internet of Things (IoT) devices has limited signal processing and computation capabilities. Consequently, extensive research efforts have been dedicated to overcome the limitations inherent in HARQ. This survey paper provides an extensive literature review of the state-of-the-art HARQ techniques and discusses their integration in various wireless technologies. Moreover, it provides insights on advantages and disadvantages of particular ARQ types and discusses open problems and future directions.

Hybrid Automatic Repeat Request (HARQ) in Wireless Communications Systems and Standards: A Contemporary Survey

Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. The high complexity is mainly caused by the complicated computations in the check node processing and the large memory requirement. In this paper, a novel check node processing scheme and corresponding VLSI architectures are proposed for the Min-max NB-LDPC decoding algorithm. The proposed scheme first sorts out a limited number of the most reliable variable-to-check (v-to-c) messages, then the check-to-variable (c-to-v) messages to all connected variable nodes are derived independently from the sorted messages without noticeable performance loss. Compared to the previous iterative forward-backward check node processing, the proposed scheme not only significantly reduced the computation complexity, but eliminated the memory required for storing the intermediate messages generated from the forward and backward processes. Inspired by this novel c-to-v message computation method, we propose to store the most reliable v-to-c messages as “compressed” c-to-v messages. The c-to-v messages will be recovered from the compressed format when needed. Accordingly, the memory requirement of the overall decoder can be substantially reduced. Compared to the previous Min-max decoder architecture, the proposed design for a (837, 726) code over GF(25) can achieve the same throughput with only 46% of the area.

Reduced-Complexity Decoder Architecture for Non-Binary LDPC Codes

Nonbinary low-density parity-check (NB-LDPC) codes constructed over GF(q) (q >; 2) can achieve higher coding gain than binary LDPC codes when the code length is moderate. A complete partial-parallel decoder architecture based on the Min-max algorithm is proposed for quasi-cyclic NB-LDPC codes in this paper. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm <; q messages are kept on each edge of the associated Tanner graph. The computation units and the scheduling of the computations are optimized in the context of layered decoding to reduce the area requirement and increase the speed. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity and latency analysis, our design is much more efficient than any previous design. Our proposed decoder for a (744, 653) code over GF(25) has also been synthesized on a Xilinx Virtex-2 Pro FPGA device. It can achieve a throughput of 9.30 Mbps when 15 decoding iterations are carried out.

Efficient Partial-Parallel Decoder Architecture for Quasi-Cyclic Nonbinary LDPC Codes

Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts at the cost of higher decoding complexity when the codeword length is moderate. The recently developed iterative reliability-based majority-logic NB-LDPC decoding has better performance-complexity tradeoffs than previous algorithms. This paper first proposes enhancement schemes to the iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Compared to the IHRB algorithm, our enhanced (E-)IHRB algorithm can achieve significant coding gain with small hardware overhead. Then low-complexity partial-parallel NB-LDPC decoder architectures are developed based on these two algorithms. Many existing NB-LDPC code construction methods lead to quasi-cyclic or cyclic codes. Both types of codes are considered in our design. Moreover, novel schemes are developed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. In addition, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous designs based on the Min-max decoding algorithm, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.

Low-Complexity Reliability-Based Message-Passing Decoder Architectures for Non-Binary LDPC Codes

Compared to binary low-density parity-check (LDPC) codes, nonbinary (NB) LDPC codes can achieve higher coding gain when the codeword length is moderate, but at the cost of higher decoding complexity. One major bottleneck of NB-LDPC decoding is the complicated check node processing. In this paper, a novel relaxed check node processing scheme is proposed for the min-max NB-LDPC decoding algorithm. Each finite field element of GF(2p) can be uniquely represented by a linear combination of p independent field elements. Making use of this property, an innovative method is developed in this paper to first find a set of the p most reliable variable-to-check messages with independent field elements, called the minimum basis. Then, the check-to-variable messages are efficiently computed from the minimum basis. With very small performance loss, the complexity of the check node processing can be substantially reduced using the proposed scheme. In addition, efficient VLSI architectures are developed to implement the proposed check node processing and the overall NB-LDPC decoder. Compared to the most efficient prior design, the proposed decoder for a (837, 726) NB-LDPC code over GF(25) can achieve 52% higher efficiency in terms of throughput-over-area ratio.

Relaxed Min-Max Decoder Architectures for Nonbinary Low-Density Parity-Check Codes

Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate. For the first time, this paper proposes a partial-parallel decoder architecture based on the Min-max algorithm for quasi-cyclic NB-LDPC codes. A novel boundary tracking based scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In addition, layered decoding is applied, and the hardware units are optimized to reduce the latency and area. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity analysis, the proposed decoder with 5 iterations for a (837,726) code over GF(25) can easily achieve 60 Mbps throughput on ASIC devices. It is 40% more efficient than prior designs.

Partial-parallel decoder architecture for quasi-cyclic non-binary LDPC codes

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