Related papers: Fountain Codes under Maximum Likelihood Decoding
Decoding strategies for generative large language models (LLMs) are a critical but often underexplored aspect of text generation tasks. Guided by specific hyperparameters, these strategies aim to transform the raw probability distributions…
A key component of generating text from modern language models (LM) is the selection and tuning of decoding algorithms. These algorithms determine how to generate text from the internal probability distribution generated by the LM. The…
In this paper we survey the various erasure codes which had been proposed and patented recently, and along the survey we provide introductory tutorial on many of the essential concepts and readings in erasure and Fountain codes. Packet…
Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a…
Network-coded multiple access (NCMA) is a communication scheme for wireless multiple-access networks where physical-layer network coding (PNC) is employed. In NCMA, a user encodes and spreads its message into multiple packets. Time is…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Top-$k$ decoding is a widely used method for sampling from LLMs: at each token, only the largest $k$ next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-$k$ and other sampling…
One key requirement for fountain (rateless) coding schemes is to achieve a high intermediate symbol recovery rate. Recent coding schemes have incorporated the use of a feedback channel to improve intermediate performance of traditional…
Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
Deep learning based decoding networks have shown significant improvement in decoding LDPC codes, but the neural decoders are limited by rate-matching operations such as puncturing or extending, thus needing to train multiple decoders with…
While a plethora of machine learning (ML) models are currently available, along with their implementation on disparate platforms, there is hardly any verifiable ML code which can be executed on public blockchains. We propose a novel…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time…
While large language models (LLMs) show promise in code generation, existing benchmarks neglect the flowchart-based code generation. To promote further research on flowchart-based code generation, this work presents Flow2Code, a novel…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…