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Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
Upper bounds on the minimum Lee distance of codes that are linear over ${\mathbb Z}_q$, $q=p^t$, $p$ prime are discussed. The bounds are Singleton like, depending on the length, rank, and alphabet size of the code. Codes meeting such bounds…
Low probability of detection (or covert) communication refers to the scenario where information must be sent reliably to a receiver, but with low probability of detection by an adversary. Recent works on the fundamental limits of this…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
Performance evaluation of particular channel coding has been a significant topic in coding theory, often involving the use of bounding techniques. This paper focuses on the new family of capacity-achieving codes, Spinal codes, to provide a…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable…
Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem,…
This work considers space-time block coding for the Rayleigh fading multiple-input multiple-output (MIMO) multiple access channel (MAC). If we suppose that the receiver is performing joint maximum-likelihood (ML) decoding, optimizing a MIMO…
Recent developments in decoding of Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally-optimal codewords with respect to two parameters. One…
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be…