We consider the design of a modern uplink for supporting machine-type communication and the confluence of sensing, communication, and distributed learning. We demonstrate that grant-free multiple access is possible even in the presence of highly time-varying channels and high delay spread. Our approach is built on enhancing the 2 -step random access procedure of the 5GNR standard. This 2 -step procedure uses Zadoff-Chu (ZC) sequences as preambles that point to radio resources which are then used to upload data. ZC sequences are processed in the delay-Doppler (DD) domain rather than the time domain. We demonstrate that it is possible to detect multiple preambles in the presence of mobility and delay spread using a receiver with no knowledge of the channel other than the worst case delay and Doppler spreads. Our approach depends on the mathematical properties of ZC sequences in the DD domain. We derive a closed form expression for ZC pilots in the DD domain, we characterize the possible self-ambiguity functions, and we determine the magnitude of the possible cross-ambiguity functions. These mathematical properties combine with Zak-OTFS modulation to enable detection of multiple pilots through solution of a compressed sensing problem. The columns of the compressed sensing matrix are the translates of individual ZC pilots in delay and Doppler. We show that columns in the design matrix satisfy a coherence property that makes it possible to detect multiple preambles in a single Zak-OTFS subframe using One-Step Thresholding, which is an algorithm with low complexity.

Current wireless infrastructure is optimized to support applications such as music/video streaming and internet browsing, where information flows from the base station to the user. This paper anticipates the emergence of applications such as distributed machine learning and automated driving, resulting in a shift of engineering focus from downlink to uplink as users become significant sources of data. The current paradigm of scheduling users on reserved uplink resources (grants) is not able to deal efficiently with unpredictable traffic patterns. As a result, Release 15, 3GPP introduced the 2 -step RACH as a mechanism to enable grant-free (random) initial access. The first of the two steps is preamble detection in a RACH slot, and in this paper we describe a very low-complexity algorithm for simultaneous detection of multiple preambles in the presence of mobility and delay spread. We provide a pathway to standards adoption by choosing Zadoff-Chu (ZC) sequences as preambles, taking advantage of the fact that ZC sequences already appear in 5G standards. We construct preambles by using the discrete Zak transform to pass from a ZC sequence of length$M N$in the time domain (TD) to a quasi-periodic$M \times N$array in the delay-Doppler (DD) domain. There are$M N$quasi-periodic Dirac pulses, each corresponding to a Zak-OTFS carrier waveform, and the ZC preamble is simply the corresponding sum of Zak-OTFS carrier waveforms. We detect multiple preambles in the presence of mobility and delay spread by sampling the received signal on the$M \times N$period grid in the DD domain. We approach detection as a compressed sensing problem. We represent a preamble as a column of length$M N$in the DD domain and apply discrete shifts in delay and Doppler to produce a block with$\mathcal{O}(M N)$columns in the compressed sensing matrix. The superposition of multiple preambles determines a block sparse sum of columns in the sensing matrix. The correlation properties of ZC sequences result in a highly structured compressed sensing matrix, making it possible to identify constituent preambles using One-Step Thresholding (OST), which has complexity$\mathcal{O}\left(M^{3} N^{3}\right)$. In this paper, we describe an algorithm with complexity that is$\mathcal{O}\left(M^{2} N^{2}\right)$in the size of an individual column ($M N$).

Orthogonal Time Frequency Space (OTFS) is a framework for communications and active sensing that processes signals in the delay-Doppler (DD) domain. It is informed by 6G propagation environments, where Doppler spreads measured in$\text{kHz}$make it more and more difficult to estimate channels, and the standard model-dependent approach to wireless communication is starting to break down. We consider Zak-OTFS where inverse Zak transform converts information symbols mounted on DD domain pulses to the time domain for transmission. Zak-OTFS modulation is parameterized by a delay period$\tau_{p}$and a Doppler period$\nu_{p}$, where the product$\nu_{p}\nu_{p}=1$. When the channel spread is less than the delay period, and the Doppler spread is less than the Doppler period, the Zak-OTFS input-output relation can be predicted from the response to a single pilot symbol. The highly reliable channel estimates concentrate around the pilot location, and we configure low-density parity-check (LDPC) codes that take advantage of this prior information about reliability. It is advantageous to allocate information symbols to more reliable bins in the DD domain. We report simulation results for a Veh-A channel model where it is not possible to resolve all the paths, showing that LDPC coding extends the range of Doppler spreads for which reliable model-free communication is possible. We show that LDPC coding reduces sensitivity to the choice of transmit filter, making bandwidth expansion less necessary. Finally, we compare BER performance of Zak-OTFS to that of a multicarrier approximation (MC-OTFS), showing LDPC coding amplifies the gains previously reported for uncoded transmission.

Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of solid-state storage devices, and in increasing the reliability of data transmission over wires. Over the years, designing practical (complexity-wise) capacity-achieving constrained codes has been an area of research gaining significant interest. We recently designed various constrained codes based on lexicographic indexing. We introduced binary symmetric lexicographically-ordered constrained (S-LOCO) codes,$q$-ary asymmetric LOCO (QA-LOCO) codes, and a class of two-dimensional LOCO (TD-LOCO) codes. These families of codes achieve capacity with simple encoding and decoding, and they are easy to reconfigure. We demonstrated that these codes can contribute to notable density and lifetime gains in magnetic recording (MR) and Flash systems, and they find application in other systems too. In this paper, we generalize our work on LOCO codes by presenting a systematic method that guides the code designer to build any constrained code based on lexicographic indexing once the finite set of data patterns to forbid is known. In particular, we connect the set of forbidden patterns directly to the cardinality of the LOCO code and most importantly to the rule that uncovers the index associated with a LOCO codeword. By doing that, we reveal the secret arithmetic of patterns, and make the design of such constrained codes significantly easier. We give examples illustrating the method via codes based on lexicographic indexing from the literature. We then design optimal (rate-wise) constrained codes for the new two-dimensional magnetic recording (TDMR) technology. Over a practical TDMR model, we show notable performance gains as a result of solely applying the new codes. Moreover, we show how near-optimal constrained codes for TDMR can be designed and used to further reduce complexity and error propagation. All the newly introduced LOCO codes are designed using the proposed general method, and they inherit all the desirable properties in our previously designed LOCO codes.

Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns, and thus prevent errors from happening. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and data transmission. LOCO codes are capacity-achieving, simple, and can be easily reconfigured. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The occurrence of errors is a consequence of parasitic capacitances in and across floating-gate transistors, resulting in charge propagation from cells being programmed to the highest charge level to neighboring cells being programmed to lower levels or unprogrammed/erased. This asymmetric nature of error-prone patterns distinguishes Flash memories. The new codes are called$q$-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (A-LOCO codes). QA-LOCO codes work for a Flash device with any number,$q$, of levels per cell. For$q \geq 4$, we show that QA-LOCO codes can achieve rates greater than$0.95 \log _{2} \!q$input bits per coded symbol. The complexity of encoding and decoding is modest, and reconfiguring a code is as easy as reprogramming an adder. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing improvement of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time, which increases their lifetime.

Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and transmission. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The new codes are called q-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (ALOCO codes). QA-LOCO codes work for a Flash device with any number, q, of levels per cell. For q ≥ 4, we show that QA-LOCO codes can achieve rates greater than 0.95log2q information bits per coded symbol. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing improvement of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time.