Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userList and Probabilistic Unique Decoding of Folded Subspace Codes
255
0
0.0
(
0
)
Added by
Hannes Bartz
Publication date
2015
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $Rin[0,1]$. An efficient interpolation-based decoding algorithm for this code construction is given which allows to correct insertions and deletions up to the normalized radius $s(1-((1/h+h)/(h-s+1))R)$, where $h$ is the folding parameter and $sleq h$ is a decoding parameter. The algorithm serves as a list decoder or as a probabilistic unique decoder that outputs a unique solution with high probability. An upper bound on the average list size of (folded) subspace codes and on the decoding failure probability is derived. A major benefit of the decoding scheme is that it enables probabilistic unique decoding up to the list decoding radius.
rate research
Read More
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank metric). List decoding in these extreme cases is well-studied, and the two code classes behave very differently in terms of list size, but nothing is known for the general case. In this paper, we derive a lower bound on the list size for LRS codes, which is, for a large class of LRS codes, exponential directly above the Johnson radius. Furthermore, we show that some families of linearized Reed-Solomon codes with constant numbers of blocks cannot be list decoded beyond the unique decoding radius.
Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of decoding algorithms with good error performance and efficient hardware implementation. One of the leading candidates in this regard is represented by successive-cancellation list (SCL) decoding. However, its hardware implementation requires a large amount of memory. Recently, a partitioned SCL (PSCL) decoder has been proposed to significantly reduce the memory consumption. In this paper, we examine the paradigm of PSCL decoding from both theoretical and practical standpoints: (i) by changing the construction of the code, we are able to improve the performance at no additional computational, latency or memory cost, (ii) we present an optimal scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an upper bound on the list size that allows MAP performance.
We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by Bocherer emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.
This paper identifies convolutional codes (CCs) used in conjunction with a CC-specific cyclic redundancy check (CRC) code as a promising paradigm for short blocklength codes. The resulting CRC-CC concatenated code naturally permits the use of the serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The CC of interest is of rate-$1/omega$ and is either zero-terminated (ZT) or tail-biting (TB). For CRC-CC concatenated code designs, we show how to find the optimal CRC polynomial for a given ZTCC or TBCC. Our complexity analysis reveals that SLVD decoding complexity is a function of the terminating list rank, which converges to one at high SNR. This behavior allows the performance gains of SLVD to be achieved with a small increase in average complexity at the SNR operating point of interest. With a sufficiently large CC constraint length, the performance of CRC-CC concatenated code under SLVD approaches the random-coding union (RCU) bound as the CRC size is increased while average decoding complexity does not increase significantly. TB encoding further reduces the backoff from the RCU bound by avoiding the termination overhead. As a result, several CRC-TBCC codes outperform the RCU bound at moderate SNR values while permitting decoding with relatively low complexity.
The list-decodable code has been an active topic in theoretical computer science since the seminal papers of M. Sudan and V. Guruswami in 1997-1998. There are general result about the Johnson radius and the list-decoding capacity theorem for random codes. However few results about general constraints on rates, list-decodable radius and list sizes for list-decodable codes have been obtained. In this paper we show that rates, list-decodable radius and list sizes are closely related to the classical topic of covering codes. We prove new simple but strong upper bounds for list-decodable codes based on various covering codes. Then any good upper bound on the covering radius imply a good upper bound on the size of list-decodable codes. Hence the list-decodablity of codes is a strong constraint from the view of covering codes. Our covering code upper bounds for $(d,1)$ list decodable codes give highly non-trivial upper bounds on the sizes of codes with the given minimum Hamming distances. Our results give exponential improvements on the recent generalized Singleton upper bound of Shangguan and Tamo in STOC 2020, when the code lengths are very large. The asymptotic forms of covering code bounds can partially recover the list-decoding capacity theorem, the Blinovsky bound and the combinatorial bound of Guruswami-H{aa}stad-Sudan-Zuckerman. We also suggest to study the combinatorial covering list-decodable codes as a natural generalization of combinatorial list-decodable codes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
