The universality of LDPC codes on wireless channels

Abstract

Roof and Variaya pmved the existence of codes that can communicate reliably over any linear Gaussian channel for which rhe mutual information exceeds the infomation rare of the code. In this paper we demonstrate rhar pmperly designed Low-Densip Parip-Check (LDPC) codes are such codes and that their performance lies in close pmximity ro rhe Root and Variaya capacity for rhe linear Gaussian vecror channels (a.k.a. space-time channels). We also demonstrate rhe robustness of the codes on the panial-band jamming channel and in fasr Rayleigh fading.However, these codes were too short for the sphere packing bound to approach Shannon capacity, and the computational resources for longer random codes were decades away from being broadly accessible.Following (1) indicates that for a given rate R and input distribution there exists a single code that can achieve reliable information transmission at rate R o n every channel H for which the input distribution induces a mutual information (MI) higher than R.The immemate implication of this result is that good error performance on one particular channel does not have to come at the expense of significant performance degradation on others. Codes that have consistently good proximity to capacity (to the extent their blocklength and decoding complexity permit) over a class of channels will he referred to as universal codes in this paper. Since the linear Gaussian vector channels are commonly called space-time channels today, we refer to such codes as universal space-time codes.The capacity promise of multiple-input multiple-output (MIMO) systems in.rich scattering environments [2] makes the existence and use of universal codes of practical interest. In Low-density parity-check (LDPC) codes were proposed by Gallager in the early 1960s [7]. The stmcture of Gallager's codes (uniform column and mw weight) led them to be called regular LDPC codes. Gallager provided simulation results for codes with block lengths on the order of hundreds of bits.California Wugh UC MICRO Grant 03-093Funded by NSF Grant CcR0209110, Texas h s~e n t s . and the Slate of ~. .(around 0.1 bits per real dimension) for all the channels that we examine. For a matrix channel, the excess mutual information per dimension is defined as the capacity margin between the operational channel MI per lransmit antenna and the information transmission rate per transmit antenna.The rest of the paper is organized as follows. Section II describes the partial-hand jamming channel and demonstrates the performance of LDPC in this channel environment. Typical p. EsIN, measures are provided, but an additional technique will he introduced specifically for the purpose of comparison to mutual information. Section 111 presents LDPC performance results across a uniform sampling of 2 x 2 MlMO channels to illustrate the universal property of the codes. The performance of the codes on any specific 2 x 2 quasi-static distribution (for instance Rayleigh) can he inferred from the provided results. Though fast Rayleigh fading does no...

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