We consider a coded compressed sensing approach for the unsourced random access and replace the outer tree code proposed by Amalladinne et al. (2020) with the list recoverable code capable of correcting$t$errors. A finite-length random coding bound for such codes is derived. The numerical experiments in the single-antenna quasi-static Rayleigh fading channel show that transition to list recoverable codes correcting$t$errors improves the performance of the coded compressed sensing scheme by 7–10 dB compared to the tree code-based scheme. We propose two practical constructions of outer codes. The first is a modification of the tree code called$t$-tree code. It utilizes the same code structure, and a key difference is a decoder capable of correcting up to$t$errors. The second is based on the Reed–Solomon codes and Guruswami–Sudan list decoding algorithm. The first scheme provides energy efficiency very close to the random coding bound when the decoding complexity (number of decoding paths) is unbounded. But when we restrict the number of decoding paths with a practical value, the second scheme outperforms the first one. Both schemes improve the performance of a tree code-based scheme for a small and moderate number of active users.

We consider the unsourced random access based on a coded compressed sensing approach. The main idea is to replace the outer tree code proposed by Amalladinne et al. with the code capable of correcting t errors. We derive a finite-length random coding bound for such codes and suggest a practical code construction. We have conducted numerical experiments in the single antenna quasi-static Rayleigh fading MAC. The results show that transition to list-recoverable codes correcting t errors allows performance improvement of coded compressed sensing scheme by 7–10 dB compared to the tree code-based scheme.

In this paper, we extend the notion of locally recoverable codes with availability to secret sharing schemes. The main problem that we considered is how to store information using locally recoverable codes with all symbol locality and availability in such way that useful information can be recovered using an only small subset of coordinates while a user who observes less than a certain number of coordinates does not get any information. In other words, we have to protect locally recoverable codes with availability over passive eavesdropper that can observe only limited number of coordinates. Upper bounds on number of bits that can be securely stored in such systems together with explicit constructions of codes with such a property are proposed.

In this paper, a low complexity scheme for unsourced random multiple access over the Gaussian channel is proposed. Following the literature by the word "unsourced" we mean the fact that the users use the same codebook codes. The proposed scheme is based on T-fold ALOHA with successive interference cancellation (SIC) procedure. In each slot, the same codebook concatenated code construction with outer non-binary (NB) low- density parity-check (LDPC) code and inner linear binary code is decoded with iterative joint decoding algorithm. Outer NB-LDPC code is decoded with low-complexity iterative q-ary sum-product algorithm (QSPA) and short inner binary code is decoded with maximum likelihood. Finally, the numerical results and comparison with theoretical bounds are represented.

We consider a new signal-code construction for a special class of multiple access system over vector-disjunctive channel when users transmit some vector of bits of finite length L. We propose a special encoding and decoding algorithms for such transmission scenario. Our suggested methods of encoding and decoding on one hand have acceptable complexity for a wide range parameters and on other one a decoding rule we considered has a performance very close to maximum likelihood (ML) decoding. We present some simulation results for relative sum-rate of our construction and for frame error rate (FER) in the case of different number of active users and different code constructions. Simulation results we obtained allow us to conclude that our scheme has a good performance even for very short codes.

In this paper we consider the low complexity majority-logic decoding algorithm for irregular non-binary low-density parity-check (LDPC) codes. The decoding algorithm is a generalization of the bit-flipping algorithm for binary LDPC codes. The lower estimate on the decoding radius realized by this algorithm is derived for the first time for irregular non-binary LDPC codes. We present the numerical results for the derived lower bound.

In this paper we propose to consider a generalized error-locating code (GEL-code) as a possible candidate for data transmission systems that require high code rates along with strict requirements on wrong decoding probability. GEL codes are one of a few that allow analytical computation of code error probability bounds and have practical construction method. The paper describes the construction of the GEL-code and the algorithms for encoding and decoding. It represents the upper and lower bounds on wrong decoding probability. It gives a method for constructing such GEL code (with the minimal redundancy) that guarantees that the probability of wrong decoding will be less than required one (for a given channel error probability). Numerical results for the upper and lower bounds for the various GEL-codes and the analysis of the energy gain for the different signal-code structures are given.

This paper deals with the irregular binary low-density parity-check (LDPC) codes with the constituent single parity check (SPC) codes and the error-correcting iterative low-complex decoding algorithm. The lower bound on the error fraction, guaranteed corrected by the considered iterative algorithm, was obtained for the irregular LDPC code for the first time in this paper. This lower bound was obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The number of decoding iterations, required to correct the errors, is a logarithmic function of the code length. The numerical results, obtained at the end of the paper for proposed lower bound achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes.

This paper deals with the method of undetected error probability estimation for a low-density parity-check (LDPC) code under any given iterative decoding algorithm. We propose such modification of a given iterative decoding algorithm, that almost preserves a decoding failure exponent and decoding complexity of this algorithm. We obtain the upper bound on the undetected error probability for the modified algorithm. We show how to use the proposed method to estimate the undetected error probability of LDPC code under the belief propagation (BP) algorithm at the end of this paper.

This paper considers new lower bound on fraction of guaranteed corrected errors while decoding the same binary low-density parity-check (LDPC) codes with constituent single parity-check (SPC) and Hamming codes using the same iterative low-complex hard-decision algorithm as in previous works of V. Zyablov and M. Pinsker in 1975 and V. Zyablov, R. Johannesson and M. Loncar in 2009. The number of decoding iterations, required to correct the errors, is a logarithmic function of the code length. The fraction of guaranteed correctable errors computed numerically for various choices of LDPC code parameters with constituent SPC and Hamming codes shows that proposed lower bound gives the better results than previously known best lower bounds obtained by V. Zyablov and M. Pinsker in 1975 for Gallager's LDPC codes and A. Barg and A. Mazumrad for Hamming code-based LDPC (H-LDPC) codes in 2011. Some of obtained numerical results are represented at the end of the paper to demonstrate these improvements.