Related papers: Capacity-achieving Polar-based LDGM Codes with Cro…
In this paper, we study codes with sparse generator matrices. More specifically, low-density generator matrix (LDGM) codes with a certain constraint on the weight of the columns in the generator matrix are considered. In this paper, it is…
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…
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…
We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binary-input…
We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes…
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields,…
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…
Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary…
This paper is concerned with a class of low density generator matrix codes (LDGM), called repetition and superposition (RaS) codes, which have been proved to be capacity-achieving over binary-input output-symmetric (BIOS) channels in terms…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords…
We evaluate typical performance of irregular low-density generator-matrix (LDGM) codes, which is defined by sparse matrices with arbitrary irregular bit degree distribution and arbitrary check degree distribution, for lossy compression. We…
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 survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of…
We show that linear codes combined with rejection sampling can yield a capacity-achieving scheme for simulating additive exchangeable noise channels. Specifically, our scheme achieves an amount of communication within $\log e + 1$ bits from…
We consider the problem of efficiently constructing polar codes over binary memoryless symmetric (BMS) channels. The complexity of designing polar codes via an exact evaluation of the polarized channels to find which ones are "good" appears…