Related papers: Concatenated Forward Error Correction with KP4 and…
Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and…
In digital baseband processing, the forward error correction (FEC) unit belongs to the most demanding components in terms of computational complexity and power consumption. Hence, efficient implementation of FEC decoders is crucial for next…
Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new…
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel (BSC)…
A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to…
In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-tooptimal decoding results when compared to full belief propagation…
A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction.…
An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS…
Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates…
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures -- variously referred to as near codewords, trapping…
We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…
The average symbol error probability (SEP) of a phase-quantized single-input multiple-output system with M-ary phase-shift keying modulation and maximum ratio combining (MRC) is analyzed under correlated Rayleigh fading and additive white…
Next-generation wireless communication systems impose much stricter requirements for transmission rate, latency, and reliability. The peak data rate of 6G networks should be no less than 1 Tb/s, which is comparable to existing long-haul…
Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large…
Different quantum error correction schemes trade off overhead, error suppression, and hardware connectivity. Code concatenation can relax these tradeoffs by using an outer code whose non-local connectivity is supplied by logical operations…
Coded modulation (CM) is the combination of forward error correction (FEC) and multilevel constellations. Coherent optical communication systems result in a four-dimensional (4D) signal space, which naturally leads to 4D-CM transceivers. A…
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
Parity measurements are central to quantum error correction (QEC). In current implementations measurements of stabilizers are performed using a number of Controlled Not (CNOT) gates. This implementation suffers from an exponential decrease…