Stochastic decoding is a new approach to iterative decoding on graphs. This paper presents a hardware architecture for fully parallel stochastic low-density parity-check (LDPC) decoders. To obtain the characteristics of the proposed architecture, we apply this architecture to decode an irregular state-of-the-art (1056,528) LDPC code on a Xilinx Virtex-4 LX200 field-programmable gate-array (FPGA) device. The implemented decoder achieves a clock frequency of 222 MHz and a throughput of about 1.66 Gb/s at Eb/N0=4.25 dB (a bit error rate of 10-8). It provides decoding performance within 0.5 and 0.25 dB of the floating-point sum-product algorithm with 32 and 16 iterations, respectively, and similar error-floor behavior. The decoder uses less than 40% of the lookup tables, flip-flops, and IO ports available on the FPGA device. The results provided in this paper validate the potential of stochastic LDPC decoding as a practical and competitive fully parallel decoding approach.

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Fully Parallel Stochastic LDPC Decoders

A grouped-parallel low-density parity-check (LDPC) decoder is designed for the (2048,1723) Reed-Solomon-based LDPC (RS-LDPC) suitable for 10GBASE-T Ethernet. A two-step decoding scheme reduces the wordlength to 4 bits while lowering the error floor to below 10-14 BER. The proposed post-processor is conveniently integrated with the decoder, adding minimal area and power. The decoder architecture is optimized by groupings so as to localize irregular interconnects and regularize global interconnects and the overall wiring overhead is minimized. The 5.35 mm2, 65 nm CMOS chip achieves a decoding throughput of 47.7 Gb/s. With scaled frequency and voltage, the chip delivers a 6.67 Gb/s throughput necessary for 10GBASE-T while dissipating 144 mW of power.

An Efficient 10GBASE-T Ethernet LDPC Decoder Design With Low Error Floors

This paper investigates VLSI architectures for low-density parity-check (LDPC) decoders amenable to low-voltage and low-power operation. First, a highly-parallel decoder architecture with low routing overhead is described. Second, we propose an efficient method to detect early convergence of the iterative decoder and terminate the computations, thereby reducing dynamic power. We report on a bit-serial fully-parallel LDPC decoder fabricated in a 0.13-mum CMOS process and show how the above techniques affect the power consumption. With early termination, the prototype is capable of decoding with 10.4 pJ/bit/iteration, while performing within 3 dB of the Shannon limit at a BER of 10-5 and with 3.3 Gb/s total throughput. If operated from a 0.6 V supply, the energy consumption can be further reduced to 2.7 pJ/bit/iteration while maintaining a total throughput of 648 Mb/s, due to the highly-parallel architecture. To demonstrate the applicability of the proposed architecture for longer codes, we also report on a bit-serial fully-parallel decoder for the (2048, 1723) LDPC code in 10 GBase-T standard synthesized with a 90-nm CMOS library.

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Power Reduction Techniques for LDPC Decoders

An LDPC decoder chip fully compliant to IEEE 802.16e applications is presented. Since the parity check matrix can be decomposed into sub-matrices which are either a zero-matrix or a cyclic shifted matrix, a phase-overlapping message passing scheme is applied to update messages immediately, leading to enhance decoding throughput. With only one shifter-based permutation structure, a self-routing switch network is proposed to merge 19 different sub-matrix sizes as defined in IEEE 802.16e and enable parallel message to be routed without congestion. Fabricated in the 90 nm 1P9M CMOS process, this chip achieves 105 Mb/s at 20 iterations while decoding the rate-5/6 2304-bit code at 150 MHz operation frequency. To meet the maximum data rate in IEEE 802.16e, this chip operates at 109 MHz frequency and dissipates 186 mW at 1.0 V supply.

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An LDPC Decoder Chip Based on Self-Routing Network for IEEE 802.16e Applications

Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders strongly affect which absorbing sets dominate in the errorfloor region. We show that conventional sum-product decoder implementations of the (2209, 1978) array-based LDPC code allow low-weight absorbing sets to have a strong effect, and, as a result, elevate the error floor. Dually-quantized sum-product decoders and approximate sum-product decoders alleviate the effects of low-weight absorbing sets, thereby lowering the error floor.

/pdf/design-of-ldpc-decoders-for-improved-low-error-rate-2z21jzpfvt.pdf

Design of LDPC Decoders for Improved Low Error Rate Performance

A CODEC fully compliant to DVB-S2 broadcast standards is implemented in both 013 /spl mu/m 8M and 90nm 7M low-leakage CMOS technologies The system includes encoders and decoders for both LDPC codes and serially concatenated BCH codes This CODEC outperforms the DVB-S2 error performance requirements by up to 01dB The 013 /spl mu/m design occupies 496mm/sup 2/ and operates at 200MHz, while the 90nm design occupies 158mm/sup 2/ and operates at 300MHz

A 135Mb/s DVB-S2 compliant codec based on 64800b LDPC and BCH codes

A DVB-S2 compliant codec is implemented in both 130nm-8M and 90nm-7M low-leakage CMOS technologies. The system includes encoders and decoders for both low-density parity check (LDPC) codes and serially concatenated BCH codes. All requirements of the DVB-S2 standard are supported including code rates between 1/4 and 9/10, block sizes of either 16,200 bits or 64,800 bits, and four digital modulation options. The 130nm core design occupies 49.6mm2 and operates at 200MHz, while the 90nm core design occupies 15.8mm2 and operates at 300MHz.

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T. Michel

Papers

A 135Mb/s DVB-S2 compliant codec based on 64800b LDPC and BCH codes

A 135Mbps DVB-S2 compliant codec based on 64800-bit LDPC and BCH codes (ISSCC paper 24.3)

Based on 64800b LDPC and BCH Codes