13 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
On Quadratic Inverses for Quadratic Permutation Polynomials over Integer Rings
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. Sun and
Takeshita have recently shown that the class of quadratic permutation
polynomials over integer rings provides excellent performance for turbo codes.
In this correspondence, a necessary and sufficient condition is proven for the
existence of a quadratic inverse polynomial for a quadratic permutation
polynomial over an integer ring. Further, a simple construction is given for
the quadratic inverse. All but one of the quadratic interleavers proposed
earlier by Sun and Takeshita are found to admit a quadratic inverse, although
none were explicitly designed to do so. An explanation is argued for the
observation that restriction to a quadratic inverse polynomial does not narrow
the pool of good quadratic interleavers for turbo codes.Comment: Submitted as a Correspondence to the IEEE Transactions on Information
Theory Submitted : April 1, 2005 Revised : Nov. 15, 200
Turbo codes and turbo algorithms
In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding
EQUALISATION TECHNIQUES FOR MULTI-LEVEL DIGITAL MAGNETIC RECORDING
A large amount of research has been put into areas of signal processing, medium design,
head and servo-mechanism design and coding for conventional longitudinal as well
as perpendicular magnetic recording. This work presents some further investigation in the
signal processing and coding aspects of longitudinal and perpendicular digital magnetic
recording.
The work presented in this thesis is based upon numerical analysis using various simulation
methods. The environment used for implementation of simulation models is C/C + +
programming. Important results based upon bit error rate calculations have been documented
in this thesis.
This work presents the new designed Asymmetric Decoder (AD) which is modified to
take into account the jitter noise and shows that it has better performance than classical
BCJR decoders with the use of Error Correction Codes (ECC). In this work, a new method
of designing Generalised Partial Response (GPR) target and its equaliser has been discussed
and implemented which is based on maximising the ratio of the minimum squared
euclidean distance of the PR target to the noise penalty introduced by the Partial Response
(PR) filter. The results show that the new designed GPR targets have consistently
better performance in comparison to various GPR targets previously published.
Two methods of equalisation including the industry's standard PR, and a novel Soft-Feedback-
Equalisation (SFE) have been discussed which are complimentary to each other.
The work on SFE, which is a novelty of this work, was derived from the problem of Inter
Symbol Interference (ISI) and noise colouration in PR equalisation. This work also shows
that multi-level SFE with MAP/BCJR feedback based magnetic recording with ECC has
similar performance when compared to high density binary PR based magnetic recording
with ECC, thus documenting the benefits of multi-level magnetic recording. It has been
shown that 4-level PR based magnetic recording with ECC at half the density of binary PR
based magnetic recording has similar performance and higher packing density by a factor
of 2.
A novel technique of combining SFE and PR equalisation to achieve best ISI cancellation
in a iterative fashion has been discussed. A consistent gain of 0.5 dB and more
is achieved when this technique is investigated with application of Maximum Transition
Run (MTR) codes. As the length of the PR target in PR equalisation increases, the gain
achieved using this novel technique consistently increases and reaches up to 1.2 dB in case
of EEPR4 target for a bit error rate of 10-5
Performance of turbo coded DS-CDMA systems in correlated and uncorrelated satellite communication channels
Word processed copy.Includes bibliographical references (leaves 82-88).This thesis aims at presenting the perfonnance of turbo codes in the correlated and uncorrelated satellite fading channel. Turbo codes are known to give very good perfonnance results in A WGN channels, especially for very large input message length codes or interleaver sizes. It can be shown that good perfonnance of the turbo codes can be achieved with small interleaver sizes in a satellite channel
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm