85 research outputs found
CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding
Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional
codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been
shown to closely approach the random-coding union (RCU) bound for short
blocklengths. This paper designs CRC polynomials for rate- (n-1)/n ZT and TB
CCs with short blocklengths. This paper considers both standard rate-(n-1)/n CC
polynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2
code. The CRC polynomials are chosen to maximize the minimum distance d_min and
minimize the number of nearest neighbors A_(d_min) . For the standard
rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al.
lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD).
CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength
of 128. This paper compares the FER performance (gap to the RCU bound) and
complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper
also explores the complexity-performance trade-off for three TBCC decoders: a
single-trellis approach, a multi-trellis approach, and a modified
single-trellis approach with pre-processing using the wrap around Viterbi
algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0792
List Decoding of Short Codes for Communication over Unknown Fading Channels
In this paper, the advantages of list decoding for short packet transmission over fading channels with an unknown state are illustrated. The principle is applied to polar codes (under successive cancellation list decoding) and to general short binary linear block codes (under ordered-statistics decoding). The proposed decoders assume neither a-priori knowledge of the channel coefficients, nor of their statistics. The scheme relies on short pilot fields that are used only to derive an initial channel estimate. The channel estimate is required to be accurate enough to enable a good list construction, i.e., the construction of a list that contains, with high probability, the transmitted codeword. The final decision on the message is obtained by applying a list. This allows one to use very few pilots, thus reducing the the Rayleigh block-fading channel and compared to finite-length performance bounds. The proposed technique provides (in the short block length regime) gains of 1 dB with respect to a traditional pilot-aided transmission scheme
Deterministic Rateless Codes for BSC
A rateless code encodes a finite length information word into an infinitely
long codeword such that longer prefixes of the codeword can tolerate a larger
fraction of errors. A rateless code achieves capacity for a family of channels
if, for every channel in the family, reliable communication is obtained by a
prefix of the code whose rate is arbitrarily close to the channel's capacity.
As a result, a universal encoder can communicate over all channels in the
family while simultaneously achieving optimal communication overhead. In this
paper, we construct the first \emph{deterministic} rateless code for the binary
symmetric channel. Our code can be encoded and decoded in time per
bit and in almost logarithmic parallel time of , where
is any (arbitrarily slow) super-constant function. Furthermore, the error
probability of our code is almost exponentially small .
Previous rateless codes are probabilistic (i.e., based on code ensembles),
require polynomial time per bit for decoding, and have inferior asymptotic
error probabilities. Our main technical contribution is a constructive proof
for the existence of an infinite generating matrix that each of its prefixes
induce a weight distribution that approximates the expected weight distribution
of a random linear code
Rate-compatible LDPC Codes based on Primitive Polynomials and Golomb Rulers
We introduce and study a family of rate-compatible Low-Density Parity-Check
(LDPC) codes characterized by very simple encoders. The design of these codes
starts from simplex codes, which are defined by parity-check matrices having a
straightforward form stemming from the coefficients of a primitive polynomial.
For this reason, we call the new codes Primitive Rate-Compatible LDPC
(PRC-LDPC) codes. By applying puncturing to these codes, we obtain a bit-level
granularity of their code rates. We show that, in order to achieve good LDPC
codes, the underlying polynomials, besides being primitive, must meet some more
stringent conditions with respect to those of classical punctured simplex
codes. We leverage non-modular Golomb rulers to take the new requirements into
account. We characterize the minimum distance properties of PRC-LDPC codes, and
study and discuss their encoding and decoding complexity. Finally, we assess
their error rate performance under iterative decoding
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Contemporary Coding Theory
Coding Theory naturally lies at the intersection of a large number
of disciplines in pure and applied mathematics. A multitude of
methods and means has been designed to construct, analyze, and
decode the resulting codes for communication. This has suggested to
bring together researchers in a variety of disciplines within
Mathematics, Computer Science, and Electrical Engineering, in order
to cross-fertilize generation of new ideas and force global
advancement of the field. Areas to be covered are Network Coding,
Subspace Designs, General Algebraic Coding Theory, Distributed
Storage and Private Information Retrieval (PIR), as well as
Code-Based Cryptography
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