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Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
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TL;DR: Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems for a continuous channel with an additive gaussian noise and subject to an average power limitation at the transmitter.
Abstract: A study is made of coding and decoding systems for a continuous channel with an additive gaussian noise and subject to an average power limitation at the transmitter. Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems. These bounds are close together for signaling rates near channel capacity and also for signaling rates near zero, but diverge between. Curves exhibiting these bounds are given.
836 citations
TL;DR: It is shown that encoding and decoding operations can both be used to investigate some of the most common questions about how information is represented in the brain, and a systematic modeling approach is proposed that begins by estimating an encoding model for every voxel in a scan and ends by using the estimated encoding models to perform decoding.
785 citations
TL;DR: Simulation results show that CA-SCL/SCS can provide significant gain over the turbo codes used in 3GPP standard with code rate 1/2 and code length 1024 at the block error probability (BLER) of 10-4.
Abstract: CRC (cyclic redundancy check)-aided decoding schemes are proposed to improve the performance of polar codes. A unified description of successive cancellation decoding and its improved version with list or stack is provided and the CRC-aided successive cancellation list/stack (CA-SCL/SCS) decoding schemes are proposed. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that CA-SCL/SCS can provide significant gain of 0.5 dB over the turbo codes used in 3GPP standard with code rate 1/2 and code length 1024 at the block error probability (BLER) of 10-4. Moreover, the time complexity of CA-SCS decoder is much lower than that of turbo decoder and can be close to that of successive cancellation (SC) decoder in the high SNR regime.
722 citations
TL;DR: A class of algebraically structured quasi-cyclic low-density parity-check (LDPC) codes and their convolutional counterparts is presented and bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described.
Abstract: A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.
695 citations
26 Oct 2000
TL;DR: A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed and it is shown that the asymptotic performance can be approached as closely as desired with a list size that does not depend on the length of the code.
Abstract: A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed. This list-decoding algorithm is algebraic in nature and builds upon the interpolation procedure proposed by Guruswami and Sudan(see ibid., vol.45, p.1757-67, Sept. 1999) for hard-decision decoding. Algebraic soft-decision decoding is achieved by means of converting the probabilistic reliability information into a set of interpolation points, along with their multiplicities. The proposed conversion procedure is shown to be asymptotically optimal for a certain probabilistic model. The resulting soft-decoding algorithm significantly outperforms both the Guruswami-Sudan decoding and the generalized minimum distance (GMD) decoding of Reed-Solomon codes, while maintaining a complexity that is polynomial in the length of the code. Asymptotic analysis for alarge number of interpolation points is presented, leading to a geo- metric characterization of the decoding regions of the proposed algorithm. It is then shown that the asymptotic performance can be approached as closely as desired with a list size that does not depend on the length of the code.
672 citations