57 research outputs found
Further Results on Quadratic Permutation Polynomial-Based Interleavers for Turbo Codes
An interleaver is a critical component for the channel coding performance of
turbo codes. Algebraic constructions are of particular interest because they
admit analytical designs and simple, practical hardware implementation. Also,
the recently proposed quadratic permutation polynomial (QPP) based interleavers
by Sun and Takeshita (IEEE Trans. Inf. Theory, Jan. 2005) provide excellent
performance for short-to-medium block lengths, and have been selected for the
3GPP LTE standard. In this work, we derive some upper bounds on the best
achievable minimum distance dmin of QPP-based conventional binary turbo codes
(with tailbiting termination, or dual termination when the interleaver length N
is sufficiently large) that are tight for larger block sizes. In particular, we
show that the minimum distance is at most 2(2^{\nu +1}+9), independent of the
interleaver length, when the QPP has a QPP inverse, where {\nu} is the degree
of the primitive feedback and monic feedforward polynomials. However, allowing
the QPP to have a larger degree inverse may give strictly larger minimum
distances (and lower multiplicities). In particular, we provide several QPPs
with an inverse degree of at least three for some of the 3GPP LTE interleaver
lengths giving a dmin with the 3GPP LTE constituent encoders which is strictly
larger than 50. For instance, we have found a QPP for N=6016 which gives an
estimated dmin of 57. Furthermore, we provide the exact minimum distance and
the corresponding multiplicity for all 3GPP LTE turbo codes (with dual
termination) which shows that the best minimum distance is 51. Finally, we
compute the best achievable minimum distance with QPP interleavers for all 3GPP
LTE interleaver lengths N <= 4096, and compare the minimum distance with the
one we get when using the 3GPP LTE polynomials.Comment: Submitted to IEEE Trans. Inf. Theor
Analysis of cubic permutation polynomials for turbo codes
Quadratic permutation polynomials (QPPs) have been widely studied and used as
interleavers in turbo codes. However, less attention has been given to cubic
permutation polynomials (CPPs). This paper proves a theorem which states
sufficient and necessary conditions for a cubic permutation polynomial to be a
null permutation polynomial. The result is used to reduce the search complexity
of CPP interleavers for short lengths (multiples of 8, between 40 and 352), by
improving the distance spectrum over the set of polynomials with the largest
spreading factor. The comparison with QPP interleavers is made in terms of
search complexity and upper bounds of the bit error rate (BER) and frame error
rate (FER) for AWGN and for independent fading Rayleigh channels. Cubic
permutation polynomials leading to better performance than quadratic
permutation polynomials are found for some lengths.Comment: accepted for publication to Wireless Personal Communications (19
pages, 4 figures, 5 tables). The final publication is available at
springerlink.co
Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes
In this work, we consider pseudocodewords of (relaxed) linear programming
(LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP
decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo
codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is
proper and -symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance and/or the stopping distance is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the and the , and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication
Enhanced Trellis Coded Multiple Access (ETCMA)
We propose an enhanced version of trellis coded multiple access (TCMA), an
overloaded multiple access scheme that outperforms the original TCMA in terms
of achieved spectral efficiency. Enhanced TCMA (ETCMA) performs simultaneous
transmission of multiple data streams intended for users experiencing similar
signal-to-noise ratios and can be employed both in the uplink and in the
downlink of wireless systems, thus overcoming one of the main limitations of
TCMA. Thanks to a new receiver algorithm, ETCMA is capable of delivering a
significantly higher spectral efficiency. We show that ETCMA approaches the
capacity of the Additive White Gaussian Noise channel for a wide range of
signal-to-noise ratios.Comment: 5 pages, 5 figure
Multi-non-binary turbo codes
International audienceThis paper presents a new family of turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes (PCCC). An MNBTC incorporates, as component encoders, recursive and systematic multi-non-binary convolutional encoders. The more compact data structure for these encoders confers some advantages on MNBTCs over other types of turbo codes, such as better asymptotic behavior, better convergence, and reduced latency. This paper presents in detail the structure and operation of an MNBTC: MNB encoding, trellis termination, Max-Log-MAP decoding adapted to the MNB case. It also shows an example of MNBTC whose performance is compared with the state-of-the-art turbo code adopted in the DVB-RCS2 standard
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
The Telecommunications and Data Acquisition Report
This quarterly publication provides archival reports on developments in programs managed by JPL's Telecommunications and Mission Operations Directorate (TMOD), which now includes the former Telecommunications and Data Acquisition (TDA) Office. In space communications, radio navigation, radio science, and ground-based radio and radar astronomy, it reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standards activity at JPL for space data and information systems and reimbursable DSN work performed for other space agencies through NASA. The preceding work is all performed for NASA's Office of Space Communications (OSC)
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