Related papers: The Golay Code Outperforms the Extended Golay Code…
A modified successive cancellation list (SCL) decoder is proposed for polar-coded probabilistic shaping. The decoder exploits the deterministic encoding rule for shaping bits to rule out candidate code words that the encoder would not…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to…
The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…
We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…
Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices,…
Polar codes are the first provably capacity-achieving forward error correction codes. To improve decoder throughput, the symbol-decision SC algorithm makes hard-decision for multiple bits at a time. In this paper, we prove that for polar…
Despite the effectiveness of large language models (LLMs) for code generation, they often output incorrect code. One reason is that model output probabilities are often not well-correlated with correctness, and reflect only the final output…
In this paper, we introduce a novel class of pre-transformed polar codes, termed as deep polar codes. We first present a deep polar encoder that harnesses a series of multi-layered polar transformations with varying sizes. Our approach to…
As reasoning LLMs increasingly trade tokens for accuracy through deliberation, search, and self-correction, a single accuracy score can no longer tell whether those tokens buy useful reasoning, recovery from hard instances, or unnecessary…
We construct supplementary difference sets (SDS) with parameters $(72;36,30;30)$. These SDSs give periodic Golay pairs of length 72. No periodic Golay pair of length 72 was known previously. The smallest undecided order for periodic Golay…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…
Fine-tuned language models use greedy decoding to answer reading comprehension questions with relative success. However, this approach does not ensure that the answer is a span in the given passage, nor does it guarantee that it is the most…
Numerous studies have shown that multimodal LLMs process speech and images well but fail in non-intuitive ways rendering trivial tasks such as object counting unreliable. We investigate this behavior from an information-theoretic…
The interesting properties of classical Goppa code and its effective decoding algorithm (algorithm of patterson) make the most appropriate candidate for use in the MC Eliece cryptosystem. Information leakage which results from the…
A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…
We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the…
In this work, a new fast-decodable space-time block code (STBC) is proposed. The code is full-rate and full-diversity for 4x2 multiple-input multiple-output (MIMO) transmission. Due to the unique structure of the codeword, the proposed code…