1,704 research outputs found
A Method to determine Partial Weight Enumerator for Linear Block Codes
In this paper we present a fast and efficient method to find partial weight
enumerator (PWE) for binary linear block codes by using the error impulse
technique and Monte Carlo method. This PWE can be used to compute an upper
bound of the error probability for the soft decision maximum likelihood decoder
(MLD). As application of this method we give partial weight enumerators and
analytical performances of the BCH(130,66), BCH(103,47) and BCH(111,55)
shortened codes; the first code is obtained by shortening the binary primitive
BCH (255,191,17) code and the two other codes are obtained by shortening the
binary primitive BCH(127,71,19) code. The weight distributions of these three
codes are unknown at our knowledge.Comment: Computer Engineering and Intelligent Systems Vol 3, No.11, 201
Subquadratic time encodable codes beating the Gilbert-Varshamov bound
We construct explicit algebraic geometry codes built from the
Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for
alphabet sizes at least 192. Messages are identied with functions in certain
Riemann-Roch spaces associated with divisors supported on multiple places.
Encoding amounts to evaluating these functions at degree one places. By
exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we
devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and
1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list)
decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent.
If \omega = 2, as widely believed, the encoding and decoding runtimes are
respectively nearly linear and nearly quadratic. Prior to this work, encoding
(resp. decoding) time of code families beating the Gilbert-Varshamov bound were
quadratic (resp. cubic) or worse
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
We introduce the notion of the stopping redundancy hierarchy of a linear
block code as a measure of the trade-off between performance and complexity of
iterative decoding for the binary erasure channel. We derive lower and upper
bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and
Bonferroni-type inequalities, and specialize them for codes with cyclic
parity-check matrices. Based on the observed properties of parity-check
matrices with good stopping redundancy characteristics, we develop a novel
decoding technique, termed automorphism group decoding, that combines iterative
message passing and permutation decoding. We also present bounds on the
smallest number of permutations of an automorphism group decoder needed to
correct any set of erasures up to a prescribed size. Simulation results
demonstrate that for a large number of algebraic codes, the performance of the
new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on
Information Theor
Refined Upper Bounds on Stopping Redundancy of Binary Linear Codes
The -th stopping redundancy of the binary
code , , is defined as the minimum number of rows in
the parity-check matrix of , such that the smallest stopping set is
of size at least . The stopping redundancy is defined as
. In this work, we improve on the probabilistic analysis of
stopping redundancy, proposed by Han, Siegel and Vardy, which yields the best
bounds known today. In our approach, we judiciously select the first few rows
in the parity-check matrix, and then continue with the probabilistic method. By
using similar techniques, we improve also on the best known bounds on
, for . Our approach is compared to the
existing methods by numerical computations.Comment: 5 pages; ITW 201
- …