Reliability-output Decoding of Tail-biting Codes.

A 16-state tail-biting trellis for the binary (24,12,8) Golay code C/sub 24/ is exhibited. This tail-biting trellis is minimal. It has many other nice properties, and may be simpler to decode than the minimal conventional trellis for C/sub 24/. Unwrapping this tail-biting trellis produces a periodically-time-varying 16-state rate- 1/2 convolutional code. This "Golay convolutional code" is the first known example of a self-dual doubly-even binary linear convolutional code. It has greater minimum distance than any 16-state time-invariant convolutional code of rate 1/2 . Demonstrably minimal tail-biting trellises are given for several other binary and nonbinary self-dual codes. For some nonbinary codes, tail-biting trellises based on code generators over a group are simpler than any tail-biting trellis based on linear generators over a field.A 16-state tail-biting trellis for the binary (24,12,8) Golay code C/sub 24/ is exhibited. This tail-biting trellis is minimal. It has many other nice properties, and may be simpler to decode than the minimal conventional trellis for C/sub 24/. Unwrapping this tail-biting trellis produces a periodically-time-varying 16-state rate- 1/2 convolutional code. This "Golay convolutional code" is the first known example of a self-dual doubly-even binary linear convolutional code. It has greater minimum distance than any 16-state time-invariant convolutional code of rate 1/2 . Demonstrably minimal tail-biting trellises are given for several other binary and nonbinary self-dual codes. For some nonbinary codes, tail-biting trellises based on code generators over a group are simpler than any tail-biting trellis based on linear generators over a field.

IEEE International Symposium on Information Theory (ISIT)Nov 27, 200212 citations

Tighter decoding reliability bound for Gallager's error-correcting code

祥介樺島, YOSHIYUKI KABASHIMA

Jan 1, 20010 citations

On Tail-Biting Polarization-Adjusted Convolutional (TB-PAC) Codes and Small-Sizes List Decoding

Bowen Feng, Yi Yang, Jian Jiao +1 more

Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes ( $N\leq 128$ ), PAC codes with a sequential decoding or a list decoding with large list-sizes ( $L\geq 128$ ) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes ( $L\leq 8$ ). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes ($N\leq 128$), PAC codes with a sequential decoding or a list decoding with large list-sizes ($L\geq 128$) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes ($L\leq 8$). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.

IEEE Communications LettersNov 28, 20225 citations

Threshold decoding

Peter J‎. Cameron, Jacobus H. Lint

Cambridge University Press eBooksSep 18, 19750 citations

Threshold decoding

Peter J‎. Cameron, Jacobus H. Lint

Cambridge University Press eBooksJul 31, 19800 citations

A Multivariate Weight Enumerator for Tail-biting Trellis Pseudocodewords

Nigel Boston

Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps track of these pseudocodewords. This enumerator is invariant under many linear transformations, often enabling us to compute it exactly. The extended binary Golay code has a particularly nice tail-biting-trellis and a famous unsolved question is to determine its minimal AWGN pseudodistance. The new enumerator provides an inroad to this problem.Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps track of these pseudocodewords. This enumerator is invariant under many linear transformations, often enabling us to compute it exactly. The extended binary Golay code has a particularly nice tail-biting-trellis and a famous unsolved question is to determine its minimal AWGN pseudodistance. The new enumerator provides an inroad to this problem.

Journal of Generalized Lie Theory and ApplicationsJan 1, 20157 citations

Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes (

N\leq 128

), PAC codes with a sequential decoding or a list decoding with large list-sizes (

L\geq 128

) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes (

L\leq 8

). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.