The eBCH-polar codes is a powerful way to construct polar codes. With high minimum Hamming distance, it outperforms ordinary Polar codes under successive cancellation list (SCL) decoder. However, the absence of cyclic redundancy check (CRC) bits in eBCH-polar codes makes it challenging to adopt SCL-flip (SCLF) decoding scheme. In this research, we propose a flip scheme activated by a Normalized Path Metric (PM) range and a mismatch criterion, which respectively leverage the properties of SCL decoding and dynamic frozen bits of eBCH-polar codes. This work also improves the selection the flipping bits by modifying metric to account for the structure of dynamic frozen bits and reduce the search space. Based on these modifications, we proposed SCLF-1 and SCLF-2 decoding algorithms for eBCH-polar codes. Simulation results show that both of the proposed decoding schemes achieve superior performance compared to other contemporary decoding algorithms for CRC aided polar (CA-polar) codes, demonstrating enhanced error rates performance within the same decoding attempt.

In this paper, we develop a new approach for rank analysis of parity-check matrices for quasi-cyclic low-density parity-check codes based on the associated polynomials of circulant matrices, applicable to general finite fields and arbitrary circulant sizes. Some formulas on the rank for parity-check matrices with one, two, and three row-blocks are first derived. For the general case with arbitrary numbers of row-blocks, lower and upper bounds on the rank are presented, and these bounds can be combined to give the exact rank result under certain conditions. We also investigate the effect on the rank by changing the circulant size. Furthermore, we study the relations between the rank of the masked matrix and that of the masking matrix, which can be used to predict the rank of the parity-check matrix after masking. The obtained rank analysis results are then applied to several classes of existing algebraically constructed parity-check matrices, along with their masked matrices. Finally, we demonstrate how rank analysis can be used in the code design procedure.

Belief propagation (BP) decoding of polar codes, which can be executed in parallel, is suitable for low-latency applications. In this paper, we first give a sparse parity-check matrix representation for polar codes, based on which several strategies for performance improvement are proposed. We then devise a scheme of which the performance can approach the maximum-likelihood lower bound and that of successive cancellation list (SCL) decoding. For cyclic redundancy check (CRC)-concatenated polar codes, a parity-check matrix representation is also presented so that joint decoding between the CRC code and polar code is possible. An improved CRC-aided BP decoder is hence proposed with performance close to that of the state-of-the-art CRC-aided SCL decoder.

In this paper, two improvements for successive cancellation list flip (SCL-Flip) decoding are presented for polar codes. First, a novel bit-selection metric based on path metric (PM) is introduced. With the proposed metric, the improved scheme can have lower complexity and saturate faster than other state-of-the-art decoders. Second, we generalize the SCL-Flip decoding, denoted SCL-Flip-ω, to flip the decision in path competition at most ω times in decoding process. We analyze the frequency of channel-induced error under various circumstances, measure the trade-off between error-correction performance and complexity, and then propose SCL-Flip-2 decoding which is the first SCL-based decoding that allows for multiple bits for flipping to the best of our knowledge. Simulation results reveal that the proposed decoding with a small list size can achieve a better performance than CA-SCL decoding with a large list size while keeping the complexity low.

Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important class of LDPC codes which can be encoded and decoded with low complexity and suitable for many applications. As the code dimension, which describes the number of protected information bits, is equal to the code length minus the rank of the parity-check matrix and the parity-check matrix for QC-LDPC codes is usually not full-rank, determining the rank of the parity-check matrix is of essential importance. In this paper, we study the rank of the parity-check matrix for QC-LDPC codes based on the associated polynomials for circulant matrices. A formula for the rank of the parity-check matrix with only one row-block is first derived. We then extend the result to matrices with two, three, or more row-blocks. Some bounds are also presented for matrices with arbitrary numbers of row-blocks. Furthermore, the exact rank is determined for a class of algebraically constructed parity-check matrices.

This paper proposes an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes. The proposed decoding algorithm combines the concepts of adapting the parity-check matrix and informed dynamic scheduling decoding. The parity-check matrix is re-arranged before each iteration, where the systematic part is mapped to the least reliable bits, consequently reducing their influence on the other bits. Using dynamic scheduling, the more important decoding messages are updated to these least reliable bits, meaning that the majority of the error bits with low reliability can be corrected. When the proposed integrated decoding is applied to (255, 239) RS code, the difference between its frame error rate performance (FER) and the maximum-likelihood (ML) bound can be reduced to 0.8 dB, and a gain of about 0.1 dB is achieved compared to all the previously recorded soft-decision decoding for RS codes.

In this paper, the algebraic constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes with the unequal error protection (UEP) property are considered. A criterion for constructing such codes via the masking technique is proposed, based on which explicit conditions on the base parity-check matrices and masking matrices to achieve UEP are provided. We also give three specific constructions of UEP QC-LDPC codes. Furthermore, a sufficient condition to ensure strict UEP is presented. Simulation results demonstrate the superiority of our constructed codes over time-sharing schemes. The constructed codes also have competitive error performance against randomly constructed equal-error-protection LDPC codes and irregular UEP LDPC codes designed based on the degree distribution.

In this paper, the unequal error protection (UEP) capability of convolutional encoders, in terms of the separation vector, is studied from an algebraic viewpoint. A simple procedure is presented for constructing a generator matrix, which is basic and has the largest separation vector for every convolutional code. Such a generator matrix would be desirable, since the corresponding encoder not only achieves UEP optimality, but also avoids undesired catastrophic error propagation. In addition, canonical generator matrices, which are both basic and reduced, are even more preferable for encoding, since they attain the lowest complexity for Viterbi decoding. However, the direct transformation from a UEP-optimal generator matrix to a canonical generator matrix may come with an unexpected loss of the separation vector. We also propose a specific type of transformation matrix that reduces the external degrees of the generator matrices, from which canonical generator matrices can be constructed that include the mitigated degradation of the separation vector. Finally, beneficial UEP convolutional codes that achieve the maximum free distances for the given code parameters are provided.

In this paper, an iterative soft-decision decoding algorithm is proposed for Reed-Solomon (RS) codes. The proposed decoding algorithm combines the concepts of adapting the parity-check matrix and informed dynamic scheduling. Before each iteration, the parity-check matrix is re-arranged according to the reliability of the codeword bits, meaning that the influence of the least reliable variable nodes on the decoding process can be reduced. Consequently, the important decoding messages can be scheduled to be updated first, and the reliability of the least reliable bits can be enhanced. The simulation results show that the proposed decoding algorithm can provide significant improvement in the error-rate performance. By using the proposed algorithm, a gain of 0.5 dB can be achieved compared to the conventional adapting belief propagation algorithm.

In this paper, we address the issue of unequal missing protection (UMP) for the design of grouping of radio-frequency identification (RFID) tags. While relying on group generation matrices, grouping of RFID tags allows verifying the integrity of a collection of RFID tags without the requirement for accessing external systems, and can be extended to identify missing RFID tags. Motivated by application needs that call for UMP among RFID tags, we first introduce the concepts of UMP for grouping of RFID tags and its extended counterpart. We then present a simple scheme to realize extended grouping of RFID tags with UMP. Simulation results are presented to demonstrate the efficiencies of the proposed UMP scheme for extended grouping of RFID tags.

In this paper, we address the issue of unequal missing protection (UMP) for the design of grouping of radio-frequency identification (RFID) tags. While relying on group generation matrices, grouping of RFID tags allows verifying the integrity of a collection of tags without the requirement for accessing external systems, and can be extended to identify missing tags. Motivated by application needs that call for UMP among the tags, we first introduce the concepts of UMP for grouping of RFID tags and its extended counterpart, with which missing tags with high missing protection levels are more easily counted or identified than those with low missing protection levels. We then present simple yet effective schemes to realize grouping of RFID tags with UMP and its extended counterpart. The proposed schemes not only can easily fulfill the requirement of UMP among the tags, but also offer flexibility in constructing UMP group generation matrices. We also characterize key objects in order to further study grouping of RFID tags with UMP and its extended counterpart, called consistent and unidentifiable sets, respectively. This characterization in turn enables theoretical analysis of the error rate from the perspective of a tag. Theoretical and simulation results are presented to demonstrate the efficiencies of the proposed schemes for the design of grouping of RFID tags with UMP.

Wireless video streaming often suffers from heavy and varying amount of packet loss. Short-length Luby Transform (SLLT) codes are often employed to offer necessary rateless or universal erasure protection. Nevertheless, a proficient method for finding the optimal degree distributions of SLLT codes is still missing although the asymptotic behaviors of infinite-length LT codes have long been deduced. In this paper, we propose a practical approach to find the optimal degree distributions of LT codes with arbitrary input block lengths. Our approach starts with a new fitness model for the LT codes based on three performance measurements: their coding overhead ε, decoding failure ratio r and failure probability p. We then employed the exponential natural evolution strategy (xNES) along with a suitable choice of initial degree distribution and a proper transformation between the genotypes and the phenotypes to search for the optimized degree distributions. The optimized SLLT codes designed using this approach far outperforms the ones obtained through asymptotic approximation. As an example application, we constructed a family of rateless convolutional UEP codes using these optimized SLLT codes as the rateless postcodes. These codes offer superb universal unequal erasure protection to wireless H.264/SVC broadcasting with only 16%-20% coding overhead. This design exercise, however, made clear the necessity of matching the rateless erasure correction capability of the SLLT postcode with the error-rate sensitive UEP capability of the convolutional precode. The effect of code matching was demonstrated clearly in the improvement of rate-distortion performance of video playback.

In this paper, we consider a system that consists of$N$independent parallel channels, where the receiver starts to decode the information being transmitted when it has access to at least$K$of them. We refer to this system as the$(N,K)$-limited access channel. No prior knowledge for the distribution about which transmissions will be received is assumed. In addition, both the channel inputs and channel disturbances can be arbitrary, except that the mutual information function for each channel is assumed strictly concave with respect to the input power. Hence, the channel capacity below which the code rate is guaranteed to be attainable by a sequence of codes with vanishing error can be determined by the minimum mutual information among any$K$out of$N$channels. We then investigate the power allocation that maximizes this minimum mutual information subject to a total power constraint. As a result, the optimal solution can be determined via a systematic algorithmic procedure by performing at most$K$single-power-sum-constrained maximizations. Based on this result, the closed-form formula of the optimal power allocation for an$(N,K)$-limited access channel with channel inputs and additive noises, respectively, scaled from two independent and identically distributed random vectors of length$N$is subsequently established, and is shown to be well interpreted by a two-phase water-filling principle. Specifically, in the first noise-power redistribution phase, the least$N-K$noise powers (equivalently, second moments) are first poured (as noise water) into a tank consisting of$K$interconnected unit-width vessels with solid base heights, respectively, equal to the remaining$K$largest noise powers. Afterward, those$W$vessels either with noise water inside or with solid base height equal to the new water surface level are subdivided into$N-K+W$vessels of rectangular shape with the same heights (as the water surface level) and widths in proportion to their noise powers. In the second signal-power allocation phase, the heights of vessel bases will be first either lifted or lowered according to the total signal power and channel mutual information functions, followed by the usual signal-power water-filling scheme. The two-phase water-filling interpretation then hints that the degree of “noisiness” for a general (possibly, nonadditive and non-Gaussian) limited access channel might be identified by composing the derivative of the mutual information function with its inverse.

Cooperative bit-interleaved coded modulation (BICM) is a key technology for the next-generation wireless communication systems. This paper investigates power allocation for the cooperative BICM systems with decode-remap-and-forward (DRF) relaying. Unlike the conventional decode-and-forward relays, the DRF relays may choose different constellation mappings from that of source so as to obtain a remapping gain. In spite of its importance, the power allocation in such a system has not yet been explored in the literature. Two new power allocation methods are proposed, aiming to minimize bit error rate at the destination. The first uses a cost function based on the minimum weighted squared-Euclidean distance (called PA-MWSED) and is optimized with the sub-gradient method. The second is based on a generalized MWSED (called PA-GMWSED) and is optimized with the Simplex method after the optimization is re-cast as a linear programming problem. Generally speaking, PA-MWSED has a better performance than PA-GMWSED but requires a higher complexity. Numerical results show that both of the proposed methods outperform the equal gain power allocation with large margins.

In this paper, we consider an (N;K)-limited access system consisting of N parallel additive noise channels with spatial dependency, where the receiver starts to decode the information being transmitted when at least K out of N channel outputs are received. We investigate the optimal power allocation that maximizes the minimum mutual information among all possible cases of partial reception. A universal guideline is then obtained for a group of permutation-invariant channels, in which the system mutual information remains unchanged when permuting the parameters that characterize the partial reception and signal-to-noise power ratio (SNR) of channels, that a channel with less noise power should have larger SNR. When all N channels belong to a permutation-invariant group, we also have that the optimal power allocation problem can be transformed to an equivalent problem for K parallel channels without limited access constraint via a water-filling noise-power-redistribution process. The merit of this transformation can be more evidently seen when the channel input-noise pairs are reduced to be spatially independent with distributions scaled from a common random vector, for which the optimal power allocation solution can be simply obtained by a two-phase water-filling process.

In this paper, decoding of LDPC convolutional codes with rational parity-check matrices (LDPC-CC-RPCM) is investigated. We show that Tanner graph of every LDPC-CC-RPCM can always be transformed into an equivalent one with enlarged girth and finite memory order suitable for practical pipeline decoder. Based on the transformed graph, a dynamic scheduling-aided decoding scheme with the enhancement of signal perturbation and error cancellation is presented to improve the convergence speed and bit-error-rate performance in both of the waterfall and error-floor regions. Simulation results also reveal that LDPC-CC-RPCM may outperform ordinary LDPC-CC with polynomial parity-check matrices in some cases under the same code rate and decoding complexity.

Wireless broadcasting of scalable video coded medium grain scalable (SVC/MGS) bit streams requires unequal erasure protection (UEP) at the transport layer in order to ensure graceful degradation of playback video quality over a wide range of frame error rates. Modern wireless broadcasting systems even employ rate less fountain codes to aid the receivers in making inevitable tradeoffs among picture quality, channel throughput and playback latency. Designing a rate less UEP channel code fits for such an application posts distinct engineering challenges as the necessary protection for SVC base and enhancement layers differ by orders of magnitude while their intradependent groups of pictures fluctuate notably in their sizes. In this paper, we present the design and implementation of a rate less UEP convolutional code that meets these demanding requirements. Use of this UEP channel code along with rate-distortion based network application layer unit extraction offer sufficient protection to SVC bit streams under different lossy conditions without the need to re-code the bit stream. We also investigated the differences in playback performance of SVC bit streams that were protected by rate less codes vs. conventional Reed-Solomon codes. The comparison makes clear the advantages and the disadvantages of employing rate less codes in protecting wireless video broad-casting.

Transmit power allocation between source and relays is a critical design issue in a cooperative relaying system where source and relays are powered by batteries. In this paper, a low-complexity power allocation method is proposed for a 3-node cooperative bit-interleaved coded modulation system with adaptive decode-and-forward relaying, aiming to minimize the bit-error-rate at the destination. The key novelty of the method lies in transforming the power allocation into a max-min optimization problem which can be solved in a first-order equation with very low-complexity. Computer simulations show that the proposed method outperforms the equal gain power allocation with large margins in different channel conditions.

In this paper, convolutional encoders are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. Given any convolutional code, UEP-optimal encoders with the smallest McMillan degree are constructed to minimize the coding complexity. The noncatastrophic property of encoder is also maintained to avoid the undesired catastrophic propagation of decoding errors.

Previous studies on low-density parity-check convolutional codes (LDPC-CC) reveal that LDPC-CC with rational parity-check matrices (RPCM) suffer from the unaffordable decoding latency/complexity due to the infinite memory order and the poor bit-error-rate performance due to the existence of length-4 cycles in the Tanner graph. However, in this paper, we show that every LDPC-CC with RPCM can be associated with an equivalent Tanner graph which can avoid the infinite memory order and undesired short length cycles but still implements the same constraints specified by the RPCM. Together with the iterative decoding based on belief propagation with proper scheduling, simulation results indicate that LDPC-CC with RPCM can also provide satisfactory decoding performance.

In this paper, a new construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed. We first give a new class of UEP block codes. QC-LDPC codes with binomial-term parity-check matrices which can avoid girths less than 8 and achieve an enlarged upper bound on the minimum distance are also introduced. An effective UEP scheme based on the proposed UEP block codes and QC-LDPC codes which can provide flexible choice of protection levels is then presented. Simulation results show that the new QC-LDPC codes can achieve good performance and low error floors. The bits with different designed protection levels can indeed have unequal bit-error-rate performance.

In the literature, a class of iterative decoding algorithms which combine the traditional reliability-based decoding (RBD) with the adaptive belief propagation (ABP) have been validated to be applicable for Reed-Solomon codes. However, in the original design of the iterative decoding, the soft-information is passed only from the ABP-part to the RBD-part such that the decoding performance is somewhat limited. In this study, we first present a new reliability updating scheme for the bidirectional exchange of soft-information in the iterative decoding, which can guarantee the correction of the most errors in both of the reliable and unreliable bits. A simple bit-flipping mechanism is also proposed to refine the initialization of the ABP-part for further performance improvement. Revealed by the simulation results, our proposed scheme can outperform the conventional design in terms of the bit-error-rate performance.

In this paper, a new construction of irregular low-density parity-check convolutional codes (LDPC-CCs) is presented. Both upper and lower bounds on the free distance are derived as well. Compared with previously constructed irregular LDPC-CCs, our design can not only avoid a girth less than 8 but also provide an enlarged free distance. Since some undesired cycles occur due to the binomial terms in the parity-check matrices of general LDPC-CCs, we provide a specific procedure to remove this kind of length-8 cycles. It can also be applied to our irregular construction. Simulation results show that the codes based on the new construction and the cycle-removal procedure can achieve better bit-error-rate performance and a lower error-floor.

Quadratic permutation polynomial (QPP) interleaver has the advantage of contention-free for parallel memory access and has been adopted in the 3GPP LTE for turbo coding. Conventional implementations of the QPP interleaver based on the look-up table or on-line calculation usually result in large circuit area or higher clock rate for parallel turbo decoding. In this paper, an architecture design of QPP interleaver for parallel turbo decoding is presented which can provide parallel memory access without extra storage of interleaving patterns or the increment of clock rate compared with the conventional approaches. The proposed design is also reconfigurable for variable interleaver lengths.

In this paper, convolutional codes are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We first show that for every convolutional code there exists at least one optimal generator matrix with respect to UEP. The UEP optimality of convolutional encoders is then combined with several algebraic properties, e.g., systematic, basic, canonical, and minimal, to establish the fundamentals of convolutional codes for UEP. In addition, a generic lower bound on the length of a UEP convolutional code is proposed. Good UEP codes with their lengths equal to the derived lower bound are obtained by computer search.

Bit-interleaved coded modulation with iterative decoding (BICM-ID) has been verified to be a powerful transmission scheme with remarkable bit-error-rate performance. Among those well-designed BICM-ID systems, we observe that some of the channel encoders and signal mappers are inherently with the capability of multilevel protection. A new scheduling rule called protection matching which can properly schedule the data flow between the channel encoder and signal mapper with respect to the multilevel protection capability is proposed to achieve further performance improvement. Not only theoretical analysis but also simulation results are given to verify the advantage of the proposed design.

In this paper, space-time coding schemes with full transmit diversity are investigated for unequal error protection (UEP). Effective performance indicies are proposed to measure the intrinsic UEP capability of space-time codes, based on which we demonstrate that space-time trellis codes and superorthogonal space-time trellis codes can be used for UEP as long as the corresponding encoders are properly designed. In addition, UEP convolutional codes are concatenated with space-time block codes to construct another full-diversity UEP scheme which can provide more choices of UEP levels. Finally, good UEP codes are given by a computer search.

We propose a pragmatic labeling design based on the extrinsic information transfer (EXIT) chart for bit-interleaved coded modulation with iterative decoding on multiple-input-multiple-output channels. In our design, the EXIT chart is used to determine a candidate set of labelings which have representative demapper transfer curves. Then, a procedure to generate these labelings is provided based on the genetic algorithm. Given fixed channel code and signal-to-noise ratio (SNR), we can search within this candidate set for a most-suitable labeling to minimize the bit-error-rate (BER) with low complexity. Simulation results show that the labeling chosen from the candidate set exhibits a controllable BER performance gap compared to the optimal labeling found through exhaustive search. Besides, even though the channel code or the SNR is changed, the same candidate set can still be directly adopted to reduce the time on re-searching a new labeling.

In this paper, canonical convolutional encoders are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We show that for any convolutional code there exists at least a canonical generator matrix which has the greatest separation vector, and hence the optimal UEP capability, among all canonical ones. A procedure for obtaining such desirable generator matrices is also proposed.

In this paper, we propose a new construction of (3, t)-regular low-density parity-check convolutional codes by properly including binomial entries in the parity-check matrices. Both of the upper and lower bounds on free distance are derived for the new codes. Compared with previous constructions, our design can not only avoid codes of girth less than 8 but also provide enlarged free distances for some code rates. Simulation results show that the codes based on the new construction can achieve better bit-error-rate performance and lower error floor.

One of the unique characteristics of ultra-wideband channels is the clustering phenomenon resolved by the ultra-wide signal bandwidth. Channel structures extended from the Saleh-Valenzuela model, e.g., the IEEE 802.15.3a and IEEE 802.15.4a models, have been proposed to describe such phenomenon. It is, however, noticed that a clear and systematic procedure to estimate the model parameters is still missing. Based on the recently developed analytical results, a new estimation approach is proposed in the paper to resolve the inconvenience and ambiguity in previous methods. The key step is to match the statistical profiles of interests by formulating an optimization problem with an explicit analytical objective function that can be systematically solved. Numerical tests have also been conducted to demonstrate the effectiveness of the proposed method.

In this paper, puncturing and path pruning are combined for convolutional codes to construct a new coding scheme for unequal error protection (UEP), called the hybrid punctured and path-pruned convolutional codes. From an algebraic viewpoint, we show that the hybrid codes not only inherit all the advantages of the conventional rate-compatible punctured convolutional codes and path-compatible pruned convolutional codes but also can provide more flexible choices of protection capability for UEP. In addition, a data-multiplexing scheme originally proposed for path-pruned codes which can guarantee smooth transition between rates without additional zero-padding for frame termination is proven applicable to the hybrid codes to improve the system throughput.

In this paper, labeling is jointly designed with the outer code by the EXIT chart based analysis to improve the performance of bit-interleaved coded modulation with iterative decoding. A systematic design methodology is proposed for regular modulation schemes which can easily obtain a set of labelings with various slopes. Given an outer code, the optimal labeling which has the steepest slope but still makes the tunnel between the decoder and demapper transfer curves open can then be chosen to optimize the BER performance. Verified by the simulation results, our design can provide remarkable SNR gain over the conventional ones.

Frequency-hopping spread-spectrum (FH-SS) is an efficient technique to combat jamming. Previous works in jamming channels pay more attention to partial band noise jamming (PBNJ). In this paper, Low-Density Parity-Check (LDPC) coded fast frequency hopping binary frequency shift keying (FFH/BFSK) spread-spectrum (SS) systems are investigated under band multitone noise jamming (BMTJ). We take the advantage of both diversity gain and coding gain for enhancing the system performance. We consider maximum-likelihood (ML) diversity combing and square-law with equal gain combing schemes which are used to compute the codeword bit decision reliability. The sum-product algorithm (SPA) based on belief propagation is exploited for iterative decoding. Simulation results reveal that our proposed system provides excellent performance against band multitone noise jamming.

In this paper, convolutional codes are studied for puncturing with irregular puncturing periods. Irregular puncturing can generate punctured codes with more available rates and better bit-error-rate performance compared with the conventional scheme with a single puncturing period. For the application to unequal error protection, a new multiplexing scheme is also proposed for rate-compatible punctured convolutional (RCPC) codes which can guarantee smooth transition between rates without extra overheads. Finally, families of good RCPC codes with irregular puncturing tables are given by a computer search

In this paper, we investigate a novel coding idea proposed previously to enable under-sampled receivers. An under-sampled receiver can sample the received baseband signals at only a fraction of the Nyquist rate and turns out to be an effective solution to the bottleneck of high-rate sampling and processing in ultra-wideband (UWB) communications. The spectrum aliasing problem can be solved by an analogy between an under-sampled system and a multiple-antenna one. However, underlying differences between the two systems exist and motivate the study of the fundamental limits of a coded under-sampled system. The study is carried out by characterizing the optimal coding structures with and without channel state information at transmitter (CSIT). A practical selective coding structure is also developed to provide satisfactory performance with reduced CSIT requirement. Finally, simulations are conducted to verify the theoretical characterization. Our results indicate that an under-sampled UWB system can benefit from power-saving, cost reduction, and full multipath diversity at the expanse of little or confined performance degradation

The performance of low-density parity-check (LDPC) codes is investigated for fast frequency hopping / binary frequency shift keying (FFH/BFSK) in partial-band noise jamming channels. We employ different diversity combining schemes to compute the codeword bit decision reliability. In this paper, we consider the maximum-likelihood (ML) diversity combining scheme and two low-complexity suboptimal diversity combining schemes: square-law with adaptive gain control (AGC) combining and square-law with equal gain combining. Simulation results show that, by combining both of the diversity and coding gain, our proposed system can provide excellent performance against partial-band noise jamming.

In this paper, a general reliability-updating formula is proposed for trellis-based soft-output decoding algorithms to optimize the tradeoff between performance and complexity. Based on the general formula, new algorithms are presented, and a concise interpretation is provided to relate new proposed algorithms and those reported previously. In addition, we devise a unified decoding structure with respect to the general formula. All trellis-based algorithms are mapped into a single decoding process under the unified structure, and different algorithms can be easily switched between one another. Owing to the modularity and flexibility, this unified structure is especially suitable for turbo decoders with programmable implementation.

Path pruning, a new coding concept to achieve free distance enlargement for convolutional codes, is proposed. Through path pruning, every convolutional code can be used for unequal error protection (UEP), no matter whether it is originally a UEP code. To avoid undesired path discontinuity and reduce possible path distance loss, a cascaded implementation together with a path-compatible criterion is proposed, under which path-compatible pruned convolutional (PCPC) codes are constructed. Necessary and sufficient conditions are also derived for a subclass of PCPC codes whose decoding can be done by a single decoder for the parent code. Finally, some PCPC codes with good UEP capabilities found by computer search are given.