469 research outputs found
Deriving Good LDPC Convolutional Codes from LDPC Block Codes
Low-density parity-check (LDPC) convolutional codes are capable of achieving
excellent performance with low encoding and decoding complexity. In this paper
we discuss several graph-cover-based methods for deriving families of
time-invariant and time-varying LDPC convolutional codes from LDPC block codes
and show how earlier proposed LDPC convolutional code constructions can be
presented within this framework. Some of the constructed convolutional codes
significantly outperform the underlying LDPC block codes. We investigate some
possible reasons for this "convolutional gain," and we also discuss the ---
mostly moderate --- decoder cost increase that is incurred by going from LDPC
block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010;
revised August 2010, revised November 2010 (essentially final version).
(Besides many small changes, the first and second revised versions contain
corrected entries in Tables I and II.
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
Rateless Coding for Gaussian Channels
A rateless code-i.e., a rate-compatible family of codes-has the property that
codewords of the higher rate codes are prefixes of those of the lower rate
ones. A perfect family of such codes is one in which each of the codes in the
family is capacity-achieving. We show by construction that perfect rateless
codes with low-complexity decoding algorithms exist for additive white Gaussian
noise channels. Our construction involves the use of layered encoding and
successive decoding, together with repetition using time-varying layer weights.
As an illustration of our framework, we design a practical three-rate code
family. We further construct rich sets of near-perfect rateless codes within
our architecture that require either significantly fewer layers or lower
complexity than their perfect counterparts. Variations of the basic
construction are also developed, including one for time-varying channels in
which there is no a priori stochastic model.Comment: 18 page
Spatially Coupled Turbo-Like Codes
The focus of this thesis is on proposing and analyzing a powerful class of codes on graphs---with trellis constraints---that can simultaneously approach capacity and achieve very low error floor. In particular, we propose the concept of spatial coupling for turbo-like code (SC-TC) ensembles and investigate the impact of coupling on the performance of these codes. The main elements of this study can be summarized by the following four major topics. First, we considered the spatial coupling of parallel concatenated codes (PCCs), serially concatenated codes (SCCs), and hybrid concatenated codes (HCCs).We also proposed two extensions of braided convolutional codes (BCCs) to higher coupling memories. Second, we investigated the impact of coupling on the asymptotic behavior of the proposed ensembles in term of the decoding thresholds. For that, we derived the exact density evolution (DE) equations of the proposed SC-TC ensembles over the binary erasure channel. Using the DE equations, we found the thresholds of the coupled and uncoupled ensembles under belief propagation (BP) decoding for a wide range of rates. We also computed the maximum a-posteriori (MAP) thresholds of the underlying uncoupled ensembles. Our numerical results confirm that TCs have excellent MAP thresholds, and for a large enough coupling memory, the BP threshold of an SC-TC ensemble improves to the MAP threshold of the underlying TC ensemble. This phenomenon is called threshold saturation and we proved its occurrence for SC-TCs by use of a proof technique based on the potential function of the ensembles.Third, we investigated and discussed the performance of SC-TCs in the finite length regime. We proved that under certain conditions the minimum distance of an SC-TCs is either larger or equal to that of its underlying uncoupled ensemble. Based on this fact, we performed a weight enumerator (WE) analysis for the underlying uncoupled ensembles to investigate the error floor performance of the SC-TC ensembles. We computed bounds on the error rate performance and minimum distance of the TC ensembles. These bounds indicate very low error floor for SCC, HCC, and BCC ensembles, and show that for HCC, and BCC ensembles, the minimum distance grows linearly with the input block length.The results from the DE and WE analysis demonstrate that the performance of TCs benefits from spatial coupling in both waterfall and error floor regions. While uncoupled TC ensembles with close-to-capacity performance exhibit a high error floor, our results show that SC-TCs can simultaneously approach capacity and achieve very low error floor.Fourth, we proposed a unified ensemble of TCs that includes all the considered TC classes. We showed that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. This unified ensemble not only helps us to understand the connections and trade-offs between the TC ensembles but also can be considered as a bridge between TCs and generalized low-density parity check codes
A survey of digital television broadcast transmission techniques
This paper is a survey of the transmission techniques used in digital television (TV) standards worldwide. With the increase in the demand for High-Definition (HD) TV, video-on-demand and mobile TV services, there was a real need for more bandwidth-efficient, flawless and crisp video quality, which motivated the migration from analogue to digital broadcasting. In this paper we present a brief history of the development of TV and then we survey the transmission technology used in different digital terrestrial, satellite, cable and mobile TV standards in different parts of the world. First, we present the Digital Video Broadcasting standards developed in Europe for terrestrial (DVB-T/T2), for satellite (DVB-S/S2), for cable (DVB-C) and for hand-held transmission (DVB-H). We then describe the Advanced Television System Committee standards developed in the USA both for terrestrial (ATSC) and for hand-held transmission (ATSC-M/H). We continue by describing the Integrated Services Digital Broadcasting standards developed in Japan for Terrestrial (ISDB-T) and Satellite (ISDB-S) transmission and then present the International System for Digital Television (ISDTV), which was developed in Brazil by adopteding the ISDB-T physical layer architecture. Following the ISDTV, we describe the Digital Terrestrial television Multimedia Broadcast (DTMB) standard developed in China. Finally, as a design example, we highlight the physical layer implementation of the DVB-T2 standar
Information-Coupled Turbo Codes for LTE Systems
We propose a new class of information-coupled (IC) Turbo codes to improve the
transport block (TB) error rate performance for long-term evolution (LTE)
systems, while keeping the hybrid automatic repeat request protocol and the
Turbo decoder for each code block (CB) unchanged. In the proposed codes, every
two consecutive CBs in a TB are coupled together by sharing a few common
information bits. We propose a feed-forward and feed-back decoding scheme and a
windowed (WD) decoding scheme for decoding the whole TB by exploiting the
coupled information between CBs. Both decoding schemes achieve a considerable
signal-to-noise-ratio (SNR) gain compared to the LTE Turbo codes. We construct
the extrinsic information transfer (EXIT) functions for the LTE Turbo codes and
our proposed IC Turbo codes from the EXIT functions of underlying convolutional
codes. An SNR gain upper bound of our proposed codes over the LTE Turbo codes
is derived and calculated by the constructed EXIT charts. Numerical results
show that the proposed codes achieve an SNR gain of 0.25 dB to 0.72 dB for
various code parameters at a TB error rate level of , which complies
with the derived SNR gain upper bound.Comment: 13 pages, 12 figure
Bandwidth efficient CCSDS coding standard proposals
The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations
- …