Related papers: Irregular Product Codes
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
An error-erasure channel is a simple noise model that introduces both errors and erasures. While the two types of errors can be corrected simultaneously with error-correcting codes, it is also known that any linear code allows for first…
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.…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the…
This paper investigates the theoretical analysis of intrinsic message passing decoding for generalized product codes (GPCs) with irregular degree distributions, a generalization of product codes that allows every code bit to be protected by…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. Using this new concept, we derive properties of maximum rank distance (MRD) codes that parallel…
This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is…
In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This exact expression…
Product codes are a concatenated error-correction scheme that has been often considered for applications requiring very low bit-error rates, which demand that the error floor be decreased as much as possible. In this work, we consider…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
A new class of codes, Extended Product (EPC) Codes, consisting of a product code with a number of extra parities added, is presented and applications for erasure decoding are discussed. An upper bound on the minimum distance of EPC codes is…