We extend earlier work on the design of convolutional code-specific CRC codes to$Q$-ary alphabets, with an eye toward$Q$-ary orthogonal signaling. Starting with distance-spectrum optimal, zero-terminated,$Q$-ary convolutional codes, we design$Q$-ary CRC codes so that the CRC/convolutional concatenation is distance-spectrum optimal. The$Q$-ary code symbols are mapped to a$Q$-ary orthogonal signal set and sent over an AWGN channel with noncoherent reception. We focus on$Q=4$, rate-1/2 convolutional codes in our designs. The random coding union bound and normal approximation are used in earlier works as benchmarks for performance for distance-spectrum-optimal convolutional codes. We derive a saddlepoint approximation of the random coding union bound for the coded noncoherent signaling channel, as well as a normal approximation for this channel, and compare the performance of our codes to these limits. Our best design is within 0.6 dB of the RCU bound at a frame error rate of 10−4.

This paper explores list decoding of convolutional and polar codes for short messages such as those found in the 5G physical broadcast channel. A cyclic redundancy check (CRC) is used to select a codeword from a list of likely codewords. One example in the 5G standard encodes a 32-bit message with a 24-bit CRC and a 512-bit polar code with additional bits added by repetition to achieve a very low rate of 32/864. This paper shows that optimizing the CRC length improves the Eb/N0performance of this polar code, where Eb/N0is the ratio of the energy per data bit to the noise power spectral density. Furthermore, even better Eb/ N0performance is achieved by replacing the polar code with a tail-biting convolutional code (TBCC) with a distance-spectrum-optimal (DSO) CRC. This paper identifies the optimal CRC length to minimize the frame error rate (FER) of a rate-1/5 TBCC at a specific value of Eb/ N0. We also show that this optimized TBCC/CRC can attain the same excellent Eb/ N0performance with the very low rate of 32/864 of the 5G polar code, where the low rate is achieved through repetition. We show that the proposed TBCC/CRC concatenated code outperforms the PBCH polar code described in the 5G standard both in terms of FER and decoding run time. We also explore the tradeoff between undetected error rate and erasure rate as the CRC size varies.

This paper presents designs and constructions of two classes of binary quasi-cyclic LDPC codes for correcting multiple random phased-bursts of erasures over the binary erasure channel. The erasure correction of codes in both classes is characterized by the cycle and adjacency structure of their Tanner graphs. Erasure correction of these codes is a very simple process which requires only modulo-2 additions. The codes in the second class are capable of correcting locally and globally distributed phased-bursts of erasures with a two-phase iterative erasure-correction process.

Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.

Protograph-based LDPC and generalized LDPC (G-LDPC) codes have the advantages of a simple design procedure and highly structured encoders and decoders. The design of such “protograph-based codes” relies on what is effectively a computer-based search. As such, following Gallager, it is prudent to restrict the search to a “good ensemble,” for example, an ensemble whose minimum distance grows linearly with codeword length. A good ensemble can also mean one with good stopping set, trapping set, or pseudocodeword properties. In this paper, ensemble codeword weight enumerators for finite-length LDPC and G-LDPC codes based on protographs were derived, and then the asymptotic case was considered. The asymptotic results allow us to determine whether or not the typical relative minimum distance in the ensemble grows linearly with codeword length. Then, the codeword weight enumerator technique is adapted to yield ensemble stopping set, trapping set, and pseudocodeword enumerators for protograph LDPC and G-LDPC codes. In this case, the asymptotic results allow us to determine whether or not the typical relative smallest stopping set size, trapping set size, and pseudoweight grows linearly with codeword length. Trapping set enumerators for G-LDPC code ensembles represent a more complex problem which we do not consider here.

This paper studies the performance of a serial turbo code on two simplified rectangular-grain models of recording media for two dimensional magnetic recording at a density of more than 0.5 bits/grain. We derive one-dimensional (1D) and two-dimensional (2D) rectangular-grain media models and from these present finite-state-machine (FSM) representations. From the FSM for the 1D model we computed achievable information rates assuming independent and uniformly distributed (i.u.d.) binary inputs. From the (approximate) FSM for the 2D model, we present a detector. We then present a serial turbo code architecture with constituent convolutional codes that is capable of achieving 80\% of i.u.d. capacity for the 1D model and 65\% of the average of published upper and lower bounds on capacity for the 2D model.

Protograph-based generalized LDPC (GLDPC) codes have the advantages of a simple design procedure and highly structured encoders and decoders. Recently, a technique for computing ensemble weight enumerators for GLDPC codes has been published. In the current paper, we investigate the existence of typical minimum distance for protograph-based GLDPC codes. That is, we first upper bound the ensemble weight enumerators for finite-length GLDPC codes based on protographs, and then we consider the sum of weight enumerators. The results allow us to determine whether or not the typical minimum distance in the ensemble grows linearly with codeword length. We provide conditions on the connections of degree-2 variable nodes to constraint nodes (short block codes) to have typical minimum distance. These conditions are related to the minimum distances of the constraint nodes.

The error-rate floor phenomenon associated with iterative LDPC decoders has delayed the use of LDPC codes in certain communication and storage systems. Error floors are known to generally be caused by so-called trapping sets which have the effect of confounding the decoder. In this paper, we introduce two techniques that lower the error-rate floors for LDPC-coded partial response (PR) channels which are applicable to magnetic and optical storage. The techniques involve, via external measures, "pinning" one of the bits in each problematic trapping set and then letting the iterative decoder proceed to correct the rest of the bits. We also extend our earlier work on generalized-LDPC (G-LDPC) decoders for error-floor mitigation on the AWGN channel to partial response channels. Our simulations on PR1 and EPR4 channels demonstrate that the floor for the code chosen for this study, a 0.78(2048,1600) quasicyclic LDPC code, is lowered by orders of magnitude, beyond the reach of simulations. Because simulation in the floor region is so time-consuming, a method for accelerating such simulations is essential for research in this area. In this paper, we present an extension of Richardson's importance sampling technique for estimating the level of error floors.

Recently, pseudocodewords of Tanner graphs of LDPC codes have been used to explain the behavior of iterative decoders for these codes. In this paper, finite-length pseudocodeword weight enumerators for protograph-based generalized-LDPC code ensembles are obtained. Then asymptotic results are derived from the finite-length results by letting the block length go to infinity. The asymptotic results allow us to determine whether or not the typical minimum pseudocodeword weight grows linearly with codeword length. We give examples with Hamming component codes.

One of the most significant impediments to the use of LDPC codes in many communication and storage systems is the error-rate floor phenomenon associated with their iterative decoders. The error floor has been attributed to certain subgraphs of an LDPC code's Tanner graph induced by so-called trapping sets. We show in this paper that once we identify the trapping sets of an LDPC code of interest, a sum-product algorithm (SPA) decoder can be custom-designed to yield floors that are orders of magnitude lower than floors of the the conventional SPA decoder. We present three classes of such decoders: (1) a bi-mode decoder, (2) a bit-pinning decoder which utilizes one or more outer algebraic codes, and (3) three generalized-LDPC decoders. We demonstrate the effectiveness of these decoders for two codes, the rate-1/2 (2640,1320) Margulis code which is notorious for its floors and a rate-0.3 (640,192) quasi-cyclic code which has been devised for this study. Although the paper focuses on these two codes, the decoder design techniques presented are fully generalizable to any LDPC code.

While LDPC codes have been widely acclaimed in recent years for their near-capacity performance, they have not found their way into many important applications. For some cases, this is due to their increased decoding complexity relative to the classical coding techniques. For other cases, this is due to their inability to reach very low bit error rates (e.g., 10-12) at low signal-to-noise ratios (SNRs), a consequence of the error rate floor phenomenon associated with iterative LDPC decoders. In the present paper, we make strides in the low-floor problem by identifying the weaknesses of the code under study and applying compensatory counter-measures. These counter-measures include: modifying the code itself, modifying the decoder, or adding a properly designed outer algebraic code. Our results demonstrate that each of these techniques can successfully lower an LDPC code's floor, and that, for the code under study, an outer BCH code appears to be particularly effective. All of our results are based on FPGA decoder simulations and so they are reliable and repeatable.

In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

We derive tight closed-form approximations of symbol and bit error probability on maximum-likelihood sequence detection (MLSD) of Nyquist-rate and oversampled OFDM systems over the AWGN, flat and frequency-selective quasi-static Rayleigh fading channels. Contrary to common knowledge, we show that on a frequency-selective channel, clipping at the transmitter leads to achievable frequency-diversity and performance gain over unclipped systems with MLSD. We derive closed-form expressions of the diversity and the performance gain over the no-clipping case, as well as the optimal clipping ratio for a given system. We show that such diversity and performance gain are a result of both clipping and channel frequency-selectivity, and they do not occur on the AWGN and flat fading channels.We also present a new near-optimum detection algorithm that achieves the MLSD performance bound with a few iterations for the clipped OFDM systems with both high and low clipping levels on the AWGN and flat Rayleigh fading channels. For the frequency selective channel, we present a receiver design that utilizes the advantage of clipping to some extent. We consider rectangular QAM signaling in this paper.

Protograph-based LDPC codes have the advantages of a simple design (or search) procedure and highly structured encoders and decoders. These advantages have also been exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. Recently, a technique for computing ensemble weight enumerators and stopping set enumerators for protograph-based LDPC codes has been published. In the current paper, we extend those results to protograph-based G-LDPC codes. That is, we first derive ensemble weight and stopping set enumerators for finite-length G-LDPC codes based on protographs, and then we consider the asymptotic case. In the weight enumerator case, the asymptotic results allow us to determine whether or not the typical minimum distance in the ensemble grows linearly with codeword length. In the stopping set enumerator case, the asymptotic results allows us to determine whether or not the typical smallest stopping set size grows linearly with codeword length.

We examine the performance of a rate-0.9 structured irregular repeat-accumulate (S-IRA) code on a perpendicular magnetic recording (PMR) channel with media noise. To account for the presence of data-dependent media noise, a pattern-dependent-noise-predictive (PDNP) channel detector is employed, in which the prediction filters are trained using the LMS algorithm. We compare the error rate performance of the S-IRA code with that of a Reed-Solomon (RS) code of the same length and rate, with the PDNP detector present in both cases. Our results show that the S-IRA code achieves a gain of over 1 dB relative to the RS code for sector error rates down past 10-4, but only if the columns of its H-matrix are properly permuted. We have also estimated that the linear density gain attainable by the S-IRA code relative to the RS code is about 8% for the operating point we have chosen.

We derive very tight closed-form lower bounds of symbol/bit error probability for the maximum-likelihood sequence detection (MLSD) on the clipped OFDM channels with AWGN and flat block fading. We present a new near-optimum detection algorithm that achieves the MLSD bound with a few iterations for the clipped OFDM channel with both high and low clipping levels. We consider both Nyquist-rate and oversampled OFDM systems with rectangular QAM signaling.

We derive very tight closed-form lower bounds of symbol/bit error probability for maximum-likelihood sequence detection (MLSD) on clipped OFDM channels with frequency- selective quasi-static Rayleigh fading. Contrary to common knowledge, we show that as a result of both clipping and channel frequency-selectivity, clipping at the transmitter leads to achievable frequency-diversity and performance gain over unclipped systems with MLSD. We derive closed-form expressions of the diversity and the performance gain over the no-clipping case, as well as the optimal clipping ratio for a given system. We consider both Nyquist-rate and oversampled OFDM systems with rectangular QAM signaling.

We propose a link adaptation technique for IEEE 802.11n MIMO-OFDM systems with convolutional coding. The technique dynamically selects the best modulation and coding scheme (MCS) based on channel conditions and on the medium access control (MAC) layer performance (coded BER or PER) requested by applications. We show that the coded performance at decoder output can be modeled as a function of decoder-input uncoded BER and the code rate. For MIMO-OFDM systems with different modulation types for different spatial streams at each subcarrier, we propose a simple and accurate method for computing the BER for each spatial stream mixed from different subcarriers. We also discuss approaches for searching and selecting the MCS.

In this paper, a novel methodology for designing structured generalized low-density parity-check (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call low-density parity-check (LDPC) code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

In this letter, we present design techniques for structured irregular repeat-accumulate (S-IRA) codes with low error-rate floors. These S-IRA codes need not be quasi-cyclic, permitting flexibility in code dimension, length, and rate. We present a simple ensemble estimate of the level of the error-rate floor of finite-length IRA codes on the additive white Gaussian noise channel. This performance estimate provides guidance on the choice of IRA code column weights which yield low floors. We also present two design algorithms for S-IRA codes accompanied by software- and hardware-based performance results which demonstrate their low floors. Lastly, we present two design algorithms for multirate S-IRA code families implementable by a single encoder/decoder

In this paper we analyze the performance of an LDPC-coded OFDM system with adaptive bit-loading based on mutual information. We demonstrate that the mutual information between the transmitted binary sequence and the soft information input to LDPC decoder well characterizes the performance of the LDPC-coded system, independent of the modulation type and the number of carriers. We design mutual information-based adaptive bit-loading and power allocation algorithms for LDPC-coded OFDM systems to maximize throughput performance under a packet-error rate constraint. To characterize the performance of the system under study, we derive the achievable information rate and a throughput upper bound for the system

We provide a new approach to analyzing the capacity of the clipped OFDM channel. Our analysis shows that existing clipping models lead to drastically underestimated capacity computations. Our approach eschews the so-called clipping noise and treats the clipper more analytically. We also introduce and analyze the clipping ratio threshold, above which error-free communication is guaranteed in an ideal clipped OFDM channel. The results are extended to the clipped OFDM channel with AWGN

We present a low-complexity soft demapper that computes bit log-likelihood ratios (LLRs) while suppressing orthogonal frequency division multiplexing (OFDM) inter-carrier interference (ICI). The proposed demapper consists of two stages and can be realized in a fully-parallel architecture. We examine uncoded and low-density parity-check (LDPC) coded performance over frequency-selective Doppler fading channels. We compare the coded and uncoded performances of our demapper with those of an MMSE detector with successive detection (MMSE-SD) and also the match-filter (MF) bound. We show that the proposed demapper achieves optimal performance in the system operating-SNR region. Given the proposed near-optimal demapper, complex receiver designs that iterate between the detector and the decoder may not be worthwhile

In this paper, we present design techniques for structured extended irregular repeat-accumulate (SeIRA) codes with low error-rate floors. These SeIRA codes permit flexibility in code dimension, length, and rate, while facilitating encoder/decoder implementation due to their structure. We present a design algorithm for SeIRA codes and software-based performance results which demonstrate their low floors. Then we present two design algorithms for multi-rate SeIRA code families implementable by a single encoder/decoder. Lastly, we present the performances of SeIRA codes on the single-carrier independent Rayleigh fading channel and SeIRA-coded OFDM over a frequency-selective correlated fading channel

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for Rayleigh fading channels, instead of implementing the complex design procedures targeted, specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also show that eIRA codes designed for the BuEC enjoy the advantage of efficient encodability and a lower error-rate floor. Finally, we demonstrate that it is the distribution of the number of faded bits per codeword which determines the difference between correlated and uncorrelated fading channel performance. Perfect channel state information is assumed in this paper.

In this paper, we propose a dual-mode decoding technique for product codes in which the rows and columns may comprise either Reed-Solomon (RS) codewords or LDPC codewords. The first decoding mode uses standard hard-decision decoding algorithms on the rows and columns, after which a maximum-likelihood (ML) packet-erasure decoding algorithm is employed for the column code in a second decoding mode. For the second mode, the column code takes on a different character in which "slices" of the row code are treated as packets which are symbols in the column code. The ML decoder for this packet-level column code resolves the erroneous packets (erasures) flagged by the row code or a packet-level CRC code during the first decoding mode. By exploring an application to tape storage, we demonstrate that this dual-mode decoding method can dramatically improve the performance of a product code. Moreover, the complexity added by the second mode is manageable.

We present a vector-based approach to modeling an orthogonal frequency division multiplexing (OFDM) system with intentional clipping and oversampling at the transmitter. We show how to model the clipping noise as a function of the transmitted signal. We also show that a clipped OFDM channel can be considered to be similar to a MIMO channel, with the addition of a clipping indicator vector which indicates which samples are clipped. This approach allows many existing equalization and detection techniques to be implemented. We then present an iterative MMSE receiver based on this model, and show that it outperforms existing techniques. We also present maximum-likelihood estimation of the clipping indicator vector. We show how to apply coding to this vector to improve performance, a technique we call coded-clipping.

In a recent paper, Yang et al. presented the class of extended irregular repeat-accumulate (eIRA) codes which are efficiently encodable LDPC codes possessing very low error-rate floors and are appropriate for code rates 1/2 or greater. While efficiently encodable, the left-most (n-k)-by-k submatrix of an eIRA code parity-check matrix is random in nature, making efficient decoder implementation problematic. In the present paper, we present structured eIRA codes. We first present some ensemble results for the general class of eIRA codes, after which the subclass of structured eIRA (SeIRA) codes is defined. Software- and hardware-based performance results for SeIRA code designs (rates 0.5 to 0.9) are then presented.

In this letter, we compute achievable information rates for finite-sized synchronous code-division multiple-access (CDMA) systems, and low-density parity-check (LDPC) codes are adopted to approach the achievable rates. The associated coding-spreading tradeoff problem is also considered using these results. We assume binary random spreading sequences, and the computed achievable rates are averaged over ensembles of spreading sequences. Unlike most prior papers, which analyze the spectral efficiency of large CDMA systems under Gaussianity assumptions (channel inputs and/or multiple-access interference), we make no such assumptions. In order to display the coding-spreading tradeoff, we plot the minimum required signal-to-noise ratio for reliable transmission as a function of information rate. It is shown that the coding-spreading tradeoff favors all coding (i.e., no spreading) when the optimal joint multiuser detector/decoder is employed, whereas for systems with a suboptimal multiuser detector and single-user decoders, there generally exists an optimal balance between coding and spreading. We also provide simulation results on the performance of LDPC-coded synchronous CDMA systems which approach the information-theoretic limits we have computed.

This correspondence presents an importance sampling (IS) simulation scheme for the soft iterative decoding on loop-free multiple-layer trees. It is shown that this scheme is asymptotically efficient in that, for an arbitrary tree and a given estimation precision, the required number of samples is inversely proportional to the noise standard deviation. This work has its application in the simulation of low-density parity-check (LDPC) codes.

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes (a class of efficiently encodable LDPC codes) for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for the Rayleigh fading channel, instead of implementing the complex design procedures targeted specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also derive a new channel statistic, the distribution of the number of faded bits per codeword which determines the difference between the performance of correlated and uncorrelated (ideally interleaved) fading channels.

This paper proposes an importance sampling design for the codeword error rate estimation of low-density parity-check codes. An error set partitioning method is introduced to reduce the error boundary complexity and to improve the simulation efficiency. This is a follow-up to the work in (B. Xia et al., 2003).

The performance evaluation of trellis-coded modulation (TCM) schemes and intersymbol interference (ISI) channels via union bounds involves a transfer function computation of an error-state diagram which enumerates all possible error events. This letter presents a new method for obtaining equivalent error-state diagrams with a reduced number of states.

This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (10/sup 3//spl les/n/spl les/10/sup 4/) and high rate (R/spl ges/3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10/sup -9/ are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.

In this paper, we take an information-theoretic approach to obtaining optimal code rates for error-control codes on a magnetic storage channel approximated by the Lorentzian channel. Code rate optimality is in the sense of maximizing the information-theoretic user density along a track. To arrive at such results, we compute the achievable information rates for the Lorentzian channel as a function of SNR and channel density, and then use these information rate calculations to obtain optimal code rates and maximal user densities. The achievable information rate calculations exploit the pioneering work of Arnold and Loeliger (2001) (see also H.D. Pfister and P.H. Siegel, 2001) who recently presented a technique for accurately estimating achievable information rates for binary-input intersymbol interference channels with additive white Gaussian noise.

We compute achievable rates for synchronous code-division multiple-access (CDMA) systems and study the associated coding-spreading tradeoff problem using these results. We assume random spreading sequences and the computed achievable rates are averaged over ensembles of spreading sequences. Unlike most prior work, which analyzed the spectral efficiency of large CDMA systems under Gaussianity assumptions (inputs and multiple access interference), we make no such assumptions. In order to display the coding-spreading tradeoff, we plot the required minimum SNR for reliable transmission as a function of information rate. It is shown that the coding-spreading tradeoff favors all coding (i.e., no spreading) when the optimal multiuser detector (MUD) is employed, whereas for systems with suboptimal MUDs and single-user decoding, there generally exist optimal code rates. We also provide simulation results on the performance of LDPC-coded synchronous CDMA systems which approach the information-theoretic limits we have computed.

We introduce an importance sampling scheme for linear block codes with message-passing decoding. This novel scheme overcomes an existing difficulty in the IS practice that requires codebook information. Experiments show large IS gains for single parity-check codes and short-length block codes. For medium-length block codes, IS gains in the order of 10/sup 3/ and higher are observed at high signal-to-noise ratio.

We consider in this paper a convolutionally coded synchronous DS-CDMA system with iterative multiuser detection and decoding. Each user's bits are convolutionally encoded, interleaved, and differentially encoded before being transmitted over the multiuser CDMA channel. In contrast to previous work in this area, a differential encoder is inserted to effect an interleaver gain. The receiver consists of a soft-in soft-out multiuser detector followed by a bank of iterative decoders matched to the convolutional code-differential encoder combination. Dramatic gains over systems which contain no differential encoder are demonstrated. We also show that there exists an optimal code rate under a bandwidth constraint. The gains and optimal code rates are demonstrated via bit error rate simulations and density evolution analyses.

We consider in this paper the possibility of a cyclic or quasi-cyclic LDPC code as the complete error control system in a magnetic recording channel. Thus, we compare the performance of selected LDPC codes with two Reed-Solomon (RS) code schemes on an EPR4 channel, with particular emphasis on their performance in noise bursts (induced by thermal asperities). We find some very promising initial results in that the LDPC codes are very robust against large noise burst (128 bits long), and are superior to the RS schemes examined in the measurable error rate region. The extent to which they are superior depends on the particular LDPC scheme involved, and the results provide motivation for further investigation in this area.

A number of papers have been published on the concatenation of an outer code with a partial response (PR) channel, where the outer code is a turbo code, a convolutional code, or a low-density parity-check code. This paper deals with the second case, assuming EPR4 and modified extended EPR4 (MEEPR4) partial response (PR) targets. The goals in this work include (1) the joint optimization of interleaver and precoder for a fixed outer convolutional code and PR target, (2) the choice of optimal code rate for both PR targets assuming a Lorentzian model, and (3) an assessment of the performance of these codes in the presence of thermal asperities. We introduce mathematical and algorithmic tools for accomplishing these goals and present simulation results that support our approach. Among the positive results is the ability to lower the well-known error rate floor of these concatenated schemes for arbitrary PR channels.

We present the design and analysis of parallel and serial concatenated codes with iterative decoding for class IV partial response (PR4) signaling. Code rates of the form K/sub 0//(K/sub 0/+1), for K/sub 0/=4, 8, 16, 32, and 64, are considered. We show that the 1/(1/spl oplus/D/sup 2/) (Tomlinson) precoder, first proposed by Wolf and Ungerboeck (1991) for trellis coded PR4 channels, is effective for both parallel and serial concatenations, but the error-rate "floor" is relatively high for the serial case. This leads to new interleaver and precoder designs for serial concatenations, the latter involving an examination of the conditional distance enumerator of each precoded PR4 channel. The new precoders substantially reduce the floors of the serial concatenated codes, but degrade the performance of the parallel concatenated codes. For a bit-error rate of 10/sup -5/, the best parallel and serial concatenated codes come within 1.7 dB of a lower bound on the capacity limit for PR4 signaling on an additive white Gaussian noise channel.

A number of papers have recently been published on the concatenation of an outer code with a partial response (PR) channel, where the outer code is a turbo code, a convolutional code, or a low density parity check code. This paper deals with the second case assuming EPR4 and modified extended EPR4 (MEEPR4) partial response targets. The goal in this work is the joint optimization of interleaver and precoder for a fixed outer convolutional code and PR target. We introduce mathematical and algorithmic tools for accomplishing this goal and present simulation results which support our approach. Among the positive results is the ability to lower the well-known error rate floor of these concatenated schemes for arbitrary partial response channels.

We consider the serial concatenation (via interleavers) of a convolutional code with two differential encoders (or accumulate codes). Simulations of such a concatenated scheme using a rate 1/2 outer convolutional code (sometimes punctured to increase the overall rate) show that, at high rates, the bit error rate (BER) and frame error rate (FER) performance of these codes is significantly better than a concatenation with only one accumulate code and a parallel concatenated convolutional code (PCCC) of similar complexity. An intuitive explanation for the performance of these codes is also given.

We discuss a procedure for designing high rate serial concatenated convolutional codes (SCCCs) via puncturing for BPSK/QPSK channels. Rate 3/4, 7/8, and 15/16 SCCCs are considered with constituent encoder memory size m up to 4. We have also analytically found that the error rate floors for the designed codes are much lower than those of the PCCCs for the rates of interest.

We modify the iterative soft-output Viterbi algorithm (SOVA) for partial response (PR) channel and examine its performance for parallel and serial concatenated codes on a precoded Class IV partial response (PR4) channel. We present a SOVA that differs slightly from what appears in the literature and compare the performance of the two versions. Code rates of the form k/sub 0//k/sub 0/+1 (k/sub 0/=4, 8, and 64) are considered. Our simulations indicate that the loss at P/sub b/=10/sup -5/ suffered by the SOVA, relative to the APP algorithm, is at most 1.2 dB for parallel concatenations and at most 1.6 dB for serial concatenations.

We consider the concatenation of a high rate punctured convolutional code and a precoded intersymbol interference (ISI) channel separated by an interleaver. The goal in this work is to develop design techniques for the interleaver and precoder for a given ISI channel where the design criterion is to obtain the lowest error rate floor. Our results show that an S-random interleaver is an appropriate choice for this system and that the optimal precoder may be selected through the use of what we call truncated conditional distance enumerators. Simulation results support the techniques developed.

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers.

We discuss a procedure for designing high-rate turbo-codes via puncturing, with applications to BPSK/QPSK channels. Rates in the form k/(k+1), 2/spl les/k/spl les/16, are considered for constituent encoders with memory sizes m=3 and 4. The algorithm includes the selection of constituent encoder generator polynomials, puncture patterns, and interleavers with the goal of maximizing the minimum codeword weight for weight-two and weight-three inputs. The performance of the proposed codes are found via computer simulation and are observed in each case to be less than 0.9 dB (m=3), and 0.75 dB (m=4), from their respective channel capacity limits at a bit-error rate of 10/sup -5/. We consider two applications of punctured turbo-codes.

We discuss a procedure for the design of high rate turbo codes via puncturing, with applications to BPSK/QPSK channels. Rates in the form k/(k+1), 2/spl les/k/spl les/16, are considered for constituent encoders with memory size m=4. The algorithm includes the selection of constituent encoder generator polynomials, puncture patterns, and interleavers with the goal of maximizing the minimum codeword weight for weight-two and weight-three inputs. The bit error rate (BER) performance of the proposed codes are found via computer simulation and are observed in each case to be about 0.7 dB from their respective channel capacity limits at a BER of 10/sup -5/.

We discuss the applicability of high rate turbo codes for magnetic recording, citing in particular the attractiveness of interleaver gain as opposed to coding gain. We then examine the performance of rate 4/5, 8/9, and 16/17 turbo codes on a PRA-equalized magnetic recording channel at a user density of S/sub u/=2.0. Simulation results show that a gain of 7.1 dB relative to the uncoded situation is attainable at an error rate of 10/sup -5/ for the rate 4/5 and 8/9 codes, whereas the rate 16/17 code achieves a gain of 6.5 dB.

Assuming the Lorentzian channel model and linearity, we compare the performance of various DC-free codes combined with PR1 signaling on the magnetic recording channel. In addition to several codes which have been presented in the literature, we consider two high rate DC-free codes (rates 8:9 and 16:18) which we have designed for the PR1 situation. Two types of Viterbi receivers are examined: one whose trellis is matched to the PR1 channel, and another whose trellis is matched to the combined trellises of the PR1 channel and the code constraint. Our results demonstrate that high rate codes with a loose charge constraint (narrow spectral null) are to be preferred over lower rate codes with a tight constraint (wide null). We also demonstrate that the rate 16:18 code, which possesses both a high rate and a tight constraint (charge Q is bounded as |Q|/spl les/4), offers the best performance among the codes considered.

We examine the design of modulation systems for meteor burst communications. In particular, we present a technique which allows the designer to determine the signal set size and the signaling rate which maximize the throughput per meteor burst. The technique, which involves the capacity and cutoff rate from information theory, is applied to a variable coding rate scheme and a variable signaling rate scheme, for both coherent MPSK (M=2, 4, 8) and noncoherent MFSK (M=2, 4, 8, 16, 32). As a fringe benefit, the method proposed also provides estimates on achievable throughputs.

We examine the design of a communication link involving the data transfer from a small, low-orbit satellite to a ground station, but through a geostationary satellite. The advantage of this approach is that a single ground station, which tracks only the geostationary satellite, may be shared by a multiplicity of small satellites. Our goal is to select certain small satellite parameters-signaling rate, small satellite antenna beamwidth, modulation scheme and coding scheme-which maximize the data throughput in bits/day. Our approach uses orbital simulations of this scenario together with theoretical analysis based on the channel capacity and cutoff rate. The throughput achievable by several practical coding schemes is also examined.

A practical definition of an erasure is presented and leads to new expressions for correct and incorrect decoding probabilities for Reed-Solomon codes, assuming an incomplete decoder. The main benefit of this approach is that, in contrast with the usual approach, one is able to analytically demonstrate the performance improvement provided by errors-and-erasures decoding relative to errors-only decoding. A technique is presented for evaluating the performance of Reed-Solomon codes for both types of decoding on an interleaved burst error channel such as is seen in digital magnetic tape recording. Several illustrative examples are included.>

Two classes of nonbinary convolutional codes for error control in communication systems employing q-ary orthogonal signaling are discussed. These classes include as special cases, the dual-k codes and the codes treated by B.D. Trumpis (1975). The types of code, extensions of previous bounds on free distance, the noncatastrophic condition for these codes, and conditions for catastrophic error propagation are described. Codes obtained by a computer search, optimal in that the truncated transfer function bound on the probability of symbol error is minimized, are presented. It is shown how good convolutional codes can be constructed from cyclic block codes. The performance of some of these codes over additive white Gaussian noise channels, Rayleigh channels, and partial-band interference channels is also discussed.>

The generalized cross correlation approach to time delay estimation is tested with direct sequence and frequency hopping spread spectrum signals in white and narrowband noise. The performance of six correlation filters [1] are evaluted via Monte Carlo simulation where sample variances and mean-square errors (MSE) are estimated for several signal-to-noise ratios. The results allow one to choose an optimal filter according to a minimum mean square error criterion. Additionally, the sample variances are compared to the lower bound developed in [2].