The design of efficiently-encodable rate-compatible LDPC codes - [transactions papers]

We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are linear-time encodable with simple shift-register circuits. For a block length of 1200 bits the codes outperform optimized irregular LDPC codes and extended irregular repeat-accumulate (eIRA) codes for all puncturing rates 0.6~0.9 (base code performance is almost the same) and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve.     

Combined Selective Mapping and Binary Cyclic Codes for PAPR Reduction in OFDM Systems

In this paper, we consider reduction of PAPR in OFDM systems with BPSK subcarriers by combining SLM and binary cyclic codes. This combining strategy can be used for both error correction and PAPR reduction. We decompose a binary cyclic code into direct sum of two cyclic subcodes: the correction subcode used for error correction and the scrambling subcode for PAPR reduction. The transmitted OFDM signal is selected that achieves minimum PAPR, from the set of binary cyclic codewords. The received signal can be easily decoded without the need of any side information. Simulations show that the proposed scheme with simplex code as scrambling subcode achieves good PAPR reduction.     

Variable-rate space-time block codes in M-ary PSK systems

We consider a multiple antenna system when combined array processing with space-time coding is used. We present variable rate space-time block codes for two, three, and four transmit antennas and optimize the transmit power so that the average bit-error rate (BER) is minimized. Numerical results show that this optimum power allocation scheme provides significant gain over the equal power allocation scheme. We then classify all the variable rate space-time block codes having the same code rates and identify the unique code that achieves the lowest BER. We explicitly compute the performance of the variable rate codes over a Rayleigh-fading channel. The proposed variable rate space-time block codes are useful for unequal error protection in multiple transmit antenna systems.     

PAPR Reduction of OFDM Signals Using Partial Transmit Sequences and Reed-Muller Codes

This letter proposes a modified PTS technique using binary Reed-Muller (RM) codes for error correction and PAPR control in BPSK OFDM systems. A RM code is divided into the direct sum of a correcting subcode for encoding information bits and a scrambling subcode for encoding PAPR bits. The transmitted signal of the resulting OFDM sequence is selected with minimum PAPR from a number of candidates which are codewords of a coset of the scrambling subcode. We consider the RM codes in natural and cyclic orderings. Numerical results show that RM codes in cyclic ordering achieve better performance in PAPR reduction than RM codes in natural ordering.     

Multilevel single-error-correcting codes

A class of pseudocyclic multilevel single-error-correcting code is described, and an example of a 5-level code is given. Some of these codes have parameters. such as block length, number of parity-check digits etc., which are unrealisable with strictly cyclic codes. Pseudocyclic codes share the mathematical structure of cyclic codes, and thus are relatively simple to implement in practical form     

空时编码在OFDM系统中的应用

研究了空时分层码（LSTC）、空时分组码（STBC）和空时网格码（STTC）3种典型的空时编码技术。讨论了各自的编码原理和译码原理。以空时分组码为重点,介绍了OFDM系统的基本原理,将空时分组码和OFDM技术相结合,对STBC-OFDM系统的基本模型加以探讨,理论分析系统接收端的信噪比性能,通过M atlab仿真对收发...     

Quasi-cyclic dyadic codes in the Walsh-Hadamard transform domain

A code is s-quasi-cyclic (s-QC) if there is an integer s such that cyclic shift of a codeword by s-positions is also a codeword. For s = 1, cyclic codes are obtained. A dyadic code is a code which is closed under all dyadic shifts. An s-QC dyadic (s-QCD) code is one which is both s-QC and dyadic. QCD codes with s = 1 give codes that are cyclic and dyadic (CD). We obtain a simple characterization of all QCD codes (hence of CD codes) over any field of odd characteristic using Walsh-Hadamard transform defined over that finite field. Also, it is shown that dual a code of an s-QCD code is also an s-QCD code and s-QCD codes for a given dimension are enumerated for all possible values of s.     

Joint Processing of Zero‐Forcing Detection and MAP Decoding for a MIMO‐OFDM System

We propose a new bandwidth‐efficient technique that achieves high data rates over a wideband wireless channel. This new scheme is targeted for a multiple‐input multiple‐output orthogonal frequency‐division multiplexing (MIMO‐OFDM) system that achieves transmit diversity through a space frequency block code and capacity enhancement through the iterative joint processing of zero‐forcing detection and maximum a posteriori (MAP) decoding. Furthermore, the proposed scheme is compared to the coded Bell Labs Layered Space‐Time OFDM (BLAST‐OFDM) scheme.     

Variable shortened-and-punctured Reed-Solomon codes for packet loss protection

Techniques using Reed-Solomon (RS) codes to recover lost packets in digital video/audio broadcasting and packet switched network communications are reviewed. Usually, different RS codes and their corresponding encoders/decoders are designed and utilized to meet different requirements for different systems and applications. We incorporate these techniques into a variable RS code and present encoding and decoding algorithms suitable for the variable RS code. A mother RS code can be used to produce a variety of RS codes and the same encoder/decoder can be used for all the derivative codes, with adding/detecting zeros, removing some parity symbols and adding erasures. A VLSI implementation for erasure decoding of the variable RS code is described and the achievable performance is quantitatively analyzed. A typical example shows that the signal processing speed is up to 2.5 Gbits/second and the processing delay is less than one millisecond, when integrating the decoder on a single chip. Therefore, the proposed algorithm and the encoder/decoder can universally be utilized for different applications with various requirements, such as transmission data rate, packet length, packet loss protection capacity, as well as layered protection and adaptive redundancy protection in DVB/DAB, Internet and mobile Internet communications.     

Complement block coding for reduction in peak-to-average power ratio of OFDM signals

In this article a new coding scheme, complement block coding (CBC), is proposed to reduce the PAPR of OFDM signals. This method utilizes the complement bits that are added to the original information bits, which can effectively reduce the PAPR of OFDM signals with random frame size N and the coding rate R /spl les/ (N - k)/N, where k is a positive integer and k /spl les/ N/2. The performance results obtained with CBC are given and compared with that of some well known schemes, such as simple block coding, modified simple block coding, simple odd parity code, and cyclic coding, for the same purpose. The results show that at the same coding rate 3/4, CBC can achieve almost the same performance as SBC and MSBC, but with lower complexity, and the same performance can be obtained with a higher coding rate using CBC. The PAPR reductions of CBC with coding rate (N - 1)/N are almost the same as with a coding rate less than (N - 1)/N, but almost the twice as these of SOPC when N /spl ges/ 16. Moreover, we can find that PAPR is the lowest for all block codes using CBC with coding rate 3/4. So modified CBC (MCBC) is also proposed and analyzed, combined with the subblock processing technique to make CBC effective for OFDM systems with large frame sizes. The flexibility in coding rate choice and low complexity make the proposed CBC more suitable for random frame size with high coding rate and can also provide error detection.     

基于扰码的CDMA-BLAST系统研究

该文提出一种新的CDMA下行链路空时编码方案,用正交扩频码区分不同用户,用扰码区分不同发射天线,由于扰码具有良好的自相关和互相关特性,可以在不牺牲码域资源的前提下,以增加少量的复杂度换取较好的链路性能。仿真结果显示,采用正交扩频码和扰码二级扩频的空时编码方案可以取得较好的链路性能。     

Some randomized code constructions from group actions

We study in this paper randomized constructions of binary linear codes that are invariant under the action of some group on the bits of the codewords. We study a non-Abelian randomized construction corresponding to the action of the dihedral group on a single copy of itself as well as a randomized Abelian construction based on the action of an Abelian group on a number of disjoint copies of itself. Cyclic codes have been extensively studied over the last 40 years. However, it is still an open question as to whether there exist asymptotically good binary cyclic codes. We argue that by using a slightly more complex group than a cyclic group, namely, the dihedral group, the existence of asymptotically good codes that are invariant under the action of the group on itself can be guaranteed. In particular, we show that, for infinitely many block lengths, a random ideal in the binary group algebra of the dihedral group is an asymptotically good rate-half code with a high probability. We argue also that a random code that is invariant under the action of an Abelian group G of odd order on k disjoint copies of itself satisfies the binary Gilbert-Varshamov (GV) bound with a high probability for rate 1/k under a condition on the family of groups. The underlying condition is in terms of the growth of the smallest dimension of a nontrivial F/sub 2/-representation of the group and is satisfied by roughly most Abelian groups of odd order, and specifically by almost all cyclic groups of prime order.     

Performance analysis of channel estimation for LDPC-coded OFDM system in multipath fading channel

In this paper, the channel estimation techniques for Orthogonal Frequency Division Multiplexing （OFDM） systems based on pilot arrangement are studied and we apply Low Density Parity Check （LDPC） codes to the system of IEEE 802.16a with OFDM modulation. First investigated is the influence of channel cstimation schemes on LDPC-code based OFDM system in static and multipath fading channels. According to the different propagation environments in 802.16a system, a dynamic channel estimation scheme is proposed. A good irregular LDPC code is designed with code rate of 1/2 and code length of 1200. Simulation results show that the performance of LDPC coded OFDM system proposed in this paper is better than that of the convolution Turbo coded OFDM system proposed in IEEE standard 802.16a.     

LDPC codes and convolutional codes with equal structural delay: a comparison

We compare convolutional codes and LDPC codes with respect to their decoding performance and their structural delay, which is the inevitable delay solely depending on the structural properties of the coding scheme. Besides the decoding performance, the data delay caused by the channel code is of great importance as this is a crucial factor for many applications. Convolutional codes are known to show a good performance while imposing only a very low latency on the data. LDPC codes yield superior decoding performance but impose a larger delay due to the block structure. The results obtained by comparison will also be related to theoretical limits obtained from random coding and the sphere packing bound. It will be shown that convolutional codes are still the first choice for applications for which a very low data delay is required and the bit error rate is the considered performance criterion. However, if one focuses on a low signal-to-noise ratio or if the obtained frame error rate is the base for comparison, LDPC codes compare favorably.     

High-rate burst-error-correcting recurrent codes (Corresp.)

A bound and construction are presented for high-rate burst-error-correcting recurrent codes. The bound is an upper bound on the block length in terms of the total redundancy used in decoding, the redundancy per block, and the burst length. The construction uses a block-code parity-check matrix as the first block of the recurrent code parity-check matrix. For a block code it is typical to find that only a portion of the redundancy need be used to detect a burst. Any block code for which this is true can be used in the construction. The recurrent code is then related as follows to the block code from which it is constructed. 1) The recurrent code block length is the same as the block-code block length. 2) The total redundancy used in decoding the recurrent code is the same as the block-code redundancy per block. 3) The recurrent code redundancy per block is the same as the block-code redundancy required for burst detection only. 4) The recurrent code is of higher rate than the block code. 5) The recurrent code requires a guard space between bursts but otherwise corrects the same bursts as the block code. It is shown that, when certain well-known cyclic codes are used in the construction, the resulting recurrent codes are close to the upper bound.     

Generalized bounds on the crest-factor distribution of OFDM signals with applications to code design

In this paper generalized bounds on the crest-factor (CF) distribution in orthogonal frequency-division multiplexing (OFDM) transmission for both independent and dependent subcarriers are derived. Here, the latter situation represents the coded case. For independent subcarriers, a general path for bounding practical constellations is provided. Moreover, a complete characterization of their asymptotic behavior is devised and discussed. The results are shown to carry over to the spherical constellations improving on recent results. For dependent subcarriers, the focus is mainly on binary codes where bounds on the CF distribution are obtained in terms of the distance distributions and their duals. The asymptotic behavior of codes is analyzed and it is shown that the upper bound on the effective crest-factor of a large class of Bose-Chaudhuri-Hocquenghem (BCH) codes behaves asymptotically as /spl radic/logN. Finally, two applications of the results to code design are presented: first, fixed phase shifts on the subcarriers for all codewords are used and an algorithm to calculate the phase shifts is designed. That way, it is proved that the effective CF of any binary code can be scaled to be of order /spl radic/logN for large N without sacrificing on rate. Furthermore, the same approach is applied to calculation of the phases of redundant subcarriers for each codeword. It is shown by simulations that the values can be effectively chosen so that the CF is significantly reduced with nonexponential complexity.     

Performance comparison of space-time block coded and cyclic delay diversity MC-CDMA systems

Spatial diversity is a widely applied technique for enhancing wireless system performance since it greatly reduces the detrimental effects of multipath fading. Space-time block codes have been considered the best choice for transmit diversity in narrowband environments, but their use in broadband channels is questionable due to their inability to pick up multipath diversity. However, when used in conjunction with an MC-CDMA system, they achieve not only full spatial but also variable multipath diversity depending on the employed spreading. In comparison, cyclic delay diversity is an attractive approach to achieve spatial and multipath diversity. Its simplicity and conformability with current standards makes it desirable for multicarrier systems. Previous studies suggest that CDD is only advantageous with an outer channel code for OFDM systems. In this article, we compare STBCs and CDD applied to an MC-CDMA system in terms of complexity and performance. It is shown that for an MC-CDMA system, CDD benefits from spreading and channel coding that makes it very competitive with STBCs, particularly since it is applicable to any number of transmit antennas with no loss in rate.     

Some long cyclic linear binary codes are not so bad

We show that when an inner linear cyclic binary code which has an irreducible check polynomial is concatenated with an appropriately chosen maximal-distance-separable outer code, then the overall code is cyclic OverGF(2). Using this theorem, we construct a number of linear cyclic binary codes which are better than any previously known. In particular, by taking the inner code to be a quadratic residue code, we obtain linear cyclic binary codes of lengthN, rateR, and distanceD geq (1 - 2R)N/ sqrt{2 log N}, which compares favorably with the BCH distanceD sim (2 ln R^{-1})N/log N, although it still fails to achieve the linear growth of distance with block length which is possible with noncyclic linear concatenated codes. While this construction yields many codes, including several with block lengths greater than10^{10^5}, we have not been able to prove that there are arbitrarily long codes of this type without invoking the Riemann hypothesis or the revised Artin conjecture, as the existence of long codes of our type is equivalent to the existence of large primespfor which the index of 2 is(p - 1)/2.     

MIMO-OFDM系统中LDPC编码和自适应比特功率分配算法研究

该文提出了将LDPC码与自适应比特功率分配相结合应用于MIMO-OFDM系统中的算法。文中分别对两种不同码率的LDPC码与自适应OFDM,自适应MIMO-OFDM相结合的算法进行了仿真,同时还对未编码的自适应OFDM以及MIMO-OFDM进行了仿真。仿真结果显示,在相同的传输带宽以及相同的传输信息量（即数据净码率）情况下,采用低码率LDPC编码的自适应OFDM系统的性能要比未编码的自适应OFDM以及自适应 MIMO-OFDM系统的性能好;采用高码率LDPC编码的自适应OFDM系统的性能比未编码的自适应OFDM系统性能好,但比未编码的自适应MIMO-OFDM系统性能差。     

Hermitian codes for frequency-hop spread-spectrum packet radio networks

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for frequency-hop transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for certain partial-band interference channels, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.