Generalized Threshold Decoding of Convolutional Codes

It is shown that any rate l/b systematic convolutional code over GF(p) can be decoded up to its minimum distance with respect to the decoding constraint length by a one-step threshold decoder. It is further shown that this decoding method can be generalized in a natural way to allow “decoding” of a received sequence in its unquantized analog form

Feedback Communication Systems with Limitations on Incremental Redundancy

This paper explores feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em finite-length} codes (with blocklength $N$) and decoding attempts only at {\em certain specified decoding times}, this paper presents the asymptotic expansion achieved by random coding, provides rate-compatible sphere-packing (RCSP) performance approximations, and presents simulation results of tail-biting convolutional codes. The information-theoretic analysis shows that values of $N$ relatively close to the expected latency yield the same random-coding achievability expansion as with $N = \infty$. However, the penalty introduced in the expansion by limiting decoding times is linear in the interval between decoding times. For binary symmetric channels, the RCSP approximation provides an efficiently-computed approximation of performance that shows excellent agreement with a family of rate-compatible, tail-biting convolutional codes in the short-latency regime. For the additive white Gaussian noise channel, bounded-distance decoding simplifies the computation of the marginal RCSP approximation and produces similar results as analysis based on maximum-likelihood decoding for latencies greater than 200. The efficiency of the marginal RCSP approximation facilitates optimization of the lengths of incremental transmissions when the number of incremental transmissions is constrained to be small or the length of the incremental transmissions is constrained to be uniform after the first transmission. Finally, an RCSP-based decoding error trajectory is introduced that provides target error rates for the design of rate-compatible code families for use in feedback communication systems.Comment: 23 pages, 15 figure

Efficient coding schemes for low‐rate wireless personal area networks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166246/1/cmu2bf01608.pd

A high throughput hardware architecture for parallel recursive systematic convolutional encoders

During the last years, recursive systematic convolutional (RSC) encoders have found application in modern telecommunication systems to reduce the bit error rate (BER). In view of the necessity of increasing the throughput of such applications, several approaches using hardware implementations of RSC encoders were explored. In this paper, we propose a hardware intellectual property (IP) for high throughput RSC encoders. The IP core exploits a methodology based on the ABCD matrices model which permits to increase the number of inputs bits processed in parallel. Through an analysis of the proposed network topology and by exploiting data relative to the implementation on Zynq 7000 xc7z010clg400-1 field programmable gate array (FPGA), an estimation of the dependency of the input data rate and of the source occupation on the parallelism degree is performed. Such analysis, together with the BER curves, provides a description of the principal merit parameters of a RSC encoder

Channel estimation strategy for LPWA transmission at low SNR: application to Turbo-FSK

International audienceTurbo Frequency Shift Keying has been considered as a promising physical layer for low power wide-area network connectivity. Because of its constant envelope amplitude and the efficiency of its iterative receiver performance close to Shannon's limit can be achieved. However, results published so far in the literature for the waveform have assumed perfect channel estimation or Signal-to-noise (SNR) levels that are higher than the SNR levels considered for these applications. This paper analyzes a channel estimation strategy based on a specifically adapted pilot sequence. Simulations have been performed to evaluate the performance of the proposed approach. Performance loss induced by imperfect channel estimation algorithms is estimated

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRC polynomials for rate- (n-1)/n ZT and TB CCs with short blocklengths. This paper considers both standard rate-(n-1)/n CC polynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2 code. The CRC polynomials are chosen to maximize the minimum distance d_min and minimize the number of nearest neighbors A_(d_min) . For the standard rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD). CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of 128. This paper compares the FER performance (gap to the RCU bound) and complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper also explores the complexity-performance trade-off for three TBCC decoders: a single-trellis approach, a multi-trellis approach, and a modified single-trellis approach with pre-processing using the wrap around Viterbi algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0792