相关论文: Bounds on the decoding complexity of punctured cod…
Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $\ell$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping…
This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless…
The past decade has seen notable advances in our understanding of structured error-correcting codes, particularly binary Reed--Muller (RM) codes. While initial breakthroughs were for erasure channels based on symmetry, extending these…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary…
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. The bit error probability for infinite block length is known by density evolution and it is…
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:…
We consider communication over memoryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational complexity of decoding (i.e., of reconstructing all the typical…
Random coding, expurgated and sphere packing bounds are derived by method of types and method of graph decomposition for $E$-capacity of discrete memoryless channel (DMC). Three decoding rules are considered, the random coding bound is…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We study fountain codes transmitted over the binary-input symmetric-output channel. For channels with small capacity, receivers needs to collects many channel outputs to recover information bits. Since a collected channel output yields a…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
In this work, we give good concatenated code ensembles for the binary erasure channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple…
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…
New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…
In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity…
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…