This document provides updates to IEEE Std 802.16's MIB for the MAC, PHY and asso- ciated management procedures in order to accommodate recent extensions to the standard.

IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems Draft Amendment: Management Information Base Extensions

Coding within noisy communications channels is essential but a theoretical maximum rate defines the rate at which information can be reliably transmitted on this noisy channel. Capacity-achieving codes with an explicit construction eluded researchers until polar codes were proposed. However, whilst asymptotically reaching channel capacity these require increasing code lengths, and hence increasingly complex hardware implementations. It would be beneficial to address architectures and decoding processes to reduce polar code decoder complexity both in terms of the number of processing elements required, but also the number of memory elements and the number of steps required to decode a codeword. Beneficially architectures and design methodologies established by the inventors address such issues whilst reducing overall complexity as well as providing methodologies for adjusting decoder design based upon requirements including, but not limited to, cost (e.g. through die area) and speed (e.g. through latency, number of cycles, number of elements etc).

Methods and systems for decoding polar codes

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2m lies in a complementary set of size 2k+1, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2 m. A new 2h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them

Complementary Sets, Generalized Reed–Muller Codes, and Power Control for OFDM

This paper provides a comprehensive analysis of nonbinary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edge-weight labeling, and refer to the former as the unconstrained nonbinary protograph-based LDPC codes (U-NBPB codes) and to the latter as the constrained nonbinary protograph-based LDPC codes (C-NBPB codes). Equipped with combinatorial definitions extended to the nonbinary domain, ensemble enumerators of codewords, trapping sets, stopping sets, and pseudocodewords are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. An EXIT chart tool for computing the iterative decoding thresholds of protograph-based LDPC codes is presented, followed by several examples of finite-length U-NBPB and C-NBPB codes with high performance. Throughout this paper, we provide accompanying examples, which demonstrate the advantage of nonbinary protograph-based LDPC codes over their binary counterparts and over random constructions. The results presented in this paper advance the analytical toolbox of nonbinary graph-based codes.

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Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2^m lies in a complementary set of size 2^{k+1}, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new 2^h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them.

Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM

This paper presents two low-complexity reliability-based message-passing algorithms for decoding LDPC codes over non-binary finite fields. These two decoding algorithms require only finite field and integer operations and they provide effective trade-off between error performance and decoding complexity compared to the non-binary sum product algorithm. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields.

Two Low-Complexity Reliability-Based Message-Passing Algorithms for Decoding Non-Binary LDPC Codes

Binary Golay complementary pairs exist for quite limited lengths whereas the binary Z-complementary pairs (ZCPs) are available for more lengths. Therefore, the ZCPs can potentially find more engineering applications. In this letter, we propose a novel construction of binary and nonbinary ( $q$ -ary for even $q$ ) ZCPs based on generalized Boolean functions. Both even- and odd-length ZCPs can be obtained by the proposed construction. Moreover, the sequence length, the width of zero correlation zone (ZCZ), and the constellation size are all very flexible. A family of ZCPs with large ZCZ widths is presented based on our construction where the width of ZCZ is larger than half of the sequence length. This proposed family includes some previous results on binary ZCPs as special cases.

A Novel Construction of Z-Complementary Pairs Based on Generalized Boolean Functions

Golay complementary sequences and complementary sets have been proposed to deal with the high peak-to-average power ratio (PAPR) problem in orthogonal frequency division multiplexing (OFDM) system. The existing constructions of complementary sets based on generalized Boolean functions are limited to lengths, which are powers of two. In this paper, we propose novel constructions of binary and nonbinary complementary sets of non-power-of-two length. Regardless of whether or not the length of the complementary set is a power of two, its PAPR is still upper bounded by the size of the complementary set. Therefore, the constructed complementary sets can be applied in practical OFDM systems where the number of used subcarriers is not a power of two. In addition, while the binary Golay complementary pairs exist only for limited lengths, the constructed binary complementary sets of size 4 exist for more lengths with PAPR at most 4.

Complementary Sets of Non-Power-of-Two Length for Peak-to-Average Power Ratio Reduction in OFDM

Due to ideal autocorrelation and cross-correlation properties, complete complementary codes (CCCs) can be employed in CDMA systems to eliminate the multiple-access interference. In this letter, we propose a direct general construction of CCCs from cosets of the first-order Reed-Muller codes, which includes previous results as a special case. The larger number of CCCs constructed by our method can provide advantages in applications to cellular CDMA systems.

/pdf/complete-complementary-codes-and-generalized-reed-muller-gabx1aq8bo.pdf

Complete complementary codes and generalized reed-muller codes

In this letter, a novel construction of Z-complementary sequence (ZCS) sets is proposed based on generalized Boolean functions. The constructed ZCS set is optimal since the set size achieves the theoretical upper bound. In addition, the proposed construction is a direct construction without the aid of other special sequences. In this letter, the peak-to-average power ratio (PAPR) property of the constructed ZCS sets is also investigated. Furthermore, the set sizes, flock sizes, sequence lengths, and the widths of zero correlation zones of the constructed ZCS sets are all very flexible.

Chao-Yu Chen

Papers

Two Low-Complexity Reliability-Based Message-Passing Algorithms for Decoding Non-Binary LDPC Codes

A Novel Construction of Z-Complementary Pairs Based on Generalized Boolean Functions

Complementary Sets of Non-Power-of-Two Length for Peak-to-Average Power Ratio Reduction in OFDM

Complete complementary codes and generalized reed-muller codes

Optimal Z-Complementary Sequence Sets With Good Peak-to-Average Power-Ratio Property