Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel to enable efficient and reliable transmission of coded symbols. In this paper, we propose using deep learning approaches to decode fixed-length and variable-length CS codes. Traditional encoding and decoding of fixed-length CS codes rely on look-up tables (LUTs), which is prone to errors that occur during transmission. We introduce fixed-length constrained sequence decoding based on multiple layer perception (MLP) networks and convolutional neural networks (CNNs), and demonstrate that we are able to achieve low bit error rates that are close to maximum a posteriori probability (MAP) decoding as well as improve the system throughput. Further, implementation of capacity-achieving fixed-length codes, where the complexity is prohibitively high with LUT decoding, becomes practical with deep learning-based decoding. We then consider CNN-aided decoding of variable-length CS codes. Different from conventional decoding where the received sequence is processed bit-by-bit, we propose using CNNs to perform one-shot batch-processing of variable-length CS codes such that an entire batch is decoded at once, which improves the system throughput. Moreover, since the CNNs can exploit global information with batch-processing instead of only making use of local information as in conventional bit-by-bit processing, the error rates can be reduced. We present simulation results that show excellent performance with both fixed-length and variable-length CS codes that are used in the frontiers of wireless communication systems.

The use of constrained sequence (CS) codes is important for the robust operation of transmission and data storage systems. While most analysis and development of CS codes have focused on fixed-length codes, recent research has demonstrated the advantages of variable-length CS codes. In our design of capacity-approaching variable-length CS codes, the construction of minimal sets is critical. In this paper, we propose an approach to construct minimal sets for a variety of constraints based on the finite-state machine (FSM) description of CSs. We develop three criteria to select the optimal state of the FSM that enables the design of a single-state encoder that results in the highest maximum possible code rate, and we apply these criteria to several constraints to illustrate the advantages that can be achieved. We then introduce FSM partitions and propose a recursive construction algorithm to establish the minimal set of the specified state. Finally, we present the construction of single-state capacity-approaching variable-length CS codes to show the improved efficiency and reduced implementation complexity that can be achieved compared with CS codes currently in use.

A technique was recently reported to construct high‐rate variable‐length constrained sequence codes. In this study, the authors outline an algorithm that simplifies the search procedure that is integral to that technique. This algorithm enables examination of a large search space limited only by length and/or number of codewords in order to determine codeword and sourceword lengths that result in high‐rate codes. They also describe a straightforward approach to construct codewords and sourcewords of the required lengths in order to complete the design of instantaneously‐decodeable capacity‐approaching codes that satisfy the specified sequence constraints. They provide results that demonstrate the usefulness of this approach.

We propose using variable-length constrained sequence codes to mitigate inter-cell interference (ICI) in all-bit-line flash memory with multi-page programming for single-level cell, multi-level cell, and triple-level cell flash memory structures. We outline constraints that mitigate ICI in these systems based on an observation of the Gray mapping of data symbols, and we derive the capacity of each constraint. Based on a finite state machine representation of each constraint, we construct variable-length constrained sequence codes with code rates very close to capacity to mitigate ICI in these flash memories. We then exploit the inherent error control capability of the proposed constrained sequence codes to alleviate error propagation. Finally, we integrate these codes with error control codes and present simulation results that demonstrate the enhanced bit error rate performance that can be achieved.

Balanced codes (also called DC‐free codes) are widely used in binary communication systems to increase the likelihood of accurate symbol recovery with practical demodulators. Guided scrambling (GS) is recognised as a viable approach to efficiently generate DC‐free binary sequences. In this study the authors extend the use of GS to generate balanced sequences of quadrature phase shift keyed (QPSK) symbols by using arithmetic from the ring of polynomials defined over the Galois field of four elements. In addition to ensuring adequate timing information and consistent decision thresholds to improve the performance of practical demodulators, balanced encoding of QPSK symbol sequences creates a null at DC in the spectrum of the equivalent complex baseband signal. This corresponds to a null at the centre frequency of the bandpass QPSK signal that enables the insertion of a pilot tone and avoidance of narrowband interference without filtering or distortion of the signal. The authors outline sufficient conditions for the generation of balanced GS QPSK sequences, and based upon these conditions the authors recommend scrambling polynomials and quotient selection criteria. The authors then present analytical and simulation results that confirm the generation of balanced sequences using this approach.

Constrained sequence codes are widely used to meet constraints imposed by digital communication systems. This study presents methods to evaluate the capacity of constrained codes that have multiple independently or dependently constrained signalling dimensions. The authors outline a straightforward analysis technique when the signalling dimensions are independent, and demonstrate how the capacity can be evaluated, estimated or upper bounded when the signalling dimensions are dependent. Their motivation for this work is capacity analysis of DC‐free codes with complex‐valued symbols, and they present results for these types of codes throughout the study.

The use of spectral shaping constrained codes is commonplace in baseband digital communication systems. In this study, the authors consider the use of constrained codes in bandpass systems through the design of DC‐free codes for the complex baseband representations of commonly used signalling constellations including quaternary phase shift keying, eight‐phase shift keying and sixteen quadrature amplitude modulation. The authors construct DC‐free codes for these signalling alphabets and present their spectral performance. They show that, similar to DC‐free codes for baseband systems, the variance of the running digital sum remains a good indicator of spectral performance and that Justesen's relationship between the sum variance and cut‐off frequency holds.

The authors investigate hybrid automatic repeat request (H-ARQ) schemes for spatially multiplexed multiple-input multiple-output (MIMO) systems with channel state information available only at the receiver. In particular, the authors compare the multiple H-ARQ scheme and the single H-ARQ scheme with repetition. The authors first propose a system model for symbol detection for the multiple H-ARQ processes, and then discuss joint and separate detection algorithms for both multiple H-ARQ and single H-ARQ. Simulation results show that with linear detection the single H-ARQ outperforms multiple H-ARQ in the high signal-to-noise ratio region. With the vertical Bell Labs space-time (V-BLAST) architecture, multiple H-ARQ always outperforms single H-ARQ. Additionally, joint detection always outperforms separate detection.

Multimode coding is a promising coding method owing to the simplicity of its code design and the attainment of high code rate. The authors present a multimode coding scheme for generating two-dimensional balanced t-conservative arrays for holographic storage. The multimode encoding process involves adding each unconstrained input array to a set of control arrays to form the selection set and selecting a pseudo-balanced t-conservative array from the selection set. By appropriately encoding the indices of the control arrays and using the remaining bits in the extra column or row appended to the selected pseudo-balanced t-conservative array to jointly balance the entire encoded array and to ensure that the extra column or row contains a sufficient number of transitions, the final output of the multimode encoder satisfies both the balanced and the t-conservative constraints. The decoding process is straightforward given the knowledge of the control array that was applied to the input array during the encoding process.

Constrained sequence codes are widely used to meet constraints imposed by digital storage and communication systems. This paper develops an algorithm for the construction of constrained codes that admit state-independent decoding. By partitioning the code into a group of alphabets, one for each state, a codebook is developed using this algorithm that will allow the code to be decoded at the receiver without the need for state information. Finally, we use this algorithm to construct DC-free runlength-limited (RLL) codes, and we present two highly efficient state-independent decodable DC-free RLL codes.

This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF(q) . We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q-1) -dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q=2p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu).

This paper proposes an extension of Knuthpsilas complementation method for constructing balanced codewords. By placing the encoding process in the context of a multimode code, we propose generating a number of alternative balanced words using Knuthpsilas method to represent each source word, and selecting the word with minimum squared weight (MSW) as the codeword in order to achieve improved spectral performance. Spectral results, which demonstrate increased suppression of low frequency components by up to 3 dB through the use of this approach, are presented.

Constrained sequence codes and pulse shapes are used to control signal characteristics in digital communication systems. This letter outlines a technique to construct codewords and pulse shapes to meet specified spectral constraints. Based on a block-coded representation of the signal, it is shown how symbol values can be evaluated to satisfy the most significant terms of a Fourier series representation of the desired spectral response. Several properties of the resulting signals are given, and examples are presented to confirm the validity of this approach.

Guided scrambling (GS) is a constrained coding technique that can be used in digital communication systems to control the characteristics of the encoded sequence. In each encoding interval, a GS encoder constructs a quotient selection set with a number of codeword candidates and selects the "best" candidate to represent the source word. Relationships between candidates in the quotient selection set impact the quality of the transmitted sequence. In particular, in some applications it is desired that the quotient relationship patterns (QRPs) be periodic, and in other applications, periodic QRPs are to be avoided. QRPs are determined by the scrambling polynomial. In this correspondence, we derive the general form for scrambling polynomials that generate all periodic quotient relationship patterns.

In order to minimize the interference between adjacent data arrays recorded in the same holographic volume, the patterns of 1's and 0's in each data array should be t- conservative, i.e., for a prescribed integer t, there should be at least t transitions of the form 1 rarr 0 or 0 rarr 1 in each column and row of the data array. In this paper, we present extensions to the algorithm proposed by Vardy et al. for encoding unconstrained binary arrays into t-conservative arrays. We set our work in the context of multimode codes. The multimode encoding process involves adding each input array to a set of control arrays to form a selection set, and selecting one that "best" satisfies the predefined selection criterion. We propose a new approach for construction of the control arrays, and demonstrate how the algorithm proposed by Vardy et al. is a special case of this approach. We also propose a novel approach for embedding the index of the control arrays into the encoded array, and propose alternatives for array selection.

In this paper the authors investigate the hybrid automatic repeat request (H-ARQ) schemes for spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems with channel state information available only at the receiver (CSIR). In particular, the authors compare the multiple H-ARQ scheme and the single H-ARQ scheme with repetition. The authors first propose a system model for symbol detection for the multiple H-ARQ processes, and then discuss joint detection algorithms and separate detection algorithms for both multiple H-ARQ and single H-ARQ. Simulation results show that with linear detection the single H-ARQ outperforms multiple H-ARQ in the high signal to noise ratio (SNR) region. With the vertical Bell Labs space time (V-BLAST) architecture, multiple H-ARQ always outperforms single H-ARQ and joint detection always outperforms separate detection.

Constrained codes are widely used in digital transmission systems and digital recording systems to generate constrained sequences with properties that comply with the given physical characteristics of the transmission or recording channels. The power spectral density (PSD) of encoded signals often plays an important role in the design of constrained codes. In this article the authors introduce a new approach for constructing finite-state sequential machine (FSSM) modeled encoders to satisfy desired spectral constraints. This approach involves constructing either a Mealy or a Moore FSSM to represent the encoder, and evaluating the state transition probabilities and codeword values in order that the PSD of the encoded signal meets a predefined shape.

Trellis-based error-control (EC) codes, such as convolutional or turbo codes, are integrated with guided scrambling (GS) multimode coding to generate DC-free GS-convolutional/turbo codes. On the basis of the generators of the convolutional/turbo code, we employ puncturing or flipping to ensure that the EC-coded sequences are DC-free. At the receiver, convolutional/turbo decoding is performed before GS decoding to circumvent the performance degradation that can occur when GS decoding is performed prior to EC decoding. Performance of the new DC-free GS-convolutional/turbo codes is evaluated in terms of both spectral suppression and bit error rate (BER). It is shown that the new codes can provide superior BER performance and approximately the same suppression of low frequencies as the conventional concatenation of convolutional/turbo codes and DC-free GS codes.

A list decoder generates a list of more than one codeword candidates, and decoding is erroneous if the transmitted codeword is not included in the list. This decoding strategy can be implemented in a system that employs an inner error correcting code and an outer error detecting code that is used to choose the correct codeword from the list. Probability of codeword error analysis for a linear block code with list decoding is typically based on the “worst case” lower bound on the effective weights of codewords for list decoding evaluated from the weight enumerating function of the code.

This paper investigates spectrum shaping in ultra-wideband (UWB) communications in order to introduce spectral nulls to limit interference with narrowband signals. Each transmitted symbol is represented by a "coded Gaussian monocycle pulse" in which Gaussian monocycles are weighted, delayed and summed in accordance with a designed codeword. The use of the Gaussian monocycle ensures that the UWB spectrum mask established by the Federal Communications Commission (FCC) is met, and the codeword is designed to generate a spectral null at the frequency or frequencies being used by existing narrowband devices. Signals obtained with different spectrum shapings (e.g., Butterworth, Chebyshev, elliptical) and by introducing nulls at multiple interference frequency bands are discussed. This approach can be used in various systems; as one application, we simulate the performance of a coded monocycle UWB system with a spectral null in the presence of narrowband interference (NBI) using single carrier block transmission with frequency domain equalization (SC-FDE), and compare its performance with that of an uncoded SC-FDE UWB system using a single Gaussian monocycle. Our results show that NBI can be effectively suppressed by transmitting and matched filtering the pulse with a spectral null at the interference frequency, therefore improving the robustness of UWB systems to NBI

In this paper, we develop a selective-repeat automatic-repeat-request (SR-ARQ) transmission scheme for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with non-linear preprocessing assuming perfect channel state information at both the transmitter and the receiver. In such a system in every time slot for ARQ transmission, there are a group of parallel channels of equal rate and differing error probability available between the transmitter and the receiver. Based on the knowledge of the signal to noise ratio (SNR) of these parallel channels, which is known to both the transmitter and the receiver, we first propose a dynamic parallel channel grouping rule to group parallel channels into effective channels, over which one packet is transmitted in one time slot, and we prove that this dynamic channel grouping rule will achieve maximum throughput. Furthermore, we adopt the dynamic channel assignment rule introduced by Shacham and Shin to assign packets to the effective channels in order to reduce resequencing delay. simulations in a frequency selective fading channel demonstrate the advantage of the proposed dynamic SR- ARQ transmission scheme over systems with a static parallel channel grouping rule and a static channel assignment rule in terms of throughput and resequencing delay.

In this paper, a type-II H-ARQ scheme with incremental redundancy is proposed for a turbo coded system that uses the sub-block structure. Sub-block recovery is applied to the decoder and a method to dynamically select the bits for retransmission according to knowledge of the decoding status is proposed. The new scheme benefits from both the frequent termination technique and the built-in CRC of the constituent recursive systematic convolutional codes of the turbo encoder. Simulations show that for a turbo coded system that employs the sub-block structure, the new type-II H-ARQ scheme outperforms both type-I H-ARQ with the sub-block recovery and the traditional type-II H-ARQ scheme without sub-block recovery on both the AWGN channel and the flat Rayleigh fading channel.

Line codes (in transmission systems) and recording codes (in magnetic and optical recording systems) are constrained sequence codes used to control the frequency-domain and time-domain characteristics of encoded signals. Pulse shaping is also used to achieve the required signal characteristics in a wide variety of communication systems. In this paper a new technique is outlined for the construction of codewords and pulse shapes to meet specified spectral constraints. The signal is interpreted as a block-coded sequence of overlapping or non-overlapping waveforms weighted by symbol values, and a general expression is given for the power spectral density of this signal. Based on this expression, the values of the symbols are evaluated in order to satisfy the most significant terms of a Fourier series representation of the desired spectral response. Examples and simulation results presented in this paper confirm the validity of this approach.

This paper investigates spectrum shaping in ultrawideband (UWB) communications in order to introduce spectral nulls to limit interference with narrowband signals. Each transmitted symbol is represented by a monocycle "coded" Gaussian pulse, where use of the monocycle Gaussian pulse ensures that the UWB spectrum mask established by the Federal Communications Commission (FCC) is met and where the codeword is designed to generate a spectral null at the frequency or frequencies being used by existing narrowband devices. Signals obtained with different spectrum shapings (e.g., Butterworth, Chebyshev, elliptical) and by introducing nulls at multiple interference frequency bands are discussed. The performance of a monocycle coded UWB system with a spectral null in the presence of narroband interference (NBI) using single carrier block transmission with frequency domain equalization (SC-FDE) is simulated and compared with that of an uncoded SC-FDE UWB system using a single Gaussian monocycle. Our results show that NBI can be effectively suppressed by transmitting and matched filtering the pulse with a spectral null at the interference frequency, therefore improving the robustness of SC-FDE UWB to NBI.

In this paper, we compare two selective-repeat automatic-repeat-request (SR-ARQ) protocols for spatial multiplexintiplexingg multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexed (OFDM) systems assuming perfect channel state information (CSI) only at the receiver. These two SR-ARQ protocols differ in the number of packets transmitted simultaneously. In one protocol, a single packet is transmitted on all subcarriers from all antennae at the same time. In the other protocol, multiple packets are simultaneously transmitted. For the latter protocol, we also consider schemes that differ in the way that the subcarriers transmitted from different antennae are grouped to support the transmission of multiple packets in parallel. We compare the throughput and the resequencing delay of these SR-ARQ protocols in a frequency selective fading channel. Simulation results suggest that in such a system, the single ARQ protocol is the best choice. If we have to transmit multiple packets in parallel, each packet should be transmitted over a subband of adjacent subcarriers emitted from all transmit antennae.

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2/sup p/-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2/sup p/-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2/sup p/-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.

In this paper, the concepts of effective weight enumerating function and generalized pairwise error event are introduced to predict the performance of linear block codes with list decoding. For the first time, a method to evaluate the actual effective codeword weights for a given code, rather than a lower bound on effective codeword weights, is proposed. Based on these actual effective codeword weights, the performance of a given code with list decoding can be predicted more accurately. We propose an analytical method to evaluate the performance of a given code with list decoding and consider terminated convolutional codes to show the validity of the analysis.

The complexity of conventional partial transmit sequence (PTS) increases largely with the number of subblocks. Conventional PTS requires generation of all partial transmit sequences through IFFT operations and optimization of the weighted partial transmit sequences. Previously published simplification methods only focus on simplifying this optimization process. In this paper, we propose additional techniques to reduce the complexity of PTS, including a new combining technique which we call sequence modification (SM). By use of SM, both the number of IFFT operations and the complexity of the optimization process can be significantly reduced. Our simulation results demonstrate that PTS using SM preserves the good PAPR performance of conventional PTS.

In this paper we integrate convolutional/turbo encoding with multimode encoding to generate dc-free convolutional/turbo codes. Based on the generators of error-control codes, we employ flipping or puncturing to ensure that the coded sequences are dc-balanced. At the receiver, the channel output is first decoded by a convolutional/turbo decoder (with consideration of detection when flipping is used during encoding), and then by a dc-free decoder. We show that good spectrum performance can be obtained at the cost of an increase in complexity in the encoder and that excellent bit error rate (BER) performance can be obtained particularly when source data logic values are not equiprobable.

DC-free codes and error-control (EC) codes are widely used in digital transmission and storage systems. To improve system performance in terms of code rate, bit-error rate (BER), and low-frequency suppression, and to provide a flexible tradeoff between these parameters, this paper introduces a new class of codes with both dc-control and EC capability. The new codes integrate dc-free encoding and EC encoding, and are decoded by first applying standard EC decoding techniques prior to dc-free decoding, thereby avoiding the drawbacks that arise when dc-free decoding precedes EC decoding. The dc-free code property is introduced into standard EC codes through multimode coding techniques, at the cost of minor loss in BER performance on the additive white Gaussian noise channel, and some increase in implementation complexity, particularly at the encoder. This paper demonstrates that a wide variety of EC block codes can be integrated into this dc-free coding structure, including binary cyclic codes, binary primitive BCH codes, Reed-Solomon codes, Reed-Muller codes, and some capacity-approaching EC block codes, such as low-density parity-check codes and product codes with iterative decoding. Performance of the new dc-free EC block codes is presented.

This paper investigate the extension of Golay complementary sequences to a larger family of sequences which we call multiple L-shift complementary sequences ( L 2 I ). It is well-known that the peak-to-average power ratio (PAPR) value of any Golay complementary sequence is less than or equal to 2. We show that the PAPR of each multiple L-shift complementary sequence is less than or equal to 2L. Other properties of multiple L-shift complementary sequences are also discussed.

The focus of this research work is the sub-optimal list decoding algorithms for parallel concatenated convolutional codes (PCCCs) which improve the frame error rate (FER) performance. Error events and weight spectra for convolutional codes and PCCCs are analyzed with emphasis on their effects on list decoding. We explain the inefficiencies of list decoding algorithms for PCCCs that use a list generated from the component codes, and introduce a new algorithm based on the sub-block structure that generates a list directly for the PCCC. The additional complexity of the new algorithm is low and does not depend on the complexity of the component code. Simulations on the additive white Gaussian noise (AWGN) channel show that the new algorithm can lower the frame error floor by more than one order of magnitude.

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer. We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasiregular construction are able to achieve higher coding gain over quasistatic fading channels than previously proposed space-time trellis and convolutional codes.

A new class of codes with high-order spectral nulls at zero frequency is introduced. The codes, called high-order spectral-null multimode codes, are constructed through state-dependent encoding by use of the guided-scrambling coding technique, and result in efficiently coded sequences with good low-frequency characteristics.

Sum-variance is a well-known metric for assessing the performance of dc-free codes (first-order spectral-null codes), however, as we show in this paper, it is unsuitable for comparing the magnitude of spectral components of high-order spectral-null (HOSN) codes at low frequencies. In this paper, we introduce a new performance metric for evaluating the spectrum compression of arbitrarily HOSN codes around zero frequency; we call this metric the low-frequency spectrum weight (LFSW). We show that the asymptotic low-frequency spectral components of Kth-order spectral-null codes (K/spl ges/1) are exclusively determined by the order K and the LFSW, and that the LFSW equals the zero-frequency value in the spectrum of the corresponding sequence of Kth-order running digital sum values. We derive this result for symbol-by-symbol encoding, and then extend it to block HOSN codes. We then derive a closed-form expression for the LFSW of HOSN codes constructed through state-independent encoding. Closed-form expressions for LFSW of first-order zero-disparity codes and for the asymptotic LSFW of maxentropic dc-free sequences are also given.

Selective mapping (SLM) and partial transmit sequences (PTS) are two approaches that significantly improve the statistics of the peak-to-average power ratio of an orthogonal frequency-division multiplexing signal. Guided scrambling (GS) is a multimode coding technique that is used to constrain the characteristics of encoded sequences in digital transmission and recording systems. We demonstrate the similarity of these techniques, and integrate GS coding with SLM and PTS. Our proposed GS-SLM and GS-PTS techniques result in very good PAPR performance with little error extension, and do not require transmission of side information.

In this letter, we present three new criteria for early stopping and error detection in turbo decoding. The approaches are based on monitoring the mean of the absolute values of the log-likelihood ratio of the decoded bits, which we show to be directly related to the variance of the metachannel. We demonstrate that this mean value increases as the number of errors in a frame decreases, and as a result, propose the simple mean-estimate criterion. We show that the systematic component of a terminated recursive systematic convolutional encoder used in turbo codes provides a built-in cyclic redundancy check (CRC). To further improve the performance, we also propose the mean-sign-change (MSC) criterion and the MSC-CRCeb criterion, in which a short external CRC code and the built-in CRC are concatenated with the MSC criterion.

We introduce a new method for enumerating codewords that can be applied to DC/sup 2/-constrained channels. Based on this method, two efficient algorithms for evaluating the number of codewords with specified characteristics are developed. Computer calculation results show that these algorithms are significantly more computationally efficient than other techniques developed to date.

Guided scrambling (GS) ensures the existence of good line code properties in encoded bit sequences through appropriate augmentation of the source bit stream prior to self-synchronizing scrambling. At the receiver, a framing algorithm is required in order to identify the location of the augmenting bits in the unscrambled bit sequence. This paper proposes and analyzes a self-framing algorithm for achieving frame synchronization in GS line codes. This technique is based on the observation of a large number of transitions at codeword boundaries in the encoded sequence, and does not require any additional overhead. Analysis and simulation results confirm the viability of this technique.

We derive a closed-form expression for the power spectral density of amplitude/phase-shift keyed bit sequences randomized through self-synchronizing scrambling when the source sequence is a stationary sequence of statistically independent bits. In addition to the dependence on the symbol pulse shape, duration, and the signal space values with which symbols are represented, we show that the power spectral density is dependent only on the probability of logic ones in the source bit stream, the period of the impulse response of the scrambling shift register, and the number of logic ones in this period. Our results confirm that optimum randomization results with use of primitive scrambling polynomials and poorest randomization occurs with "two-tap" polynomials of the form x/sup D/+1.

We derive several properties of guided scrambling (GS) encoders and the sequences they generate. We first highlight symmetrical aspects of the GS encoding mechanisms proposed to date, and then show that the existence of discrete components in the power spectrum of the pulse-amplitude-modulated encoded sequence can be predicted from the weight of the scrambling polynomial. We also show that with equiprobable source words, the block or continuous nature of the code has no effect on the statistics of the encoded sequence. We conclude by demonstrating how these properties simplify evaluation of the spectral characteristics of GS coded sequences.

Guided scrambling (GS) is a line coding technique developed specifically for high bit rate fiber optic transmission systems. This paper continues the development of GS coding by introducing more scrambling polynomials that can be used with this technique. First, a method is presented for constructing polynomials which can be used with balanced encoding. Then it is shown that these polynomials can be used as bases for large families of polynomials, an expansion whose usefulness is demonstrated with the presentation of power spectra for several code configurations. These results indicate that polynomials can be selected from these families to exercise control over average as well as worst-case statistics of the encoded bit stream, a property not available with any other single efficient, balanced line coding technique developed to date. Criteria for polynomial selection are given, and polynomials are recommended for several GS code configurations.>

The technique introduced has relatively simple encoding and decoding procedures which can be implemented at the high bit rates used in optical fiber communication systems. Because it is similar to the established technique of self-synchronizing scrambling but is also capable of guiding the scrambling process to produce a balanced encoded bit stream, the technique is called guided scrambling, (GS). The concept of GS coding is explained, and design parameters which ensure good line code characteristics are discussed. The performance of a number of guided scrambling configurations is reported in terms of maximum consecutive like-encoded bits, encoded stream disparity, decoder error extension, and power spectral density of the encoded signal. Comparison of guided scrambling with conventional line code techniques indicates a performance which approaches that of alphabetic lookup table codes with an implementation complexity similar to that of current nonalphabetic coding techniques.>