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We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric $q$. Our bound is obtained by considering a multicast transmission…
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average…
We study the theoretical performance of a combined approach to demodulation and decoding of binary continuous-phase modulated signals under repetition-like codes. This technique is motivated by a need to transmit packetized or framed data…
The optimal decoder achieving the outage capacity under imperfect channel estimation is investigated. First, by searching into the family of nearest neighbor decoders, which can be easily implemented on most practical coded modulation…
Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical…
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
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 provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight…
In this paper, we study error exponents for a concatataned coding based class of DNA storage codes in which the number of reads performed can be variable. That is, the decoder can sequentially perform reads and choose whether to output the…
Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random…
Optimal decoding of bit interleaved coded modulation (BICM) MIMO-OFDM where an imperfect channel estimate is available at the receiver is investigated. First, by using a Bayesian approach involving the channel a posteriori density, we…
In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under…
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…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…