3,535 research outputs found
PAC Codes: Sequential Decoding vs List Decoding
In the Shannon lecture at the 2019 International Symposium on Information
Theory (ISIT), Ar{\i}kan 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.Comment: 14 pages, 12 figures, 1 table, 6 algorithm
On the symmetry of good nonlinear codes
It is shown that there are arbitrarily long "good" (in the sense of Gilbert) binary block codes that are preserved under very large permutation groups. This result contrasts sharply with the properties of linear codes: it is conjectured that long cyclic codes are bad, and known that long affine-invariant codes are bad
Efficient Termination of Spatially-Coupled Codes
Spatially-coupled low-density parity-check codes attract much attention due
to their capacity-achieving performance and a memory-efficient sliding-window
decoding algorithm. On the other hand, the encoder needs to solve large linear
equations to terminate the encoding process. In this paper, we propose modified
spatially-coupled codes. The modified (\dl,\dr,L) codes have less rate-loss,
i.e., higher coding rate, and have the same threshold as (\dl,\dr,L) codes
and are efficiently terminable by using an accumulator
On the error probability of general tree and trellis codes with applications to sequential decoding
An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random binary tree codes is derived and shown to be independent of the length of the tree. An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n is derived which separates the effects of the tail length T and the memory length M of the code. It is shown that the bound is independent of the length L of the information sequence. This implication is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication and further suggest an empirical formula for the true undetected decoding error probability with sequential decoding
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