In the unsourced random access (U-RA), only a portion of users in a large number of users are active during the same time slot. Each user employs the same codebook, and the task of the decoder is to recover a list of transmitted messages, regardless of the user's identity. A concatenated coding approach, referred to as a coded compressed sensing scheme, decreases the computational complexity. However, there is a limitation that the inner CS decoding only decodes the support of a sparse vector, which leads to each user at the same sub-slot must send a different message, and the maximum tolerable active user number is low. In this paper, we consider an inner CS decoding scheme that initially decodes the amplitudes of a sparse vector and quantifies them to determine the number of active users choosing the same columns. This eliminates the constraint of requiring each user to send different messages in the same sub-slot, thereby increasing the maximum tolerable number of active users. We also show the maximum tolerable active user number with various codelengths. Next, we improve the survival probabilities' upper and lower bounds of the outer tree encoder.

Polar codes are provably capacity-achieving errorcorrecting codes suitable for error correction and source coding, constrained coding, and multiple access channels. Many decoding schemes have been proposed for Polar codes, including CRCaided successive cancellation list decoding (CA-SCL), known for its superior error-correcting performance. Belief propagation (BP) techniques have also been explored for decoding polar codes. BP decoding with partially permuted factor graphs (PPFG) exhibits good performance despite being inferior to CA-SCL decoding. Guess Random Additive Noise Decoding (GRAND) is a general decoding scheme for linear codes. Soft-GRAND (SGRAND) exhibits excellent performance for Polar codes despite its high time complexity. We introduce a novel decoding scheme that combines BP decoding with PPFG and SGRAND, advancing the state-of-the-art in Polar code decoding. Our proposed scheme, which fuses BP decoding with PPFG and SGRAND, demonstrates performance similar to that of CA-SCL decoding, representing a significant step forward in Polar code decoding.

User identification (UI) and channel estimation (CE) are essential in wireless networks with numerous users. Signature-code-based UI and CE schemes are widely used owing to their high spectral efficiency. Traditional signature code uses a discrete sensing matrix as a dictionary to generate codewords. Subsequently, the sparse vector recovery algorithm is used to recover the user state and channel state information in the received signal to complete the UI and CE. In this study, we propose an end-to-end machine-learning-aided signature code scheme under a multiple-access Rayleigh fading channel called machine-learning signature code (ML-SC). The ML-SC consists of a binarized-neural-networks-based (BNNs-based) trainable encoder and a trainable-iterative-soft-threshold-algorithm-based (TISTA-based) trainable decoder. To improve the accuracy, the dictionary is optimized by minimizing the mean squared error between the original and recovered information. Our proposed scheme achieved better performance and efficiency than the conventional schemes in the simulation. Moreover, it was confirmed that the dictionary generated by the ML-SC is suitable for various conventional decoders. Finally, by analyzing the results of the simulations, we found that ML-SC improves the restricted isometric constants and coherence of the dictionary.

The user identification scheme for a multiple-access fading channel based on the binary signature code is considered. In previous works, the signature code was used over a noisy multiple-access adder channel, and only the status of uses was decoded by the signature decoder. In this study, by considering the communication model as a compressed sensing process, it is possible to estimate the channel coefficients while identifying users. To improve the efficiency of the decoding process, we proposed an iterative deep neural network (DNN)-based decoder. Our simulation results show that for the binary signature code, our proposed DNN-based decoder requires less computing time to achieve higher active user detection accuracy and channel estimation accuracy than the classical signal recovery algorithm used in compressed sensing.

Two dimensional magnetic recording systems are investigated extensively to achieve higher recording density. Since the recording density is very high, a small physical defect may cause many two dimensional errors. Hence many two dimensional signal processing of magnetic recording systems are also proposed and investigated. Matcha et al. have proposed a two dimensional LDPC code and investigated the error correcting performance of the code. In this paper we propose a code which is a variant of their code but we can show that the theoretical lower bound of the burst erasure correction capability of our code is better than that of Matcha's code.

A T -user UD k-ary codes for MAAC is proposed. First, a coding scheme for a Tf+g-user UD k-ary code with code length f + g is proposed that is constructed from a Tf-user UD k-ary code and a Tg-user UD (2k - 1)-ary difference set. In fact, the Tg-user UD (2k - 1)-ary difference set is associated with Tg-user UD (2k - 1)-ary code. Second, originally from the multi-user UD (2i(k - 1) + 1)-ary (i = 0, 1, 2,..., m) codes with unitary code length, by recursively employing the coding scheme, 2m+1-user k-ary code with code length 2mis obtained. Finally, by recursively employing the coding scheme, 2n-user UD k-ary code with arbitrary code length n from the codes with length 2i(i = 0, 1,..., ⌊log2n⌋) is given. Since introducing the high-order multiary difference sets, the total rates of the proposed codes are higher those of conventional codes.

A recursive construction of k-ary uniquely decodable multiuser codes is proposed for use in a noiseless multiple-access adder channel. The code rates of the proposed codes are higher than those of previous uniquely decodable multiuser codes. A recursive decoding algorithm is also proposed.

Permutation codes with various metrics have recently been studied for flash memory applications. In this work, we derive a tighter upper bound on the generalized Cayley distance using the block permutation distance proposed by Yang, Schoeny, and Dolecek. Furthermore, we employ our upper bound to derive a tighter upper bound on the optimal rate for codes with the generalized Cayley distance when the code length is relatively small.

A kind of multiuser k-ary codes for the multiple-access adder channel is proposed. Given any Tf-user and Tg-user k-ary uniquely decodable (UD) codes with code lengths f and g, respectively, a (Tf+ Tg+ 1)-user k-ary UD code with code length f + g is obtained. The proposed scheme has no restriction on the code structure, e.g., affine, and can be constructed from any arbitrary two UD codes. Moreover, a recursive construction of a kind of k-ary UD codes with arbitrary code length is given. The proposed codes have the higher code rate and the shorter code length than those of the previous codes for a fixed number of users.

Recent years have seen increasing efforts to improve the input/output performance of multilevel flash memory. In this regard, we propose a coding scheme for two-page unrestricted-rate parallel random input-output (P-RIO) code, which enables different code rates to be used for each page of multilevel memory. On the second page, the set of cell-state vectors for each message consists of two complementary vectors with length n. There are a total of 2n-1sets that are disjoint to guarantee that they are uniquely decodable for 2n-1messages. On the first page, the set of cell-state vectors for each message consists of all weight-u vectors with their non-zero elements restricted to the same (2u-1) positions, where the non-negative integer u is less than or equal to half of the code length. Finding cell-state vector sets such that they are disjoint on the first page is equivalent to the construction of constant-weight codes, and the number of disjoint sets is the best-known number of code words in the constant-weight codes. Our coding scheme is constructive, and the code length is arbitrary. The sum rates of our proposed codes are higher than those of previous work.

Index-less indexed flash code (ILIFC) is a coding scheme for flash memories in which one bit of a data sequence is stored in a slice consisting of several cells but the index of the bit is stored implicitly. Although several modified ILIFC schemes have been proposed, in this study we consider an ILIFC with inversion cells (I-ILIFC). The I-ILIFC reduces the total number of cell level changes at each write request. Computer simulation is used to show that the I-ILIFC improves the average performance of ILIFC in many cases. This paper presents our derivation of the lower bound on the number of write operations by I-ILIFC. Additionally, we consider another lower bound thereon and show that the threshold of the code length that determines whether the I-ILIFC improves the worst-case performance of the ILIFC is smaller than that in the first lower bound. Lastly, we analyze the asymptotic performance of the I-ILIFC in the worst case.

An asymmetric multiple access channel (AMAC) is a multiple-access channel where a portion of the users can observe the messages of other users. We first propose three 2-user uniquely decodable (UD) codes for two-user AMAC, which are shown to achieve higher sum-rate than the previous 2-user codes. Then, we consider multiuser error correcting codes for T-user noisy AMAC. A theorem shows that given a Ta-user δa-decodable k-ary code A and a Td-subset δa-decodable difference set D a priori, a larger error-correcting T-user code C is obtained by Hadamard matrices. For practical construction, we give 2-user difference sets based on the 2-user UD codes, and obtain multiuser correcting codes for multiuser AMAC. The proposed correcting codes have increasing sum-rate and error-correcting capability with an increasing code length.

Random input/output (RIO) code is a coding scheme that enables reading of one logical page using a single read threshold in multilevel flash memory. The construction of RIO codes is equivalent to the construction of WOM codes. Parallel RIO (P-RIO) code is a RIO code that encodes all pages in parallel. In this paper, we utilize coset coding with Hamming codes to construct P-RIO codes. Coset coding is a technique that constructs WOM codes using linear binary codes. We leverage the information on the data of all pages to encode each page. Our constructed codes store more pages than RIO codes constructed via coset coding.

WOM-codes are constrained codes for memory devices whose state transition is irreversible. If we use the code, n-bit data can be written more than once on write-once cells of length greater than n. Error correcting WOM-codes have also been proposed. In this paper, a method for constructing multiple error correcting WOM-codes by modifying and simplifying the previously proposed error correcting WOM-code is presented. Codes constructed with our method have better code rates for some cases than the previously proposed code for some cases and no restrictions on the number of correctable errors. A single-symbol and a two-symbols error correcting code are also proposed.

DNA sequences can be regarded as sequences consisting of 4 symbols A (adenine), C (cytosine), G (guanine), and T (thymine). Many constraints for the DNA sequences are studied because when the DNA sequences are used as fundamental ingredients for computation or processing information, the DNA sequences should satisfy constraints so that molecular biological processes are done with small error probabilities. We explain constraints of the DNA sequences for hybridization. We also show some results on outfix-free and intercode constraints for DNA sequences.

Floating codes are codes for multi-level flash memories. There are two main properties which those codes have, the worst-case block erasure period and the average block erasure period. Codes with large average block erasure period can be constructed from the Gray code. First it is shown that a construction method for the floating codes can be interpreted by using labelled graphs. Floating codes are proposed for cases (a) n = 5 and k = 4, l = 2, q >; 2; (b) n = 8, k = 4, I = 2, q>; 2, where n is the number of cells in a block, k the number of information variables, I the number of levels of information variables and q the number of levels of cells. It is shown that if input data do not distribute uniformly, then the frequency of block erasure is low when the proposed code is used.

It was recently shown that the code rate of a simple coding scheme is better than a previously established maxentropic bound for the Wijngaarden-Immink reversed modulation and error control scheme(W-I coding scheme). This paper analyzes code rates of coding schemes for a given insertion rate of the W-I coding scheme using finite state transition diagrams. A new coding scheme is proposed and a new bound for the code rate of the W-I coding scheme is derived. It is proved that the new bound is better than the maxentropic bound when the insertion rate is 1/2.

We investigate a model for 2 dimensional (2D) input constraints. The model is an analogy of a model for 1 dimensional input constraints. We show that the model for 2D constraints is complete for 2D (d,k) Run-Length-Limited(RLL) constraints for positive integers d and k with 2d < k and that the model is incomplete for 2D (2, 4) RLL constraints.

Lower bounds of the capacities of 2-dimensional run-length-limited (RLL) constraints is studied in this paper. We also present a coding algorithm for encoding data sequences into two-dimensional binary arrays satisfying a (1,2)-RLL constraint along both horizontal and vertical directions.

Three-dimensional spectral null constraints for two dimensional storage devices are studied. These constraints may be useful when we use circular pits to store information on physical devices.

Irreducible components of canonical diagrams for spectral null constraints at f=f/sub s/k/n are studied, where k and n are integers and f/sub s/ is the symbol frequency. To identify systematically all irreducible components of the canonical diagrams for first-order spectral nulls at f, we give a set of channel symbol sequences specifying all of them. If n is a prime number, then each sequence in the set corresponds to exactly one label-preserving graph isomorphism class of irreducible components. We also give a set of channel symbol sequences specifying all irreducible components of canonical diagrams for second-order spectral nulls at DC (i.e., f=0).>

Spectral lines of signals that are given by functions of finite Markov chains are investigated. A problem of characterizing encoders in such a manner that the messages emitted from these encoders have some amount of information about clock, independent of the source statistics, is considered. Necessary and sufficient conditions are established for the encoded message to have a spectral line of a given amplitude for every transition probability matrix of the underlying Markov chain. Several other related results about spectral lines are given. A biased coboundary condition is defined at a frequency f, and it is shown that this condition is necessary and sufficient for the encoded message to have a spectral density null at f.>

Some properties of state splitting are established. The properties are then used to develop an algorithm for searching the sliding block decoder mapping of minimum scope obtained by state splitting. The algorithm is applied to the (d, k)-constraints of magnetic recording.>