The code-based McEliece cryptosystem is a promising candidate for post-quantum cryptography. The sender encodes a message, using a public scrambled generator matrix, and adds a random error vector. In this work, we consider q-ary codes and restrict the Lee weight of the added error symbols. This leads to an increased error correction capability and a larger work factor for information-set decoding attacks. In particular, we consider codes over an extension field and use the one-Lee error channel, which restricts the error values to Lee weight one. For this channel model, generalized concatenated codes can achieve high error correction capabilities. We discuss the decoding of those codes and the possible gain for decoding beyond the guaranteed error correction capability.

Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced.

The Hurwitz lattice provides the densest four-dimensional packing. This fact has motivated research on four-dimensional Hurwitz signal constellations for optical and wireless communications. This work presents a new algebraic construction of finite sets of Hurwitz integers that is inherently accompanied by a respective modulo operation. These signal constellations are investigated for transmission over the additive white Gaussian noise (AWGN) channel. It is shown that these signal constellations have a better constellation figure of merit and hence a better asymptotic performance over an AWGN channel when compared with conventional signal constellations with algebraic structure, e.g., two-dimensional Gaussian-integer constellations or four-dimensional Lipschitz-integer constellations. We introduce two concepts for set partitioning of the Hurwitz integers. The first method is useful to reduce the computational complexity of the symbol detection. This suboptimum detection approach achieves near-maximum-likelihood performance. In the second case, the partitioning exploits the algebraic structure of the Hurwitz signal constellations. We partition the Hurwitz integers into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is larger than in the original set. This enables multilevel code constructions for the new signal constellations.

Error correction coding based on soft‐input decoding can significantly improve the reliability of non‐volatile flash memories. This work proposes a soft‐input decoder for generalised concatenated (GC) codes. GC codes are well suited for error correction in flash memories for high reliability data storage. The authors propose GC codes constructed from inner extended binary Bose–Chaudhuri–Hocquenghem (BCH) codes and outer Reed–Solomon (RS) codes. The extended BCH codes enable an efficient hard‐input decoding. Furthermore, a low‐complexity soft‐input decoding method is proposed. This bit‐flipping decoder uses a fixed number of test patterns and an algebraic decoder for soft‐decoding. An acceptance criterion for the final candidate codeword is proposed. Combined with error and erasure decoding of the outer RS codes, this acceptance criterion can improve the decoding performance and reduce the decoding complexity. The presented simulation results show that the proposed bit‐flipping decoder in combination with outer error and erasure decoding can outperform maximum‐likelihood decoding of the inner codes.

Generalized concatenated (GC) codes with soft-input decoding were recently proposed for error correction in flash memories. This work proposes a soft-input decoder for GC codes that is based on a low-complexity bit-flipping procedure. This bit-flipping decoder uses a fixed number of test patterns and an algebraic decoder for soft-input decoding. An acceptance criterion for the final candidate codeword is proposed. Combined with error and erasure decoding of the outer Reed-Solomon codes, this bit-flipping decoder can improve the decoding performance and reduce the decoding complexity compared to the previously proposed sequential decoding. The bit-flipping decoder achieves a decoding performance similar to a maximum likelihood decoder for the inner codes.

This work proposes a construction for low-density parity-check (LDPC) codes over finite Gaussian integer fields. Furthermore, a new channel model for codes over Gaussian integers is introduced and its channel capacity is derived. This channel can be considered as a first order approximation of the additive white Gaussian noise channel with hard decision detection where only errors to nearest neighbors in the signal constellation are considered. For this channel, the proposed LDPC codes can be decoded with a simple non-probabilistic iterative decoding algorithm similar to Gallager's decoding algorithm A.

This paper proposes a soft input decoding algorithm and a decoder architecture for generalized concatenated (GC) codes. The GC codes are constructed from inner nested binary Bose-Chaudhuri-Hocquenghem (BCH) codes and outer Reed-Solomon codes. In order to enable soft input decoding for the inner BCH block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In this paper, a representation of the block codes based on the trellises of supercodes is proposed in order to reduce the memory requirements for the representation of the BCH codes. This enables an efficient hardware implementation. The results for the decoding performance of the overall GC code are presented. Furthermore, a hardware architecture of the GC decoder is proposed. The proposed decoder is well suited for applications that require very low residual error rates.

Codes over quotient rings of Lipschitz integers have recently attracted some attention. This work investigates the performance of Lipschitz integer constellations for transmission over the AWGN channel by means of the constellation figure of merit. A construction of sets of Lipschitz integers that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations is presented. In particular, it is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number. It is shown that it is always possible to partition such quotient rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. The resulting signal constellations have a better performance for transmission over an additive white Gaussian noise channel compared to Gaussian integer constellations and to ordinary Lipschitz integer constellations. In addition, we present multilevel code constructions for the new signal constellations.

Codes over Gaussian integers have been proposed for coding over two‐dimensional (2D) signal spaces, for example, using quadrature amplitude modulation. Here, it is demonstrated that the concept of set partitioning can be applied to Gaussian integer constellations that are isomorphic to 2D modules over rings of integers modulo p . This enables multilevel code constructions over Gaussian integers. The authors derive upper bounds on the achievable minimum distance in the subsets and present a construction for the set partitioning. This construction achieves optimal or close to optimal minimum distances. Furthermore, it is demonstrated that this set partitioning can be applied to an interleaving technique for correcting 2D cyclic clusters of errors. The authors propose a novel combination of generalised concatenated codes with 2D interleaving to correct 2D error clusters and independent errors.

This work presents block codes over Gaussian integers. We introduce Gaussian integer rings which extend the number of possible signal constellations over Gaussian integer fields. Many well-known code constructions can be used for codes over Gaussian integer rings, e.g., the Plotkin construction or product codes. These codes enable low complexity decoding in the complex domain. Furthermore, we demonstrate that the concept of set partitioning can be applied to Gaussian integers. This enables multilevel code constructions. In addition to the code constructions, we present a low complexity soft-input decoding algorithm for one Mannheim error correcting codes. The presented decoding method is based on list decoding, where the list of candidate codewords is obtained by decomposing the syndrome into two sub-syndromes. Considering all decompositions of the syndrome we construct lists of all possible errors of Mannheim weight two. In the last decoding step the squared Euclidean distance is used to select the best codeword from the list. Simulation results for the additive white Gaussian noise channel demonstrate that the proposed decoding method achieves a significant coding gain compared with hard-input decoding.

New wideband speech coding standards like the AMR-WB and the ITU G.729.1 codecs will improve the speech quality of telecommunication applications in the near future. To provide the same speech quality with hands-free devices that have a Bluetooth link, a bandwidth extension for the speech transmission with Bluetooth is required. This work presents a low complexity and low latency speech coding scheme that is backward compatible to the current Bluetooth standard and can be implemented with off-the-shelf Bluetooth chips.

A decision feedback scheme for block codes is investigated for binary symmetric channel. The corresponding decision rule is based on a simple threshold test. We derive an asymptotic performance bound on the achievable block error rates. This bound improves the best known results for the threshold test. The achievable error exponent is close to Forney's feedback exponent.

In this correspondence, we investigate a decision feedback strategy for convolutional codes which is based on a sliding window decoding procedure and a threshold test as decision rule. For this purpose, we introduce the burst distance spectrum of a convolutional code and derive asymptotic bounds for the ensemble of periodically time-varying convolutional codes. These results are helpful for the asymptotic analysis of the decision feedback scheme. We show that unit memory codes are particularly suited for such a transmission scheme. For these codes, the decoding procedure is reduced to the decoding of block codes with lengths in the order of the overall constraint length of the convolutional code. This leads to a significantly smaller decoding complexity compared with other known decoding and decision rules. Whereas the achievable asymptotic performance is close to the best known bounds. For low rates, our results even improve these bounds.

Widrow's interference canceller adapted by the normalized LMS (NLMS) is a standard approach for separating signals from multiple speakers, for example from the driver (target) and the codriver (interference) in a car. In practice, the adaptation must be carried out only when the interferer is dominant, i.e. only when some estimate of the signal-to-interference ratio (SIR) is below a certain threshold. In this paper, we present the implicitely controlled LMS (ILMS), a modification of the NLMS. ILMS adaptation is performed continuously using a variable step-size, whose design implicitly detects dominance of the interferer over target activity. Specific measures are taken to guarantee the stability during adaptation. Theoretical analysis of the ILMS transient convergence and stability conditions prove significant improvement with respect to the original NLMS. Experimental results on real in-car data assess the predicted behavior.

Abstract In this paper we consider a two-channel diversity technique thatcombines the processed signals of two separate microphones.Forin-car applications, this enables a better compromise forthemicrophone positions. The advantage of the proposed systemis its insensitivity with respect to varying speaker sizes or lo-cal noise sources. To achieve this we choose the microphoneposition in that way that one microphone is optimum for a tallspeaker, and the second one is suitable for a small speaker. Forlocal noise sources we may apply a similar design to choosethe microphone position in accordance with the location of thenoise sources. A corresponding signal combiner has to tasks:compensation of phase shifts and weighting proportional to thesignal strength. We propose solutions for both problems anddemonstrate the effectiveness of diversity combining. 1. INTRODUCTION Due to the obvious dangers of holding a telephone in one hand,and steering a car with the other, many countries either stronglyrecommended, or legally enforced hands-free telephone oper-ation in all moving vehicles. Thus for safety and comfort rea-sons,ahands-freetelephonesystemthatprovidesthesamequal-ity of speech as conventional fixed telephones is desirable. Anatural bottleneck for the speech quality of a hands-free car kitis the position of the microphone. Obviously, speech has tobe picked up as close to the mouth as possible. The importantquestion, where to place the microphone inside the car, is how-ever difficultto answer. The

We investigate a decision feedback strategy for convolutional codes which is based on a sliding window decoding procedure and a threshold test as decision rule. For this purpose, we introduce the burst distance spectrum of a convolutional code and derive asymptotic bounds for the ensemble of periodically time-varying convolutional codes. These results are helpful for the asymptotic analysis of the decision feedback scheme. Unit memory codes are particularly suited for such a transmission scheme. For these codes, the decoding procedure is reduced to the decoding of block codes with lengths in the order of the overall constraint length of the convolutional code. This leads to a significantly smaller decoding complexity compared with other known decision rules. Whereas the achievable asymptotic performance is close to the best known bounds. For low rates, our results even improve these bounds.

We present a new concatenated code construction. The resulting codes can be viewed as intermediate between parallel and serially concatenated convolutional codes. Proper partitioning of the outer code sequence provides a new degree of freedom for code design. Various methods are considered to analyze code properties.

Let the Viterbi algorithm be applied for maximum-likelihood decoding of a terminated convolutional code using a trellis. We propose an additional procedure that permits a receiver to locate unreliable segments within an estimated code sequence. This reliability output may be used, for example, to request retransmissions, in systems with error concealment, or in channel-coding systems with unequal error protection.

We consider convolutional and block encoding schemes which are variations of woven codes with outer warp. We propose methods to evaluate the distance characteristics of the considered codes on the basis of the active distances of the component codes. With this analytical bounding technique, we derived lower bounds on the minimum (or free) distance of woven convolutional codes, woven block codes, serially concatenated codes, and woven turbo codes. Next, we show that the lower bound on the minimum distance can be improved if we use designed interleaving with unique permutation functions in each row of the warp of the woven encoder. Finally, with the help of simulations, we get upper bounds on the minimum distance for some particular codes and then investigate their performance in the Gaussian channel. Throughout this paper, we compare all considered encoding schemes by means of examples, which illustrate their distance properties.