293,976 research outputs found
Constructions of Generalized Concatenated Codes and Their Trellis-Based Decoding Complexity
In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis omplexity than Euclidean geometry (EG), Reed–Muller (RM), or Bose–Chaudhuri–Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed
Computing coset leaders and leader codewords of binary codes
In this paper we use the Gr\"obner representation of a binary linear code
to give efficient algorithms for computing the whole set of coset
leaders, denoted by and the set of leader codewords,
denoted by . The first algorithm could be adapted to
provide not only the Newton and the covering radius of but also to
determine the coset leader weight distribution. Moreover, providing the set of
leader codewords we have a test-set for decoding by a gradient-like decoding
algorithm. Another contribution of this article is the relation stablished
between zero neighbours and leader codewords
Duality of Channel Encoding and Decoding - Part I: Rate-1 Binary Convolutional Codes
In this paper, we revisit the forward, backward and bidirectional
Bahl-Cocke-Jelinek-Raviv (BCJR) soft-input soft-output (SISO) maximum a
posteriori probability (MAP) decoding process of rate-1 binary convolutional
codes. From this we establish some interesting explicit relationships between
encoding and decoding of rate-1 convolutional codes. We observe that the
forward and backward BCJR SISO MAP decoders can be simply represented by their
dual SISO channel encoders using shift registers in the complex number field.
Similarly, the bidirectional MAP decoding can be implemented by linearly
combining the shift register contents of the dual SISO encoders of the
respective forward and backward decoders. The dual encoder structures for
various recursive and non-recursive rate-1 convolutional codes are derived.Comment: 32 pages, 20 figures, to appear in ET
Fast Exact Search in Hamming Space with Multi-Index Hashing
There is growing interest in representing image data and feature descriptors
using compact binary codes for fast near neighbor search. Although binary codes
are motivated by their use as direct indices (addresses) into a hash table,
codes longer than 32 bits are not being used as such, as it was thought to be
ineffective. We introduce a rigorous way to build multiple hash tables on
binary code substrings that enables exact k-nearest neighbor search in Hamming
space. The approach is storage efficient and straightforward to implement.
Theoretical analysis shows that the algorithm exhibits sub-linear run-time
behavior for uniformly distributed codes. Empirical results show dramatic
speedups over a linear scan baseline for datasets of up to one billion codes of
64, 128, or 256 bits
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