Partial Sums Generation Architecture for Successive Cancellation Decoding of Polar Codes

Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes partial sums computations. We take advantage of the recursive structure of polar codes to introduce an efficient partial sums computation unit that can also implements the encoder. The proposed architecture is synthesized for several codelengths in 65nm ASIC technology. The area of the resulting design is reduced up to 26% and the maximum working frequency is improved by ~25%.Comment: Submitted to IEEE Workshop on Signal Processing Systems (SiPS)(26 April 2012). Accepted (28 June 2013

Partial Sums Computation In Polar Codes Decoding

Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums computation unit. We explain in this paper how the partial sums computation can be seen as a matrix multiplication. Then, an efficient hardware implementation of this product is investigated. It has reduced logic resources and interconnections. Formalized architectures, to compute partial sums and to generate the bits of the generator matrix k^n, are presented. The proposed architecture allows removing the multiplexing resources used to assigned to each processing elements the required partial sums.Comment: Accepted to ISCAS 201

Analysis of the Convergence Process by EXIT Charts for Parallel Implementations of Turbo Decoders

International audienceIterative process is a general principle in decoding powerful FEC codes such as turbo codes. However, the mutual information exchange during the iterative process is not easy to analyze and to describe. A useful technique to help the designer is the EXtrinsic Information Transfer (EXIT) chart. Unfortunately, this method cannot be directly applied to the decoding convergence analysis if parallel processing has to be exploited for the design of turbo decoders. In this letter, an extension of the EXIT charts method is proposed in order to take into account the constraints introduced by parallel implementations. The corresponding analysis associated with Monte-Carlo simulations gives additional understanding of the convergence process for the design of parallel architectures dedicated to turbo decoding

Near maximum likelihood soft-decision decoding of a particular class of rate-1/2 systematic linear block codes

International audiencePresented is a soft-decision decoding algorithm for a particular class of rate-1/2 systematic linear block codes. The proposed algorithm performs successive re-encoding of both the data and parity bits, to produce a list of codewords among which the most likely candidate is chosen. Simulation results show that close to optimal performance can be obtained at reasonable complexity. They validate the potential of the proposed algorithm as a practical approach for soft-decision decoding

High speed low complexity radix-16 Max-Log-MAP SISO decoder

International audienceAt present, the main challenge for hardware implementation turbo decoders is to achieve the high data rates required by current and future communication system standards. In order to address this challenge, a low complexity radix-16 SISO decoder for the Max-Log- MAP algorithm is proposed in this paper. Based on the elimination of parallel paths in the radix-16 trellis diagram, architectural solutions to reduce the hardware complexity of the different blocks of a SISO decoder are detailed. Moreover, two complementary techniques are introduced order to overcome BER/FER performance degradation when turbo decoders based on the proposed SISO decoder are considered. Thus, a penalty lower than 0.05dB is observed for a 8 state binary turbo code with respect to a traditional radix-2 turbo decoder for 6 decoding iterations

A Space-Time Redundancy Technique for Embedded Stochastic Error Correction

International audienceAn error-correction algorithm, referred as to Low Density Parity Check (LDPC) stochastic decoding technique, has recently been introduced for implementing iterative LDPC decoders in logic technologies with a high rate of transient faults. In this work, a modified algorithm that includes a feedback mechanism is first presented. A temporal majority logic is also applied at the decoder's output, providing an additional dimension of redundancy. By comparison to Gallager-A decoding method, the combination of feedback with temporal redundancy is shown to significantly increase the decoder's resilience against a high rate of internal upsets as a gain of up to three orders of magnitude

Scarce state transition turbo decoding based on re-encoding combined with a dummy insertion

International audienceAn efficient way to reduce the dynamic power dissipation in the turbo decoder is presented. This technique is based on a dynamic re-encoding of the received messages. The idea is to decrease the state transition activity of the trellis-based algorithms by replacing the classical direct decoding of the random noisy codewords by an equivalent decoding of an almost “all zero” codewords in order to keep the survivor path on the “zero path”

A highly parallel Turbo Product Code decoder without interleaving resource

International audienceThis article presents an innovative turbo product code (TPC) decoder architecture without any interleaving resource. This architecture includes a full-parallel SISO decoder able to process n symbols in one clock period. Syntheses show the better efficiency of such an architecture compared with existing previous solutions. Considering a 6-iteration turbo decoder of a (32,26)2 BCH product code, synthetized in a 90 nm CMOS technology, the resulting information throughput is 2.5 Gb/s with an area of 233 Kgates. Finally a second architecture enhancing parallelism rate is described. The information throughput is 33.7 Gb/s while an area estimation gives A=10 mum2

Stochastic multiple-stream decoding of Cortex codes

International audienceCortex codes are short length block codes having a large Hamming distance. Their modular construction, based on simple and very short block codes, yield to difficulties in efficiently decoding them with digital decoders implementing the Sum-Product algorithm. However, this construction lends itself to analog decoding with performance close to ML decoding as was recently demonstrated. A digital decoding method close to analog decoding is stochastic decoding. This paper brings the two together to design a Cortex stochastic architecture with good decoding performance. Moreover, the proposed stochastic decoder architecture is simplified when compared to the customary one. Instead of edge or tracking forecast memories the proposed architecture uses multiple streams to represent the same probability and deterministic shufflers. This results in a more efficient architecture in terms of ratio between data throughput and hardware complexity. Finally, the proposed method offers decoding performance similar to a Min-Sum decoder with 50 iterations

Reed-Solomon turbo product codes for optical communications: from code optimization to decoder design

International audienceTurbo product codes (TPCs) are an attractive solution to improve link budgets and reduce systems costs by relaxing the requirements on expensive optical devices in high capacity optical transport systems. In this paper, we investigate the use of Reed-Solomon (RS) turbo product codes for 40 Gbps transmission over optical transport networks and 10 Gbps transmission over passive optical networks. An algorithmic study is first performed in order to design RS TPCs that are compatible with the performance requirements imposed by the two applications. Then, a novel ultrahigh-speed parallel architecture for turbo decoding of product codes is described. A comparison with binary Bose-Chaudhuri-Hocquenghem (BCH) TPCs is performed. The results show that high-rate RS TPCs offer a better complexity/performance tradeoff than BCH TPCs for low-cost Gbps fiber optic communications