List decoding for noisy channels

We study relationships between worst-case and random-noise properties of error correcting codes. More concretely, we consider connections between minimum distance, list decoding radius, and block error probability on noisy channels. A recent result of Pernice, Sprumont, and Wootters established the tight connection between list decoding radius and symmetric channel performance for linear codes. We extend this result to general codes. The proof proceeds by directly bounding the weight distribution rather than by sharp threshold techniques. We then turn to the relation between minimum distance and symmetric channel performance. The results we just described imply that a $q$ -ary code of relative distance $δ$ has vanishing error probability on the symmetric channel up to the Johnson radius $J_q(δ)$ . We improve upon this bound in the case of linear codes, for a range $δ$ , for $q\ge 4$ . In our proof we consider the \emph{erasure} properties of codes, and bound their weight distribution through inequalities introduced by Samorodnitsky. The latter part of the proof gives a more general technique that bounds the symmetric channel performance of a linear code with constant relative distance and good erasure channel performance.We study relationships between worst-case and random-noise properties of error correcting codes. More concretely, we consider connections between minimum distance, list decoding radius, and block error probability on noisy channels. A recent result of Pernice, Sprumont, and Wootters established the tight connection between list decoding radius and symmetric channel performance for linear codes. We extend this result to general codes. The proof proceeds by directly bounding the weight distribution rather than by sharp threshold techniques. We then turn to the relation between minimum distance and symmetric channel performance. The results we just described imply that a $q$-ary code of relative distance $δ$ has vanishing error probability on the symmetric channel up to the Johnson radius $J_q(δ)$. We improve upon this bound in the case of linear codes, for a range $δ$, for $q\ge 4$. In our proof we consider the \emph{erasure} properties of codes, and bound their weight distribution through inequalities introduced by Samorodnitsky. The latter part of the proof gives a more general technique that bounds the symmetric channel performance of a linear code with constant relative distance and good erasure channel performance.

arXiv:2604.02994Apr 3, 20260 citations

Guessing Random Additive Noise Decoding

Syed Mohsin Abbas, Marwan Jalaleddine, Warren J. Gross

Springer eBooksJan 1, 20233 citations

Error-correcting codes for list decoding

Peter Eliaš

In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. Consideration is given to (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n,e,L) codes. They show that a jammer who can change a fixed fraction p>In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. Consideration is given to (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n,e,L) codes. They show that a jammer who can change a fixed fraction p>

IEEE Transactions on Information TheoryJan 1, 1991180 citations

On superdense coding with noisy channels

Z. Shadman, Hermann Kampermann, Dagmar Bruß

Verhandlungen der Deutschen Physikalischen GesellschaftJan 1, 20090 citations

Symbol-Based Successive Cancellation List Decoder for Polar Codes

Chenrong Xiong, Jun Ting Lin, Zhiyuan Yan

Abstract—Polar codes is promising because they can provably achieve the channel capacity while having an explicit construc-tion method. Lots of work have been done for the bit-based decoding algorithm for polar codes. In this paper, generalized symbol-based successive cancellation (SC) and SC list decoding algorithms are discussed. A symbol-based recursive channel combination relationship is proposed to calculate the symbol-based channel transition probability. This proposed method needs less additions than the maximum-likelihood decoder used by the existing symbol-based polar decoding algorithm. In addition, a two-stage list pruning network is proposed to simplify the list pruning network for the symbol-based SC list decoding algorithm. Index Terms—Error control codes, polar codes, successive cancellation decoding, list decoding I.Abstract—Polar codes is promising because they can provably achieve the channel capacity while having an explicit construc-tion method. Lots of work have been done for the bit-based decoding algorithm for polar codes. In this paper, generalized symbol-based successive cancellation (SC) and SC list decoding algorithms are discussed. A symbol-based recursive channel combination relationship is proposed to calculate the symbol-based channel transition probability. This proposed method needs less additions than the maximum-likelihood decoder used by the existing symbol-based polar decoding algorithm. In addition, a two-stage list pruning network is proposed to simplify the list pruning network for the symbol-based SC list decoding algorithm. Index Terms—Error control codes, polar codes, successive cancellation decoding, list decoding I.

Aug 16, 201618 citations

Stochastic Decoding of Error-Correcting Codes

François Leduc-Primeau, Saied Hemati, Vincent Gaudet +1 more

Springer eBooksJan 1, 20191 citation

q

-ary code of relative distance

δ

has vanishing error probability on the symmetric channel up to the Johnson radius

J_q(δ)

. We improve upon this bound in the case of linear codes, for a range

δ

, for

q\ge 4

. In our proof we consider the \emph{erasure} properties of codes, and bound their weight distribution through inequalities introduced by Samorodnitsky. The latter part of the proof gives a more general technique that bounds the symmetric channel performance of a linear code with constant relative distance and good erasure channel performance.