Matched information rate codes for Partial response channels (original) (raw)
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IEEE Transactions on Information Theory, 1999
The multilevel coding approach of Imai and Hirakawa is used to construct trellis-matched codes for binary-input partial-response channels. For the codes to be trellis-matched, the signal constellations are selected according to certain constraints, but no conditions are imposed on the component codes. New codes for the (1 0 D)(1 + D) n channel compare favorably to existing codes.
Improved trellis-coding for partial-response channels
IEEE Transactions on Magnetics, 2000
New code design methods and Viterbi detector architectures are presented for high-rate trelliscoded partialresponse (TCPR) systems. The methods, which extend the matched-spectral-null (MSN) coding technique, use novel code constraints and time-varying detector trellis structures to reduce path memory requirements by as much as a factor of two, relative to previously reported codes, while retaining the other attractive features of MSN codes. The design methods and corresponding time-varying trellis structures are illustrated with several examples.
Low complexity LDPC codes for partial response channels
2002
This paper constructs and analyzes a class of regular LDPC codes with column weight of j=2, in contrast to the often-used j≥3 setting. These codes possess several significant features. First, they are free of 6-cycle, and can be easily constructed for a large range of code rates. Secondly, the parity check matrix of the code can be represented by a simple set, thus lending itself to a low complexity implementation. Thirdly, the proposed codes concatenated with proper precoder outperform j≥3 LDPC codes for partial response (PR) channels. Finally, they exhibit block error statistics significantly different from LDPC codes with j≥3, making them more compatible with Reed-Solomon error correction codes. The LDPC coded partial response (PR) channel is formulated as a dynamical model and analyzed using density evolution technique, which is used to explain the behavior of the concatenated system. A high rate (8/9) code with block size 4608 is constructed as an example, and its bit error rate (BER), block error statistics, and decoding convergence over ideal PR channel are investigated using simulation. The simulation results are consistent with the density evolution analysis, both indicating that LDPC codes with j=2 are attractive for partial response channels. PR targets for magnetic recording channel are used as examples to illustrate the performance of the proposed codes.
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory, 2001
We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry. Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief-propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution.
Maximum transition run codes for generalized partial response channels
IEEE Journal on Selected Areas in Communications, 2001
A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at dc and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrained or-constrained are studied. Deterministic finite-state transition diagrams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between () constraints and MTR() constraints is clarified. Code design methodologies that are based on look-ahead coding in combination with violation detection/substitution as well as on state splitting are used to obtain several specific constructions of high-rate MTR codes.
We consider block and convolutional codes for improving the reliability of data transmission over the binary precoded noisy (1 -D ) partial response channel. We concentrate on a class of codes for which the maximum likelihood decoder, matched to the encoder, precoder, and the channel has the same trellis structure as the encoder. Thus, doubling the number of states due to the channel memory is avoided. We show that the necessary and sufficient condition to belong to this class is that all codewords be of the same parity. The Reed-Muller and Golay codes belong to this class.
On Construction of Rate-Compatible Low-Density Parity-Check Codes
IEEE Communications Letters, 2004
In this letter, we present a framework for constructing rate-compatible low-density parity-check (LDPC) codes. The codes are linear-time encodable and are constructed from a mother code using puncturing and extending. Application of the proposed construction to a type-II hybrid automatic repeat request (ARQ) scheme with information block length = 1024 and code rates 8/19 to 8/10, using an optimized irregular mother code of rate 8/13, results in a throughput which is only about 0.7 dB away from Shannon limit. This outperforms existing similar schemes based on turbo codes and LDPC codes by up to 0.5 dB.
IEEE Transactions on Magnetics, 2001
The performance of low-density parity-check (LDPC) codes serially concatenated with generalized partial response channels is investigated. Various soft-input/soft-output detection schemes suitable for use in iterative detection/decoding systems are described. A low-complexity near-optimal detection algorithm that incorporates soft-input reliability information and generates soft-output reliability information is presented. A reduced-complexity algorithm for decoding LDPC codes is described. Simulation results on the performance of high-rate LDPC codes on generalized PR channels at various recording densities are presented. These results indicate that a judicious selection of the inner detector target polynomial and the choice of a good LDPC code are important in optimizing the performance of the overall recording system. Furthermore, the results also show that iterative detection/decoding schemes using LDPC codes can outperform hard-decision decoding of Reed-Solomon codes by over 2 dB at a sector error rate of 10 3 .
Deterministic Design of Low-Density Parity-Check Codes for Binary Erasure Channels
IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference, 2007
We propose a deterministic method to design irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels (BEC). Compared to the existing methods, which are based on the application of asymptomatic analysis tools such as density evolution or Extrinsic Information Transfer (EXIT) charts in an optimization process, the proposed method is much simpler and faster. Through a number of examples, we demonstrate that the codes designed by the proposed method perform very closely to the best codes designed by optimization. An important property of the proposed designs is the flexibility to select the number of constituent variable node degrees P. The proposed designs include existing deterministic designs as a special case with P = N-1, where N is the maximum variable node degree. Compared to the existing deterministic designs, for a given rate and a given δ > 0, the designed ensembles can have a threshold in δ-neighborhood of the capacity upper bound with smaller values of P and N. They can also achieve the capacity of the BEC as N, and correspondingly P and the maximum check node degree tend to infinity. Index Terms-channel coding, low-density parity-check (LDPC) codes, binary erasure channel (BEC), deterministic design. I. INTRDOUCTION Low-Density Parity-Check (LDPC) codes have received much attention in the past decade due to their attractive performance/complexity tradeoff on a variety of communication channels. In particular, on the Binary Erasure Channel (BEC), they achieve the channel capacity asymptotically [1-4]. In [1],[5],[6] a complete mathematical analysis for the performance of LDPC codes over the BEC, both asymptotically and for finite block lengths, has been developed. For other types of channels such as the Binary Symmetric Channel (BSC) and the Binary Input Additive White Gaussian Noise (BIAWGN) channel, only asymptotic analysis is available [7]. For irregular LDPC codes, the problem of finding ensemble
Design of Low-Density Parity-Check Codes with Optimized Complexity-Rate Tradeoff
2009
The optimal complexity-rate tradeoff for errorcorrecting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the joint optimization of rate and decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallel-update schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsic-information transfer chart analysis of the code. Under certain mild conditions, the complexity measure is a convex function of the variable edge-degree distribution of the code, allowing an efficient design of complexity-optimized LDPC codes using convex optimization methods. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform thresholdoptimized codes at long block lengths.