Design and characterization of an error-correcting code for the SONET STS-1 tributary

Error control coding improves reliability and efficiency of wireless communication systems. This research delves into the latest advancements in error control coding schemes for wireless communication systems, with a specific focus on their application within the domain of Low Power Wide Area Networks (LPWANs) such as Narrowband Internet of Things (NB-IoT) systems, LoRa energy-efficient hardware design, random access control systems, and wireless sensor networks. In the context of LPWANs, particularly NB-IoT systems, we investigate the adaptive coding and modulation (ACM) in NB-IoT systems, which adapts coding rates and modulation techniques to changing channel circumstances. Comprehensive analysis of the literature review shows that the proposed approaches are more energy efficient and less error-prone than fixed coding and modulation schemes. Using Cell Design Methodology (CDM), Single Error Correction (SEC) codes are optimized for energy efficiency. Power and energy efficiency have improved in standard CMOS and CDM logic systems. This impacts IoT devices, memory storage, and security systems. Next, Forward Error Correction (FEC) is examined for ALOHA-based random-access control systems wherein packet loss rate and spectral efficiency metrics are mathematically calculated. FEC is beneficial, especially when time and frequency synchronization diverge. Monte Carlo simulations studied in the literature shows that FEC improves satellite communication systems. This review establishes benefits of FEC, notably in satellite communications systems. In addition, Wireless Sensor Networks (WSNs) error control techniques and network reliability and performance are examined along with Convolutional, Turbo, Low density parity check codes(LDPC), and Polar error correction coding (ECC) methods. We learn about their benefits, drawbacks, and implementation challenges by assessing their efficacy, efficiency, and applicability in wireless sensor networks (WSN) applications. This study further highlights advancements of energy-efficient error control coding when, integrated into network designs alongwith the trade-offs between efficacy and intricacy to help improve wireless communication networks. Finally, this study summarizes current error control coding approaches for wireless communication systems. We provide insights into improving reliability, energy conservation, and efficacy by examining ACM, CDM, FEC, and error correction coding (ECC) across varied domains including LPWAN and IoT technologies with earnest hope to facilitate researchers, engineers, and professionals working in the field of error control coding in wireless communication.

In this paper, efficient implementation of error correction code (ECC) processing circuits based on single error correction and double error detection (SEC-DED) code with check bit pre-computation is proposed for memories. During the write operation of memory, check bit pre-computation eliminates the overall bits computation required to detect a double error, thereby reducing the complexity of the ECC processing circuits. In order to implement the ECC processing circuits using the check bit precomputation more efficiently, the proper SEC-DED codes are proposed. The H-matrix of the proposed SEC-DED code is the same as that of the odd-weightcolumn code during the write operation and is designed by replacing 0’s with 1’s at the last row of the H-matrix of the odd-weight-column code during the read operation. When compared with a conventional implementation utilizing the oddweight-column code, the implementation based on the proposed SEC-DED code with check bit precomputation achieves reductions in the number of gates, latency, and power consumption of the ECC processing circuits by up to 9.3%, 18.4%, and 14.1% for 64 data bits in a word.

As the size of on-chip SRAM caches is increasing rapidly and the physical dimension of the SRAM devices is decreasing, reliability of caches is becoming a growing concern. This is because with increased size of caches, the likelihood of radiation-induced soft faults also increases. As a result, information redundancy in the form of Error Correcting Codes (ECC) is becoming extremely important, especially to protect the larger sized last level caches (LLCs). In typical ECCs, extra redundancy bits are added to every row to detect and correct errors. There is additional encoding (while writing data) and decoding (while reading data) procedures required as well. In caches, these additional area, power and latency overheads need to be minimized as much as possible. To address this problem, we present in this paper Parity++: a novel unequal message protection scheme for last level caches that preferentially provides stronger error protection to certain "special messages". This protection scheme provides Single Error Detection (SED) for all messages and Single Error Correction (SEC) for a subset of messages. Thus, it is stronger than just a basic SED parity and has much lower parity storage overhead (4X lower for a 64-bit memory) and lower error detection energy than a traditional Single Error Correcting, Double Error Detecting (SECDED) code. We also evaluate Parity++ with a memory speculation procedure that can be used with any ECC scheme to hide the decoding latency while reading messages when there are no errors.

Error correction codes (ECCs) are commonly used in computer systems to protect information from errors. For example, single error correction (SEC) codes are frequently used for memory protection. Due to continuous technology scaling, soft errors on registers have become a major concern, and ECCs are required to protect them. Nevertheless, using an ECC increases delay, area and power consumption. In this way, ECCs are traditionally designed focusing on minimizing the number of redundant bits added. This is important in memories, as these bits are added to each word in the whole memory. However, this fact is less important in registers, where minimizing the encoding and decoding delay can be more interesting. This paper proposes a method to develop codes with 1-gate delay encoders and 4-gate delay decoders, independently of the word length. These codes have been designed to correct single errors only in data bits to reduce the overhead.

Efficient error detection in Double Error Correction BCH codes for memory applications

Soft errors caused by radiation particles are becoming an increasingly important issue for memory reliability. Traditionally, Single Error Correction (SEC) codes have been used to correct soft errors. Such codes can correct one error per memory word, but as errors become more frequent they may be insufficient. More complex error correction codes (ECCs) could be used, but they typically require complex decoders which impact memory area and speed. In this paper, the use of Euclidean geometry (EG) Codes for memory applications is studied. The results show that these codes, which provide powerful error correction capabilities, can be implemented efficiently in terms of area and latency.

Error-correcting codes (ECC) are widely used during data transfer in wireless communication systems as well as in computer memory architectures. The error-correcting process is based on sending data with extra parity bits and decoding the received data for error correction. The first error detection and correction code, introduced in 1950, Hamming Code (7,4) is a linear error-correcting code able to detect and correct a single-bit error by encoding 7-bit data from 4-bit data, including 3 parity bits. Previous efforts using unipolar resistive random access memory (ReRAM) based in-memory computation of Hamming Code (7,4) resulted in 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> times lower power consumption compared to GPU and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> times less than CPU-based computations. However further reduction of power consumption can be achieved by vector-matrix multiplication (VMM) using bipolar ReRAM arrays. In the VMM based approach, an encoding or decoding code matrix is stored in the array where it leverages the nonvolatile properties of ReRAM. With the VMM approach, the total number of computation cycles is not limited by the endurance of the ReRAM devices. Here we report the first experimental results of encoding and decoding Hamming code (7,4) using 1 transistor 1 hafnium oxide-based ReRAM (1T1R) arrays fabricated using 65nm CMOS technology. Our results show bipolar 1T1R arrays can correctly encode 4-bit message data to 7 bit encoded data as well as error position detection with overall 3 fold less power consumption than previously reported unipolar ReRAM crossbar array-based computation. Furthermore, we propose and simulate a peripheral circuit to convert the analog column output from a 1T1R array to single-bit binary output using the Cadence Spectre simulator. Our results pave the way for using a memristor-based fast and scalable hardware solution for encoding decoding of error-correcting codes

We propose an explicit construction of full-diversity space-time block codes, under the constraint of an error correction capability. Furthermore, these codes are constructed in order to be suitable for a serial concatenation with an outer linear forward error correcting (FEC) code. We apply the binary rank criterion, and we use the threaded layering technique and an inner linear FEC code to define a space-time error-correcting code. When serially concatenated with an outer linear FEC code, a product code can be built at the receiver, and adapted iterative receiver structures can be applied. An optimized hybrid structure mixing MMSE turbo equalization and turbo product code decoding is proposed. It yields reduced complexity and enhanced performance compared to previous existing structures.

Circuit techniques for reducing the minimum supply voltage (V MIN ) of last-level and intermediate static random-access memory (SRAM) caches enhance processor energy efficiency. For the first time at a 16nm technology node, projections of a high-density 6-transistor SRAM bit cell indicate that the VMIN of a 4Mb or larger cache exceeds the maximum supply voltage (V MAX ) for reliability. Thus, circuit techniques for cache VMIN reduction are transitioning from an energy-efficient solution to a requirement for cache functionality. Traditionally, error-correcting codes (ECC) such as single-error correction, double-error detection (SECDED) aim to protect the cache operation from radiation-induced soft errors. Moreover, during the qualification of a system-on-chip (SoC) processor, test engineers monitor the rate of correctable cache errors from SECDED for observing the on-die interactions between integrated components (e.g., CPU, GPU, DSP, etc.). This presentation highlights the opportunity to exploit ECC for reducing the cache V MIN while simultaneously providing coverage for radiation-induced soft errors. Silicon test-chip measurements from a 7Mb data cache in a 20nm technology demonstrate a V MIN reduction of 19% from SECDED. In addition, silicon measurements provide a salient insight in that only 0.12% of the cache words contain an error when operating at the cache V MIN with SECDED. Therefore, SECDED improves V MIN by 19% while maintaining 99.88% coverage for radiation-induced soft errors. In applying SECDED for a lower cache VMIN, the rate of correctable errors exponentially increases, thus eliminating a useful metric for on-die observability. The presentation concludes by offering alternative solutions for on-die observability.

Fault tolerant encoders for Single Error Correction and Double Adjacent Error Correction codes

Modified Packet Combining (MPC) scheme is an error correction scheme, which can correct double or, higher bit errors. In some earlier work, a scheme known as Packet Reversed Packet Combining (PRPC) scheme that will correct error if occurs at same bit location of erroneous copies, was studied. Both PRPC and MPC scheme are believed to offer higher throughput and better error correction capability at high bit error rate (BER) and large packet size only. Exact analysis was performed to substantiate this claim of higher throughput and better error correction capability in high as well as in low bit error rate (BER) for large and medium packet size. To combat high bit error rate some researches proposed to use Error Correction Code (ECC) in place of Error Detection Code (EDC) in ARQ scheme. But no conclusive result is found to justify the idea in terms of throughput. The current investigation is an attempt to explore the basic gap. In this paper, we investigate the exact analysis of both PRPC and MPC in a Modified way over Conventional PRPC, and report the findings thereof. We propose a combined protocol of Modified PRPC and MPC, and find that it will offer higher throughput and better error correction capability at high and low BER with medium and large packet size as we have used MPC (Modified Packet Combining) scheme with PRPC (Packet Reverse Packet Combining) scheme in a Modified way by combining BEC (Backward Error Correction) with FEC (Forward Error Correction) Codes for Mobile Communication and Networks.

6 - Applications to Communication Systems

Soft errors have been a concern in memories for many years. In older technologies, soft errors typically affected a single memory cell but as technology scaled, Multiple Cell Upsets (MCUs) that affect a group of nearby cells have become more common. This trend is expected to continue making MCUs more frequent and also increasing the number of cells affected. To avoid data corruption in memories, Error Correction Codes (ECCs) are used. Single Error Correction (SEC) codes that can correct one bit error per word are effective only against single errors. To protect against MCUs, one option is to use more sophisticated error correction codes like for example, Orthogonal Latin Squares Codes (OLSC). In this paper, a modification of the OLSC decoding algorithm is proposed for codes that can correct two random errors. This modification has little impact on circuit complexity and enables triple adjacent error correction which is interesting when MCUs are present.

Error correction codes are used in semiconductor memories to protect information against errors. Simple error correction codes are preferred due to their low redundancy and encoding/decoding latency. Hamming codes are simple and can be easily built for any word length. They only allow single error correction, so a multiple error can lead to a wrong decoding. Multiple errors often manifest as burst errors, and they are becoming more frequent as integration scale increases. This paper proposes modified Hamming codes, with the same redundancy and coverage as the original versions, but adding short burst error detection. Three code examples, with different error correction and detection capabilities, are presented. They are especially well-suited for memories, where the length of the data word is commonly a power of 2, and low redundancy and fast and simple encoder and decoder circuits are required.

This paper presents a compact, low-power UART architecture integrated with Single Error Correction and Double Error Detection (SECDED) for reliable serial communication in noisy and resource-constrained environments. The design incorporates an extended Hamming encoder—decoder within an FSM-controlled pipelined framework, enabling real-time error correction without violating standard UART timing conventions. Operating at only six times the baud rate, the proposed approach reduces hardware complexity and power consumption compared to traditional oversampling schemes. Implemented in Verilog and synthesized on 150 nm ASIC and FPGA platforms, the architecture achieves error-free data transfer while consuming just 0.099 W, with dynamic power limited to 2% through optimized clock gating. FPGA resource utilization remains below 1%. Extensive verification—including unit tests, errorinjection, and timing analysis—confirms protocol compliance and robust SECDED operation. With minimal area overhead and enhanced reliability, the proposed UART is well suited for IoT, smart home, and other safety-critical applications requiring energy-efficient and fault-tolerant serial links.