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Generalized integrated interleaved (GII) codes nest Reed-Solomon (RS) or BCH sub-codewords to generate codewords belonging to stronger RS or BCH codes. Their hyper-speed decoding and good error-correction capability make them one of the best candidates for next-generation terabit/s digital storage and communications. The key equation solver (KES) in the nested decoding stage causes clock frequency bottleneck and takes a large portion of the GII decoder area. Recent architectures reduce the critical path to two multipliers and rely on the application of the slow-down technique to further reduce it to one. The slow-down technique requires two sub-codewords to be interleaved in the nested KES. However, most of the time, the nested decoding only needs to be carried out on one sub-codeword and half of the clock cycles are wasted. This paper proposes two fast nested KES algorithms, both of which have one multiplier in the critical path without applying slow-down and accordingly reduce the latency of the nested KES to almost a half. The short critical path is achieved by algorithmic reformulations that enable the pre-computation of the scalars in parallel with polynomial updating. Our second design adopts scaled versions of the polynomials to enable product term sharing so that the number of multipliers in each pair of processing elements is reduced from 8 as in the first design to 4. Novel scaling and combined scalar computations are developed to keep the critical path one multiplier. For an example GII code over $GF(2^{8})$ that has 3 nested codewords, our designs achieve 49.9% reduction on the number of clock cycles needed in the nested KES compared to prior designs. Besides, our second design requires 22% less area than the first one under the same timing constraint. [ABSTRACT FROM AUTHOR]

Generalized integrated interleaved (GII) codes nest linear block codewords to generate codewords belonging to stronger linear block codes. They can achieve very high throughput with excellent error-correcting capability. GII codes can be based on either Reed-Solomon (RS) or BCH codes. GII-BCH codes are the most promising candidate for error correction in next-generation terabit/s Flash and storage class memories, and optical communications. On the other hand, GII decoder implementation faces many challenges. In particular, the key equation solver (KES) in the nested decoding process causes not only clock frequency bottleneck but also large area. Although techniques have been developed recently to address these issues for GII-RS codes, they cannot be directly extended for binary GII-BCH codes if every other iteration of the nested KES is skipped to reduce the latency. Two instead of one higher-order syndromes need to be incorporated into each nested KES iteration and this makes the implementation much more challenging. In this paper, algorithmic reformulations and architectural modifications are developed to eliminate the clock frequency bottleneck and reduce the area of GII-BCH nested KES. Additionally, the number of processing elements is substantially reduced by analyzing the minimum number of coefficients to keep for the involved polynomials without undesirable degradation on the error-correcting performance. The critical path of the proposed scaled nested BCH KES architecture with reduced processing elements is only one multiplier and three adders. For an example GII-BCH code over ${GF}(2^{12})$ that has a ${t}_{v}=58$ -error-correcting code as the most powerful code generated by the nesting, our design also further reduces the area by 33%. [ABSTRACT FROM AUTHOR]

Recently, symmetric block-wise concatenated-BCH (SBC-BCH) codes are proposed as strong error-correcting codes (ECCs) based on hard-decision channel outputs, which is especially suited for storages using NAND flash memories. Targeting energy-efficient NAND flash memory applications, this paper presents an energy-optimized decoder architecture which includes an iterative decoder for a SBC-BCH code as a main decoder and a low-complexity auxiliary decoder for a block-wise single parity-check (BSPC) code. The auxiliary decoder is opportunistically in action to break the dominant error bound associated with the SBC-BCH code, which allows one to lower the uncorrectable bit-error-rate (UBER) to 10−15 in an energy efficient way. This work presents several design-level optimizations for further enhancing the energy-efficiency of the iterative SBC-BCH decoder. More precisely, the new initialization scheme is proposed for ensuring the energy-efficient seamless decoding scenario. The syndrome tracking is applied to eliminate the previous syndrome calculation and the reordered Chien search further enhances the energy-efficiency as well as the decoding throughput. Targeting a 0.9-rate 4KB SBC-BCH code for commercialized storages using NAND flash memories, a prototype decoder consisting of both the iterative main and auxiliary decoders is designed in a 65-nm CMOS process. By applying the proposed optimizations, the prototype decoder achieves an energy-efficiency of 3.43 pJ/b while providing a decoding throughput of 13.2 Gb/s, which is superior to the previous state-of-the-art decoders for mobile storages. [ABSTRACT FROM AUTHOR]

Generalized integrated interleaved (GII) codes allow localized decoding of short sub-codewords. They are essential to hyper-speed data storage, communications, and continued scaling of distributed storage. Sub-codewords, which are usually Reed–Solomon (RS) or BCH codewords, are nested to generate codewords of higher correction capabilities. If the decoding of individual sub-codewords fails, the higher-order syndromes from the nested codewords are utilized to correct more errors. GII decoder design faces many challenges. The major ones include: 1) high-speed nested decoding utilizing the higher-order syndromes; 2) efficient updating of higher-order syndromes after sub-codewords are corrected; 3) computation of nested syndromes and matrix inversion for converting them to higher-order sub-codeword syndromes; and 4) efficient architectures capable of addressing the variable correction capabilities of the nested codewords. This paper proposes novel algorithmic reformulations and architectural transformations to address each bottleneck. For an example, GII code that has the same rate and length as eight un-nested (255, 223) RS codes, the proposed GII decoder achieves more than seven orders of magnitude improvement in error-correcting performance with less than 30% area overhead compared to the RS decoder. With a critical path of seven XOR gates, the proposed decoder can easily achieve more than 40 GB/s throughput. [ABSTRACT FROM AUTHOR]

For high-rate low-density parity-check (LDPC) codes, layered decoding processing can be reordered such that the first-in-first-out (FIFO) buffer that stores variable-to-check (V2C) messages is not needed and, hence, the memory area can be minimized, but at the cost of increased data dependency. This paper presents three techniques that can be used to implement an efficient reordered layered decoder. First, with the assistance of a graph coloring method, the required minimum number of V2C sign memory banks can be theoretically determined, with the corresponding pipeline architecture also designed. After that, the integer linear programming technique is adopted so as to arrange the V2C sign memory banks in a manner that minimizes the number of pipeline stalls, thereby increasing throughput. In order to further simplify the decoder, the first minimum values are not stored if the proposed modified min-sum algorithm is used. The proposed techniques are demonstrated by implementing a rate-0.905 (18396,16644) QC-LDPC decoder using 90-nm CMOS technology. When using the proposed techniques, implementation results show that the throughput-to-area ratio (TAR) increases by 58.9% without sacrificing error-rate performance. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel decoding algorithm to enhance the throughput of turbo decoding in LTE-Advanced systems and its hardware realization. The proposed method completely removes the undesired phase-switching latency by partially overlapping in-ordered and interleaved decoding phases, and as a result, achieves a significant increase of decoding throughput. Moreover, the algorithm does not degrade error-correcting performance for high-rate codes which are essential to achieve the maximum data rate of LTE-Advanced systems. The proposed method called tail-overlapped decoding can be easily applied to the conventional parallel decoding architecture designed for standardized communication systems. In addition, a new structure for the extrinsic information memory is proposed to eliminate memory contentions. A 3GPP LTE-Advanced turbo decoder supporting both decoding methods is implemented in 0.13\mum CMOS technology to show the effectiveness of the proposed algorithm. The decoder exhibits a decoding rate greater than 1Gbps with six iterations, meeting the peak data rate of the LTE-Advanced standard with much less hardware complexity than those of the previous works. [ABSTRACT FROM AUTHOR]