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About 1,887 papers for “Sequential decoding”

Sequential decoding,

Wozencraft, John M., Reiffen, Barney. · The Journal of the Abraham Lincoln Association

Cited by 0Open access

Sequential decoding

Shin‐Yi Lin · Rice Digital Scholarship Archive (Rice University) · 2016

In this investigation, the coding problem for a binary symmetric channel (BSC) has been studied in detail, in order to provide a clear exposition of the work done by Wozencraft and Reiff en on sequential decoding. A new exposition of the random coding technique and a precise formulation in terms of set concepts of a mathematical model for the probability of the decoding error are presented. A suitable threshold IT for the threshold block decoding has also been derived. The sequential decoding scheme proposed by Wozencraft has been examined carefully and certain modifications have been made. The new analysis enables us to obtain a tighter bound on the average number of computations per message digit for any transmission rate Rt which is less than a certain critical value. Finally, several random variables encountered in random coding have been rigorously studied, and a proof of their independence has been worked out.

Cited by 0Open access

Bidirectional sequential decoding

Li, Kaiping · Open Collections · 2009

The main drawback of sequential decoding is the variability of its decoding effort which could cause decoding erasures. We propose and analyze in this dissertation efficient bidirectional sequential decoding (B SD) techniques to alleviate this drawback, In the proposed BSD, two decoders are used; one is called forward decoder (PD), and is used to search the tree from forward direction; while the other is called backward decoder (BD), and is used for the backward search of the tree. Forward decoding and backward decoding are performed simultaneously, and stop somewhere in the tree. In one class of BSD, to which we refer as BSD-merge, decoding stops whenever FD and BD merge at a common encoder state some where in the tree. In the other class of BSD, that is BSD no-merge, no common encoder state is required, and decoding stops when FD meets BD. Different BSD algorithms based on the stack algorithm are constructed; namely Algorithm TAmeet which belongs to the class of BSD-no-merge, Algorithm TAmerge and Algorithm Timerge which belong to BSD-merge, and finally Algorithm HTTmerge which is a hybrid version of BSD-merge and BSD-no-merge. The relationships between backward coding and forward coding are examined in detail. Good convolutional codes, with memory m ranging from 2 to 25, suitable for bidirectional decoding, found through extensive computer search, are provided. These codes possess the same distance properties from both forward and backward directions. It is found by analysis and computer simulations that the distribution of the total number of computations per decoded block of the proposed BSD is still Pareto, as that of unidirectional sequential decoding (USD). However, the advantage of the proposed BSD appears as an increase in the Pareto exponent, and hence as a decrease in the computational variability and erasure probability. More specifically, we prove by using the random coding approach that the Pareto exponent of BSD using Algorithm TAmeet is asymptotically twice that of USD, and conjecture that this also applies to Algorithm TAmerge. On the other hand, it is found that the computational cutoff rate remains unchanged, but the use of our BSD reduces the average number of computations per decoded bit. Using the random coding approach, we show that the error performance of BSD merge is asymptotically the same as that of USD. Moreover, we show that the bit error probability of Algorithm TAmeet satisfies the random coding bound for block codes. Computer simulations are provided to confirm the analytical findings. The use of BSD-merge substantially reduces the computational variability of con ventional sequential decoding without compromising the error performance, However, BSD does not completely eliminate the erasure problem. We therefore combine our BSD idea in conjunction with the multiple stack algorithm (MSA), which is an erasure-free decoding algorithm. It is shown through analysis and computer simulations that the new bidirectional multiple stack algorithm (BMSA) offers substantial advantages over the MSA in terms of computational effort, memory requirements and error performance. The BMSA appears as an attractive alternative to the Viterbi algorithm (VA) where low error probabilities and high decoding speeds are required.

Cited by 0Open access

PAC Codes: Sequential Decoding vs List Decoding

Mohammad Rowshan, Andreas Burg, Emanuele Viterbo · 2021

In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Arıkan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this concatenation are called polarization-adjusted convolutional (PAC) codes. In this scheme, a pair of polar mapper and demapper as pre- and postprocessing devices are deployed around a memoryless channel, which provides polarized information to an outer decoder leading to improved error correction performance of the outer code. In this paper, the list decoding and sequential decoding (including Fano decoding and stack decoding) are first adapted for use to decode PAC codes. Then, to reduce the complexity of sequential decoding of PAC/polar codes, we propose (i) an adaptive heuristic metric, (ii) tree search constraints for backtracking to avoid exploration of unlikely sub-paths, and (iii) tree search strategies consistent with the pattern of error occurrence in polar codes. These contribute to the reduction of the average decoding time complexity from 50% to 80%, trading with 0.05 to 0.3 dB degradation in error correction performance within FER=10^-3 range, respectively, relative to not applying the corresponding search strategies. Additionally, as an important ingredient in Fano decoding of PAC/polar codes, an efficient computation method for the intermediate LLRs and partial sums is provided. This method is effective in backtracking and avoids storing the intermediate information or restarting the decoding process. Eventually, all three decoding algorithms are compared in terms of performance, complexity, and resource requirements.

Cited by 7Open access

Low latency sequential decoding

Gregory J. Pottie · 2002

Sequential decoding has traditionally been considered for applications where large buffers are permitted, but the speed factor is low. However, there is a need for coding techniques which achieve relatively large gain (on the order of 6 dB) with relatively low latency (a few hundred symbols). While the very name suggests serial operations, sequential decoders have potential for high speed and efficient parallel decoding operations. We consider the desirable algorithmic features for high speed factor operations using the stack and Fano algorithm families as the point of reference.

Cited by 6

L-STEP SEQUENTIAL DECODING

Reed,I S · Defense Technical Information Center (DTIC) · 1985

In the final report of an earlier yearly contract with NAVAIR a new decoding technique was found for minimum error-path decoding of convolutional codes. This new technique was called piece-wise L-steps minimum-error decoding or more simply L-step decoding. In a general sense L-step decoding is a method for decoding convolutional codes which appears to bridge the gap between the full implementation of a specific ideal decoder type and its less than ideal version in which memory paths are truncated. Although L-step decoding was introduced to save steps in an error trellis decoding algorithm, it can be extended to apply to most major types of decoding algorithms for convolutional codes, including Viterbi, stack, Fano, and their associated error-trellis algorithms.

Cited by 0

Forced sequence sequential decoding: a concatenated coding system with iterated sequential inner decoding

Ole Jensen, Erik Paaske · IEEE Transactions on Communications · 1998

We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low as E/sub b//N/sub 0/=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported by simulation results that are also extended to other parameters.

Cited by 5

AN INVESTIGATION OF SEQUENTIAL DECODING

WADDEN,W.R., JONES,D.M., PENNYPACKER,J.C. · Defense Technical Information Center (DTIC) · 1961

The technique of sequential decoding described by Wozencraft makes possible the practical implementation of error-correcting codes having large constraint lengths. This paper describes another sequential decoding scheme, and presents theoretical results on the associated average number of decoding steps and probability of error. Simultaneous studies of this decoding scheme are currently being performed on a digital computer. A summary is given of the result obtained to date. (Author)

Cited by 3

Sequential Decoding for Wireless Communications

Pål Orten, Arne Svensson · Chalmers Publication Library (Chalmers University of Technology) · 1998

Sequential decoding of long constraint length convolutional codes is proposed as a candidate coding scheme for high quality wireless services. Performance of sequential decoding on Rayleigh fading channels is obtained theoretically and by simulations. Results show that sequential decoding is a good candidate for data oriented services in future wireless communication systems. The applicability of such a coding and decoding scheme for FRAMES Multiple Access is then discussed.

Cited by 1

Sequential decoding with partial retransmissions

Kallel, Samir, Haccoun, David · PolyPublie (École Polytechnique de Montréal) · 1988

ABSTRACT: Sequential decoding -- Partial retransmissions strategy -- Partial code combining with sequential decoding -- Sequential decoding with partial retransmissions and partial code combining -- Improvement of partial retransmission strategy -- Improvement of partial retransmission strategy.

Cited by 0